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\begin_layout Chapter*
Summary
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\begin_layout Standard
This thesis has been developed as part of the Cajal Blue Brain research
 project, whose long-term goal is simulating an anatomically correct human
 brain inside a supercomputer.
 One of the main areas of involvement of the UPM in this project is in the
 development of new technologies for image analysis and visualization.
 These new technologies are needed to extract useful information from 3D
 images obtained with modern electronic microscopes from real cortical tissue.
 This task presents a series of challenges, derived amongst other things
 from the large amount of images that can be obtained from a small volume
 of tissue as well as from the characteristics innate to this images.
 Today, the analysis of the images is done by hand by trained scientists,
 this represents a huge bottleneck for the project, as a well as a very
 expensive and error prone process.
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\begin_layout Standard
The objective of this master thesis is the development of an interactive
 tool for segmenting a stack of brain tissue images.
 This tool will use segmentation techniques based on curve evolution or
 Snakes.
 A major limitation of curve evolution algorithms is their robustness and
 computational complexity, which prevents them from being used in an interactive
 segmentation tool.
 In this thesis we will implement two recent evolution algorithms proposed
 by 
\begin_inset CommandInset citation
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key "Marquez_2012"

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, that are based on the use of morphological operators to overcome some
 of the limitations of traditional Snakes evolution methods.
 The result of the implementation is a plug-in for a neuronal analysis system,
 called ESPina, which is being developed by various research groups in the
 UPM.
 In the thesis we also analyze the challenges that arise during the implementati
on of these algorithms as well as the improvements and opportunities that
 this work opens.
\end_layout

\begin_layout Chapter*

\lang spanish
Resumen
\end_layout

\begin_layout Standard

\lang spanish
Esta tesis ha sido desarrollada como parte del proyecto de investigación
 Cajal Blue Brain cuyo principal objetivo a largo plazo es el de realizar
 una simulación anatómicamente correcta de un cerebro humano en un supercomputad
or.
 Una de las principales áreas del proyecto en la cual está involucrada la
 UPM es en el desarrollo de nuevas tecnologías de análisis y visualización
 de imágenes.
 Estas tecnologías son necesarias para extraer información útil de imágenes
 en 3D obtenidas mediante técnicas modernas de microscopia electrónica aplicadas
 a especímenes reales de tejido cortical.
 Esta tarea presenta una serie de retos, derivados entre otras cosas por
 el inmenso volumen de imágenes que se generan a partir de un volumen muy
 pequeño de tejido así como por las características propias de las imágenes.
 Hoy en día, este análisis se hace a mano por científicos entrenados, esto
 representa además de un cuello de botella importante para el proyecto,
 un proceso sumamente costoso y propenso a errores.
 
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\lang spanish
El objetivo de esta tesis es el desarrollo de una herramienta interactiva
 de segmentación de imágenes de tejido cerebral.
 Esta herramienta utilizará tecnicas de segmentacion de imagenes basadas
 en evolucion de curvas o Snakes.
 Los algoritmos de evolución de curvas presentan limitaciones en cuanto
 a robustez y complejidad computacional que limitan su utilidad en una herramien
ta interactiva.
 En esta tesis implementaremos dos algoritmos propuestos recientemente por
 
\begin_inset CommandInset citation
LatexCommand citet
key "Marquez_2012"

\end_inset

, los cuales se basan en el uso de operadores morfológicos para superar
 algunas de las limitaciones de los enfoques tradicionales de evolución
 de Snakes.
 El resultado de la implementación es un un plug-in para el sistema de visualiza
ción y análisis neuronal ESPina, el cual está siendo desarrollando por varios
 grupos de investigación de la UPM.
 En la tesis también analizamos los retos que se nos presentaron para la
 implementación de los algoritmos así como las posibles mejoras y avenidas
 de investigación que se abren a partir de nuestro trabajo.
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\begin_layout Chapter
Introduction
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\begin_layout Section
The problem
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\begin_layout Standard
The Blue Brain Project, a collaboration between Switzerland's EPFL and IBM,
 is a project with a bold objective.
 Their goal is to make a virtual model of the human brain, down to the last
 neuron, and host it on a supercomputer.
 Needless to say, this kind of project has a very big set of challenges
 to overcome.
 The Technical University of Madrid (UPM) as well as some other Spanish
 scientific institutions are strategic partners in this project and the
 entity that represents these Spanish contributions is called Cajal Blue
 Brain Project.
\end_layout

\begin_layout Standard
In order to obtain morphological information about the structure of the
 brain directly from actual brain tissue modern electronic microscopy techniques
 are being used to obtain highly detailed images from samples of cerebral
 cortex.
 These images are extremely useful because when properly analyzed by trained
 scientist they can yield important quantitative as well as qualitative
 data.
 When done by hand, the processing of the images is a very time consuming
 task that is labor intensive and therefore expensive.
 Combine the cost (in every sense) of this process to the fact that the
 amount of images that have to be processed is immense and you have a really
 hard problem in your hands 
\end_layout

\begin_layout Standard
One of the main techniques used for the extraction of meaningful data from
 digital images, and that could be a possible solution for the problem at
 hand, is image segmentation.
 Image segmentation is the process of labeling or clustering the pixels
 of an image according to their characteristics.
 A good example of image segmentation would be to label all the pixels in
 an aerial image depending if they are part of a road or not.
 The result of the process would be that every pixel would be given a label
 (road or not-road) depending on whether or not the pixel belongs to the
 road.
 When applied to a medical image, the proper segmentation of an image might
 allow the user to obtain data, for example, about the amount of instances
 of a given structure in a given area, the average shape or size of an interesti
ng feature, etc.
 
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Example of a segmented image.
 Image A is the original picture.
 Image B is the result of the segmentation, with blue labeled pixels representin
g the road and red labeled pixels representing not-road.
 
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[Figure created by the author, source of base image
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http://www.flickr.com/photos/liao/2549120611
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]
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\begin_layout Standard
To summarize, the problem is the following: how can the scientists of the
 Cajal Blue Brain segment images of brain tissue obtained with electronic
 microscopes with the objective of differentiating several types of structures
 within those cells (e.g.
 synapses, vesicles, spines, dendrites) in the easiest, fastest and most
 automated way?
\end_layout

\begin_layout Section
The solution
\end_layout

\begin_layout Standard
Given the previous description of the problem, we propose a solution based
 on two elements.
 First, an environment or framework on which the scientists can interact
 with the images in a useful way and secondly an implementation of an algorithm
 (or algorithms) that allows the scientist to segment the images in a time
 efficient manner.
 
\end_layout

\begin_layout Standard
For the first part of the solution we are going to develop a plug-in for
 a system called ESPina, created as part of the Cajal Blue Brain initiative.
 This program allows a user to load a 3D stack of images and interact with
 them in useful ways.
 It also provides two key functionalities, first it was designed from the
 ground up to support image segmentation and provides a system for categorizing
 hierarchically the labeled structures and secondly and more importantly,
 it provides an open architecture that can be enhanced with external plug-ins
 which will allow us to build a tool to do segmentation interactively using
 two selected algorithms.
 
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\begin_layout Standard
The second component of the solution is the implementation of the two algorithms
 mentioned before.
 The segmentation problem has been around for quite some time and a lot
 of approaches have been tried in solving it.
 In the next chapter we provide an overview of those approaches and their
 limitations.
 Our solution is based on the use of active contours, also known as Snakes.
 This approach is based on the idea of iteratively evolving a curve using
 a gradient descent technique based on the minimization of some energy function.
 The classical way of solving this problem is using Partial Differential
 Equations (PDEs) but, as will be discussed later on, this process has some
 limitations that can be solved by the use of certain morphological operators
 that have been proposed recently.
 The use of morphological operators, has the advantage of being simpler,
 faster and numerically more stable than the their differential counterparts.
 
\end_layout

\begin_layout Standard
The ESPina tool, is built as an extension of ParaView, an open-source, multi-pla
tform data analysis and visualization application.
 In order to be compatible with ESPina/ParaView, the implementation of the
 segmentation algorithms has to be done using Kitware's Visualization Toolkit
 (VTK) which is a free, open source software system for 3D computer graphics,
 image processing and visualization created by the same company that created
 ParaView, Kitware Inc..
 
\end_layout

\begin_layout Standard
One of the main objectives in the design of the segmentation tool is for
 the user to be able to interactively control the segmentation process,
 even the evolution of the active contour curve.
 This approach allows us to overcome some of the limitations of the segmentation
 algorithms by incorporating the knowledge of the experts in the process.
 
\end_layout

\begin_layout Chapter
Some context.
 The Cajal Blue Brain Project.
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name "chap:Context"

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\begin_layout Standard
In 2005, a neuroscientist named Henry Markram at Ecole Polytechnique Fédérale
 de Lausanne (EPFL)  joined efforts with IBM with a very ambitious objective,
 they planned to build a perfect replica of the human brain inside a computer.
 According to their website (
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http://bluebrain.epfl.ch
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) the objectives of this project were:
\end_layout

\begin_layout Enumerate
Create a Brain Simulation Facility with the ability to build models of the
 healthy and diseased brain, at different scales, with different levels
 of detail in different species.
\end_layout

\begin_layout Enumerate
Demonstrate the feasibility and value of this strategy by creating and validatin
g a biologically detailed model of the neocortical column in the somatosensory
 cortex of young rats.
\end_layout

\begin_layout Enumerate
Use this model to discover basic principles governing the structure and
 function of the brain.
\end_layout

\begin_layout Enumerate
Exploit these principles to create larger more detailed brain models, and
 to develop strategies to model the complete human brain.
\end_layout

\begin_layout Standard
As the project advanced, a collaboration effort with several Spanish institution
s was forged (namely Madrid Technical University (UPM) and the Instituto
 Cajal, part of the Consejo Superior de Investigaciones Cientificas (CSIC)).
 This Spanish contribution to the project was designated Cajal Blue Brain,
 in honor to the Nobel laureate Santiago Ramon y Cajal.
 Ramon y Cajal received the Nobel Prize in Physiology or Medicine in 1906
 for his discoveries in neuroscience and for setting up the foundations
 of what would eventually become the "neuron theory".
\end_layout

\begin_layout Standard
According to the memory of the project, its Vision, Mission and Objectives
 are:
\end_layout

\begin_layout Subsection*
Vision
\end_layout

\begin_layout Standard
Biologically accurate computer models of mammalian and human brains could
 provide a new foundation for understanding functions and malfunctions of
 the brain and for a new generation of information-based, customized medicine.
 
\end_layout

\begin_layout Subsection*
Mission
\end_layout

\begin_layout Standard
To gather all existing knowledge of the brain, accelerate the global research
 effort of reverse engineering the structure and function of the components
 of the brain, and to build a complete theoretical framework that can orchestrat
e the reconstruction of the brain of mammals and man from the genetic to
 the whole brain levels, into computer models for simulation, visualization
 and automatic knowledge archiving by 2015.
\end_layout

\begin_layout Subsection*
Objectives
\end_layout

\begin_layout Enumerate
Assemble all existing knowledge of the brain by providing a new model and
 informatics platform as a service to "publish" their data and models.
\end_layout

\begin_layout Enumerate
Accelerate the process of reverse engineering the brain by stimulating and
 facilitating neuroscientists to shift towards industrial-scale neuroscience.
 
\end_layout

\begin_layout Enumerate
Align experimentalists and theoreticians to further derive the structure
 and function of the brain in a manner that allows the construction of computer
 models for all components of the brain.
 
\end_layout

\begin_layout Enumerate
Construct a new generation data-driven, model-oriented, emergent and evolvable
 and database-architecture that allows dynamic assembling of the components
 of the brain into whole brain models that can be used to simulate the functions
 and malfunctions of the brain and to explore new treatments.
 
\end_layout

\begin_layout Enumerate
Establish an international brain simulation capability to serve as a foundation
 for future basic and clinical research and medical treatment.
 
\end_layout

\begin_layout Enumerate
Couple future brain research funding to the global industry that it produces
 and supports.
 
\end_layout

\begin_layout Standard
This general definition of the project echoes the definition of the Internationa
l Blue Brain Projects that it belongs to.
\end_layout

\begin_layout Standard
To attain its objectives, the CBBP is organized according to two more tactical
 axes:
\end_layout

\begin_layout Itemize
The anatomical and functional micro organization of the cortical column.
 
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\begin_layout Itemize
The development of potentially transferable biomedical technology.
 
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\begin_layout Standard
Of these technologies that have to be developed some of the must crucial
 ones are image analysis and visualization technologies.
 
\end_layout

\begin_layout Standard
The use of modern electronic microscopy techniques (cross-beam type microscopes)
 allows for the automatic obtention of highly detailed 3D images of brain
 tissue samples, a very large number of these can be obtained very fast
 using these new microscopes when compared to traditional ways of doing
 image acquisition via electronic microscopy.
 This images are obtained by serially imaging "cuts" of the brain tissue
 (e.g.
 every 25 nm) and then stacking this slices into 3D representations of the
 sampled tissue.
 These images have to be analyzed with the objective of obtaining morphological
 data about the cerebral cortex.
 
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A slice of a brain tissue image stack obtained with a cross-beam microscope.
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name "fig:Brain-tissue"

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\begin_layout Standard
The problem is that these images have to be analyzed by hand by trained
 scientists that are capable of labeling the different structures within
 the image and thus enable the quantification of, for example, the density
 of synapses in a given volume.
 It goes without saying that is a very expensive, error prone and time consuming
 task that could be addressed by new advances in image segmentation and
 analysis.
 To give the reader an idea of the magnitude of the amount of data that
 this task requires, in order to visualize a volume equivalent to 1 cubic
 mm of brain tissue, we would have to process 35 petabytes of data (to put
 this into perspective, as of this writing (2012) Google's worldwide servers
 are reported to handle between 20 and 30 petabytes of data every day).
\end_layout

\begin_layout Standard
The images collected pose a number of challenges to be processed automatically
 (noise, blurred edges, large number of objects), so new techniques will
 have to be developed in order to achieve this goal.
 
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\begin_layout Section
ESPina
\end_layout

\begin_layout Standard
The ESPina Interactive Neuron Analyzer, is a tool developed by the Cajal
 Blue Brain Project to allow the scientists to visualize the images obtained
 with the electronic microscopes.
 
\end_layout

\begin_layout Standard
The tool is built on top of ParaView, a parallel visualization framework.
 It is designed as a client/server model that allows the use of processing
 in a massive cluster (using MPI messaging technology), a single stand-alone
 server or in a local machine.
 It was designed around the workflow of the neuroscientists that are working
 on CBBP and BBP, and so the visualization and interaction with the images
 is done in way that it's natural for them.
\end_layout

\begin_layout Standard
ESPina provides some basic interaction and segmentation tools "out of the
 box", but its greatest potential comes from the fact that it can be enhanced
 by the use of plug-ins that can be built to include almost any new functionalit
y into the system (new segmentation tools, ways to extract information from
 images, interaction techniques, etc.).
 The tool that is being presented in this work is built as a plug-in for
 ESPina, in order to harness all the functionality that it has already built
 in as well as the familiarity that the neuroscientists already posses with
 the system.
 
\end_layout

\begin_layout Chapter
Previous Work
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name "chap:Previous-Work"

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\begin_layout Section
Image Segmentation
\end_layout

\begin_layout Standard
Image segmentation is the process of labeling the pixels of an image in
 a way that allows us to group together pixels that share certain characteristic
s.
 A common use of segmentation is to separate an object in an image from
 its background, because of this, it is common to refer to the pixels that
 are part of the structure that is being segmented as foreground pixels
 and every other pixel as background pixels even on the cases when this
 names do not make much sense.
 The segmentation problem has been approached from several directions: Split
 and merge techniques (
\begin_inset CommandInset citation
LatexCommand citet
key "Pavlidis_Liow_1990"

\end_inset

), normalized cuts (
\begin_inset CommandInset citation
LatexCommand citet
key "Shi_Malik_2000"

\end_inset

), graph cuts (
\begin_inset CommandInset citation
LatexCommand citet
key "Boykov_Jolly_2001"

\end_inset

), and active contours/Snakes (
\begin_inset CommandInset citation
LatexCommand citet
key "Kass_Witkin_Terzopoulos_1988"

\end_inset

,
\begin_inset CommandInset citation
LatexCommand citet
key "Malladi_Sethian_Vemuri_1995"

\end_inset

).
\end_layout

\begin_layout Standard
The algorithms we are going to use in our tool are based on the active contours
 approach so we are going to discuss it in a little more detail.
 Some examples of the utilization of Snakes for image segmentation can be
 found in 
\begin_inset CommandInset citation
LatexCommand citet
key "Nilsson_Heyden_2003,Chan_Vese_2001,Mortensen_Barrett_1995"

\end_inset

.
 
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\begin_layout Standard
Active contour methods iteratively move towards a solution (segmentation)
 under the combination of image and optional user guidance forces (
\begin_inset CommandInset citation
LatexCommand citet
after "p. 270"
key "Szeliski_2010"

\end_inset

).
 The first active contour models relied on parametric curves, but they had
 difficulty adapting the topology of the curve as it evolved.
 As an alternative, level-set methods represent the curve as the zero-crossing
 of a characteristic function (
\begin_inset CommandInset citation
LatexCommand citet
after "p. 281"
key "Szeliski_2010"

\end_inset

) and the evolution of the curve is done by modifying the underlying embedding
 function.
 We are going to analyze two models that use this representation: 
\shape italic
Geodesic Active Contours 
\shape default
(GAC) was proposed by 
\begin_inset CommandInset citation
LatexCommand citet
key "Caselles_Kimmel_Sapiro_1997"

\end_inset

, the main idea in this model is that the evolution of the curve is dictated
 by the minimization of an energy functional whose gradient dictates the
 direction of movement for the curve, this energy functional is dependent
 on a function (normally called the "stop criterion" and noted 
\begin_inset Formula $g\left(I\right)\left(x\right)$
\end_inset

) thats takes low values in the areas of interest of the image.
 Another model, originally proposed by 
\begin_inset CommandInset citation
LatexCommand citet
key "Chan_Vese_2001"

\end_inset

, is called 
\shape italic
Active Contours Without Edges
\shape default
 (ACWE), it does not require a stop criterion function for minimizing its
 energy functional, but instead relies in global information regarding the
 contents (i.e.
 the gray levels) of pixels inside and outside of the evolving curve.
 In figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:chan_vese_curve"

\end_inset

 we can see a schematic representation of an evolving curve, notice how
 the curve 
\begin_inset Formula $C$
\end_inset

 is represented by the zero level-set of the function 
\begin_inset Formula $\phi$
\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename Images/ACC.png
	display false

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
A curve being evolved using Active Contours Without Edges.
 [Image source: 
\begin_inset CommandInset citation
LatexCommand citet
key "Chan_Vese_2001"

\end_inset

]
\begin_inset CommandInset label
LatexCommand label
name "fig:chan_vese_curve"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Both of these approaches require the calculation of partial differential
 equations which can be computationally costly, add complexity to the implementa
tion, can introduce numerical instabilities and require frequent reinitializatio
ns of the level-set function as it degrades over time.
 
\end_layout

\begin_layout Standard
As a proposed solution to this shortcomings of the traditional approach
 to snakes evolution 
\begin_inset CommandInset citation
LatexCommand citet
key "Alvarez_2010"

\end_inset

 and 
\begin_inset CommandInset citation
LatexCommand citet
key "Marquez_2012"

\end_inset

 propose a method that replaces the terms of the PDEs in traditional algorithms
 with infinitesimally equivalent morphological operators.
 Using these new operators the representation of the curve is simpler and
 the operations required to obtain it become less costly.
 
\end_layout

\begin_layout Subsection
Morphological Geodesic Active Contours (MGAC)
\begin_inset CommandInset label
LatexCommand label
name "sub:Morphological-Geodesic-Active"

\end_inset


\end_layout

\begin_layout Standard
As seen in 
\begin_inset CommandInset citation
LatexCommand citet
key "Alvarez_2010"

\end_inset

 and 
\begin_inset CommandInset citation
LatexCommand citet
key "Marquez_2012"

\end_inset

, it is possible to approximate the behavior of the PDE that controls curve
 evolution in the traditional GAC as the composition of three morphological
 operators.
 In general the PDE can be divided in three components, one represents the
 attraction applied to the curve by the areas of interest in the image (e.g.
 edges), one represents the balloon force that ensures that the curve does
 not get stuck in parts of the image with little information and the third
 component is the mean curvature operator which can be seen as a smoothing
 force on the curve.
 
\end_layout

\begin_layout Standard
The PDE that we will approximate using the morphological operators is:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\frac{\partial u}{\partial t}=g\left(I\right)|\nabla u|\text{div}\left(\frac{\nabla u}{|\nabla u|}\right)+g\left(I\right)|\nabla u|\nu+\nabla g\left(I\right)\nabla u\label{eq:pde_gac}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Where 
\begin_inset Formula $u$
\end_inset

 represents the embedding function, 
\begin_inset Formula $g\left(I\right)$
\end_inset

 represents a function that has low values in the areas of interest of the
 image and 
\begin_inset Formula $\nu$
\end_inset

 is a parameter that controls the effect of the balloon force
\end_layout

\begin_layout Standard
In theory 
\begin_inset Formula $g\left(I\right)$
\end_inset

 could be any function that takes low values in the areas of interest of
 the image, a good example of a function that can be used here is:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
g\left(I\right)=\frac{1}{\sqrt{1+\alpha|G_{\sigma}*I|}},\label{eq:stopf}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\noindent
which takes low values in the edges of the image.
\end_layout

\begin_layout Standard
With this in mind, the following steps applied sequentially are equivalent
 to the PDE 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:pde_gac"

\end_inset

:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{flalign}
u^{n+\frac{1}{3}}\left(x\right) & =\begin{cases}
\left(D_{d}u^{n}\right)\left(x\right) & \text{if }|\nu|g\left(I\right)\left(x\right)>\theta\\
\left(E_{d}u^{n}\right)\left(x\right) & \text{if }|\nu|g\left(I\right)\left(x\right)<\theta\\
u^{n}\left(x\right) & \text{otherwise}
\end{cases}\nonumber \\
u^{n+\frac{2}{3}}\left(x\right) & =\begin{cases}
1 & \text{if }\nabla u^{n+\frac{1}{3}}\nabla g\left(I\right)\left(x\right)>0\\
0 & \text{if }\nabla u^{n+\frac{1}{3}}\nabla g\left(I\right)\left(x\right)<0\\
u^{n+\frac{1}{3}}\left(x\right) & \text{if }\nabla u^{n+\frac{1}{3}}\nabla g\left(I\right)\left(x\right)=0
\end{cases}\label{eq:mgac}\\
u^{n+1}\left(x\right) & =\begin{cases}
\left(\left(SI_{d}\circ IS_{d}\right)^{\mu}u^{n+\frac{2}{3}}\right)\left(x\right) & \text{if }g\left(I\right)\left(x\right)>\theta\\
u^{n+\frac{2}{3}}\left(x\right) & \text{otherwise}
\end{cases}\nonumber 
\end{flalign}

\end_inset


\end_layout

\begin_layout Standard
In this equation the first step represents the balloon force (
\begin_inset Formula $D_{d}$
\end_inset

 and 
\begin_inset Formula $E_{d}$
\end_inset

 represent the discretized dilation and erosion operators respectively),
 the second step represents the attraction of the interesting areas of the
 image and the third step is the application of the smoothing force.
 Parameter 
\begin_inset Formula $\theta$
\end_inset

 is a threshold that controls the effect of both the balloon force and the
 smoothing force.
 
\end_layout

\begin_layout Subsection
Morphological Active Contours Without Edges (MACWE)
\begin_inset CommandInset label
LatexCommand label
name "sub:Morphological-ACWB"

\end_inset


\end_layout

\begin_layout Standard
In the same manner that GAC can be approximated with morphological operators,
 the ACWE model can also be approximated in a similar fashion by composing
 several morphological operators, as shown by 
\begin_inset CommandInset citation
LatexCommand citet
key "Marquez_2012"

\end_inset

.
 In the case of ACWE the energy functional to be minimized is not dependent
 on an external function but is derived directly from information from the
 image, in particular it takes into account the levels of gray of the pixels
 that are inside vs.
 outside of the curve.
 In that sense, is different from GAC in that it uses more global information
 instead of just local information around the curve.
 It can also be divided in three terms: a smoothing term, a balloon term
 and an image attachment term.
 
\end_layout

\begin_layout Standard
The PDE that needs to be solved in this case is:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\frac{\partial u}{\partial t}=|\nabla u|\left(\mu\text{div}\left(\frac{\nabla u}{|\nabla u|}\right)-\nu-\lambda_{1}\left(I-c_{1}\right)^{2}+\lambda_{2}\left(I-c_{2}\right)^{2}\right)\label{eq:pde_acwe}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Where 
\begin_inset Formula $\lambda_{1}$
\end_inset

, 
\begin_inset Formula $\lambda_{2}$
\end_inset

, 
\begin_inset Formula $\nu$
\end_inset

 and 
\begin_inset Formula $\mu$
\end_inset

 represent the strength of each term and 
\begin_inset Formula $c_{1}$
\end_inset

 and 
\begin_inset Formula $c_{2}$
\end_inset

 represent the mean values of the image inside and outside the contour.
\end_layout

\begin_layout Standard
As with MGAC the steps necessary to model the evolution of the curve with
 morphological operators are the following:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{flalign}
u^{n+\frac{1}{3}}\left(x\right) & =\begin{cases}
\left(D_{d}u^{n}\right)\left(x\right) & \text{if }\nu>0\\
\left(E_{d}u^{n}\right)\left(x\right) & \text{if }\nu<0\\
u^{n}\left(x\right) & \text{otherwise}
\end{cases}\nonumber \\
u^{n+\frac{2}{3}}\left(x\right) & =\begin{cases}
1 & \text{if }|\nabla u^{n+\frac{1}{3}}|\left(\lambda_{1}\left(I-c_{1}\right)^{2}-\lambda_{2}\left(I-c_{2}\right)^{2}\right)\left(x\right)<0\\
0 & \text{if }|\nabla u^{n+\frac{1}{3}}|\left(\lambda_{1}\left(I-c_{1}\right)^{2}-\lambda_{2}\left(I-c_{2}\right)^{2}\right)\left(x\right)>0\\
u^{n+\frac{1}{3}}\left(x\right) & \text{otherwise}
\end{cases}\label{eq:macwb}\\
u^{n+1}\left(x\right) & =\left(\left(SI_{d}\circ IS_{d}\right)^{\mu}u^{n+\frac{2}{3}}\right)\left(x\right)\nonumber 
\end{flalign}

\end_inset


\end_layout

\begin_layout Standard
These steps represent respectively: the balloon force, the image attachment
 and the smoothing force.
 
\end_layout

\begin_layout Chapter
Implementation
\begin_inset CommandInset label
LatexCommand label
name "chap:Implementation"

\end_inset


\end_layout

\begin_layout Standard
This chapter will document the work that was necessary to get a functional
 tool that a scientist could use for segmenting an image using the ESPina
 system.
 First a small section specifying the requisites necessary for anyone trying
 to replicate or do some derivative work based on the work presented.
 We will then present the work done to implement the algorithms and finally
 the implementation of the user interaction logic and the ESPina plug-in.
\end_layout

\begin_layout Section
Prerequisites
\end_layout

\begin_layout Standard
In order to be able to replicate this work, the interested party would need
 the following components:
\end_layout

\begin_layout Itemize
Cmake: a cross-platform, open-source build system.
 It is necessary to build from sources all the other required libraries
 as well as our own code.
 
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

www.cmake.org
\end_layout

\end_inset

.
 
\end_layout

\begin_layout Itemize
ITK: an open-source, cross-platform system that provides developers with
 an extensive suite of software tools for image analysis.
 It is required by ESPina.
 
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

www.itk.org
\end_layout

\end_inset

.
 
\end_layout

\begin_layout Itemize
ParaView: an open-source, multi-platform data analysis and visualization
 application.
 It is designed as a client-server application aimed at allowing the use
 of a massively parallel architecture for data processing.
 ESPina is built as an extension to the ParaView ecosystem, and uses its
 server implementation as a backbone.
 
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

www.paraview.org
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
VTK: is an open-source, freely available software system for 3D computer
 graphics, image processing and visualization.
 VTK consists of a C++ class library and several interpreted interface layers.
 It is used extensively in our work.
 
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

www.vtk.org
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
ESPina: the ESPina Interactive Neuron Analyzer is the system that hosts
 our plug-in and provides user interaction capabilities.
 A copy should be available upon request in.
 
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

http://cajalbbp.cesvima.upm.es/espina
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
QuaZIP: is a simple C++ wrapper that can be used to access ZIP archives.
 It is required by ESPina.
 
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

http://quazip.sourceforge.net/
\end_layout

\end_inset

.
 
\end_layout

\begin_layout Itemize
The source code for our tool, which should be available from the same source
 as this document.
 
\end_layout

\begin_layout Section
Implementation Of The Algorithms
\begin_inset CommandInset label
LatexCommand label
name "sec:ImplementationAlgorithms"

\end_inset


\end_layout

\begin_layout Standard
The most straightforward way to implement new image segmentation algorithms
 to be used in ESPina is to program them as VTK filters and then make them
 available for the ParaView server instance behind ESPina.
 In order for that to work, the filters have to comply with the following
 conventions:
\end_layout

\begin_layout Itemize
Images are represented as objects of type 
\family typewriter
vtkImageData
\family default
 and are gray-scale.
 The pixels are stored as 
\family typewriter
unsigned char
\family default
, that is scalars between 0 and 255.
 
\end_layout

\begin_layout Itemize
The curve to be evolved by our morphological operators will be represented
 as a binary image, where black pixels (gray level 0) are considered outside
 of the curve and white pixels (gray level 255) are considered inside of
 the curve.
\end_layout

\begin_layout Itemize
The filter will receive as an input the image that is being processed and
 the output it provides must be a binary image that represents the labeling
 of the pixels in the image (background pixels are black and foreground
 pixels are white).
\end_layout

\begin_layout Itemize
Upon receiving the output from the filter, ESPina will add a new segmentation
 object to its model.
\end_layout

\begin_layout Standard
The use of VTK provides several advantages because it provides an abundant
 library of filters that can be used internally by the new filters (e.g.
 Gaussian smooth operators, dilate and erode operators).
 This filters are very efficient and by lowering the amount of work that
 has to be done "by hand" they help to reduce the amount of code needed
 to implement new filters.
 
\end_layout

\begin_layout Standard
For performance reasons, it is not advisable to always use the whole image/stack
 when executing the algorithms.
 To address this issue in our implementation we pass along the pipeline
 only a fraction of the image, called the Volume of Interest (VOI), right
 now that parameter is fixed, it is a box that is 121 x 121 x 121 voxels,
 centered around the initial seed of the curve.
 As will be discussed in chapter 
\begin_inset CommandInset ref
LatexCommand ref
reference "chap:Results"

\end_inset

 this selection seems to be having a negative effect in some cases on the
 performance of the WACWE.
\end_layout

\begin_layout Subsection
Morphological Geodesic Active Contours
\end_layout

\begin_layout Standard
The execution of the MGAC is divided in two stages, implemented separately
 as independent VTK filters.
 
\end_layout

\begin_layout Standard
As was explained earlier, in this model the evolution is dependent on an
 energy function 
\begin_inset Formula $g\left(x\right)$
\end_inset

 so the first stage is obtaining the values of this function.
 The motivation to separate the evaluation of this function from the actual
 evolution of the curve is that it gives us the flexibility to eventually
 use different functions as stop criteria for the evolution of the snakes
 on images with different characteristics (for example, you might be interested
 on using a function that favors stopping the curve evolution on the edges
 of the image, or in the center of dark segments).
 
\end_layout

\begin_layout Standard
The stop function that is being used is the one shown in equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:stopf"

\end_inset

 that takes low values on the edges of the image.
 The filter that evaluates this function takes as an input an image and
 the parameters 
\begin_inset Formula $\alpha$
\end_inset

 and 
\begin_inset Formula $\sigma$
\end_inset

 (a scaling parameter and the standard deviation for the Gaussian filter,
 respectively), and returns the values of the function for the specified
 image.
 This is done by sequentially applying several VTK filters to the image,
 by doing it like this it is very easy to develop any number of stop functions
 that could be used for trying out alternatives.
 
\end_layout

\begin_layout Standard
This implementation can be found in the class 
\family typewriter
vtkStopCriterion
\family default
 of the solution.
\end_layout

\begin_layout Standard
The second filter necessary for the execution of MGAC takes as input the
 result of the previous stage, optionally it takes a second image that represent
s an initial curve to be evolved.
 If this second image is not present then the filter expects amongst its
 inputs a "seed" parameter and a radius.
 Additionally the filter takes four additional parameters: the number of
 evolution iterations that have to be executed, the size of the dilation/erosion
 kernel (typically 3) and 
\begin_inset Formula $v$
\end_inset

 and 
\begin_inset Formula $\theta$
\end_inset

 that were already explained in subsection  
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Morphological-Geodesic-Active"

\end_inset

.
 
\end_layout

\begin_layout Standard
Upon beginning its execution the filter will check for the existence of
 an input curve, if it finds one it goes straight to the curve evolution
 steps.
 If it doesn't, then it will create one using the seed parameter which is
 nothing more than the three values corresponding to a point in space around
 which the filter will create a disc of the specified radius that becomes
 the curve to be evolved.
 
\end_layout

\begin_layout Standard
Once the initial phase is over, the filter will execute the specified number
 of iterations of the steps in equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:mgac"

\end_inset

.
 Most of the operations that have to be performed during this steps could
 be done with a combination of VTK filters.
 One exception to that is the SIoIS operator, which was implemented as an
 independent filter, details about this implementation are provided in a
 following section.
 
\end_layout

\begin_layout Standard
This implementation can be found in the class 
\family typewriter
vtkMGAC
\family default
 of the solution.
\end_layout

\begin_layout Subsection
Morphological Active Contours Without Edges
\end_layout

\begin_layout Standard
The execution of the MACWE is relatively simpler, because it works directly
 with the data from the image, so its not necessary to precalculate an energy
 function, as was the case with the MGAC.
 
\end_layout

\begin_layout Standard
The MACWE filter takes as input the image being processed, optionally it
 takes a second image that represents an initial curve.
 If this second image is not present then the filter expects amongst its
 inputs a "seed" parameter and a radius, additionally the filter takes as
 a parameter the number of evolution iterations that have to be executed.
 
\end_layout

\begin_layout Standard
Upon beginning its execution the filter will check for the existence of
 an input curve, if it finds one it goes straight to the curve evolution
 steps.
 If it doesn't, then it will create one using the seed and radius parameters,
 with the difference that in this case the initial curve created around
 this point is a sphere and not a disk.
 
\end_layout

\begin_layout Standard
Once the initial phase is over, the filter will execute the specified number
 of iterations of the steps in equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:macwb"

\end_inset

.
 Again, this filter uses functionality already implemented in VTK's libraries
 and the SIoIS operator.
 
\end_layout

\begin_layout Standard
This implementation can be found in the class 
\family typewriter
vtkMACWE
\family default
 of the solution.
\end_layout

\begin_layout Subsection
Morphological Curvature Operator
\end_layout

\begin_layout Standard
Both MGAC and MACWE require a morphological curvature operator that acts
 as a kind of "smoothing" force on the evolving curve.
 It is based on the composition of the Sup-Inf (SI) and Inf-Sup (IS) morphologic
al operators (this composition is noted from now on as 
\begin_inset Formula $SI\circ IS$
\end_inset

).
 For a demonstration of how this composition is equivalent to its continuous
 counterparts please refer to 
\begin_inset CommandInset citation
LatexCommand citet
key "Marquez_2012"

\end_inset

.
 Since this operator was needed by both the previous filters it was developed
 as a standalone filter that could be included in their internal pipelines.
 
\end_layout

\begin_layout Standard
In order to get an intuitive idea about what this operator does, one could
 think of it as applying sand-paper to the figure to eliminate all rough
 edges and protruding parts while at the same time applying filling paste
 in order to fill in small gaps and indentations.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename Images/effectSIIS.png
	display false
	width 100col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
A demonstration of the effect of the SI (a) and IS(b) operators.
\begin_inset CommandInset label
LatexCommand label
name "fig:effectSIIS"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Float algorithm
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset listings
inline false
status open

\begin_layout Plain Layout

for (z = 0, i< maxZ, i++)
\end_layout

\begin_layout Plain Layout

 for (y = 0, i< maxY, i++)
\end_layout

\begin_layout Plain Layout

  for (x = 0, i< maxX, i++)
\end_layout

\begin_layout Plain Layout

   pixel = image(x,y,z)
\end_layout

\begin_layout Plain Layout

   if (operator = = SI and pixel = = white) OR 
\end_layout

\begin_layout Plain Layout

      (operator = = IS and pixel = = black)
\end_layout

\begin_layout Plain Layout

    if the pixel is in an edge or a vertex
\end_layout

\begin_layout Plain Layout

	 ignore it
\end_layout

\begin_layout Plain Layout

    else 
\end_layout

\begin_layout Plain Layout

     try to find a straight edge
\end_layout

\begin_layout Plain Layout

     if straight edge not found
\end_layout

\begin_layout Plain Layout

      the pixel is switched
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
SIoIS Algorithm
\begin_inset CommandInset label
LatexCommand label
name "alg:Algorithm1"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
When applied to a binary image the SI operator only affects white pixels
 and the IS operator only affects black pixels.
 These operators will switch those pixels (white for SI and black for IS)
 that are not found to belong to a straight edge, this is shown more clearly
 in figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:effectSIIS"

\end_inset

.
 What constitutes a straight edge, depends on whether we are dealing with
 a bi-dimensional or a three-dimensional image.
 In the first case a straight edge would be a straight line and in the second
 case it would be a plane.
 Please refer to algorithm 
\begin_inset CommandInset ref
LatexCommand ref
reference "alg:Algorithm1"

\end_inset

 for a pseudo-code representation of our implementation.
 To make this more clear, figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:2dbase"

\end_inset

 shows what straight edges the algorithm will be looking for in each case.
 
\end_layout

\begin_layout Standard
As we can see the filter does only one of the operations each time it's
 called, so it has to be called twice in order to count as one application
 of the 
\family roman
\series medium
\shape up
\size normal
\emph off
\bar no
\strikeout off
\uuline off
\uwave off
\noun off
\color none

\begin_inset Formula $SI\circ IS$
\end_inset

 operator.
 It has been found that better results are obtained by alternating the order
 on which the operators are called (sometimes using 
\begin_inset Formula $SI\circ IS$
\end_inset

 and sometimes using 
\begin_inset Formula $IS\circ SI$
\end_inset

), so in practice we have to call this filter two times for every smoothing
 pass we want to take on a curve.
\end_layout

\begin_layout Standard
This implementation can be found in the class 
\family typewriter
vtkSIoISFilter
\family default
 of the solution.
\end_layout

\begin_layout Standard
\begin_inset Float figure
placement H
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename Images/bases.png
	display false
	width 100col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Straight edges in a bi-dimensional image (a) and a three-dimensional image
 (b).
 [Figure taken from 
\begin_inset CommandInset citation
LatexCommand citet
key "Marquez_2012"

\end_inset

] 
\begin_inset CommandInset label
LatexCommand label
name "fig:2dbase"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Segmentation Logic Filter
\end_layout

\begin_layout Standard
In addition to the VTK filters required for the segmentation algorithm,
 we needed to develop an additional filter that would be necessary for the
 user interaction model.
 
\end_layout

\begin_layout Standard
This filter is relatively simple, it receives two images (in our use of
 it, these will always be representations of snakes) and an operation parameter
 (Addition or Subtraction), and returns a binary image that represents the
 result of applying the selected operation.
 Addition is a simple disjunction of the binary images and the subtraction
 is equivalent to first negating the first image and then doing a conjunction
 with the second one, effectively subtracting the second image from the
 first one (
\begin_inset Formula $Img_{1}\vee Img_{2}$
\end_inset

 and 
\begin_inset Formula $\neg Img_{1}\wedge Img_{2}$
\end_inset

, respectively).
\end_layout

\begin_layout Standard
In VTK an image doesn't necessarily start at the origin, but it can start
 from any point in space as needed.
 The property of the image that contains this information is called the
 
\family typewriter
\shape slanted
extent
\family default
\shape default
.
 In case this filter receives two images with different extents, the resulting
 image will have an extent large enough to accommodate both images.
 This sets off a warning when used in ESPina, but it works correctly.
 
\end_layout

\begin_layout Standard
This implementation can be found in the class 
\family typewriter
vtkSegmentationLogicFilter
\family default
 of the solution.
 
\end_layout

\begin_layout Section
ESPina Plug-in 
\end_layout

\begin_layout Standard
The plug-in for ESPina has two primary functions: to wrap the functionality
 of the VTK filters already built in a way compatible with ESPina/ParaView
 and also to model the interface for the user.
\end_layout

\begin_layout Subsection
Wrapping VTK functionality
\end_layout

\begin_layout Standard
In ESPina's architecture all VTK filters have to be wrapped in an object
 of type 
\family typewriter
pqFilter
\family default
.
 This object will handle all calls to the VTK filter in ParaView's server,
 ensuring that all parameters are of the right type.
 Additionally, every VTK filter's interface must be made known to the server
 via an XML file that describes its expected inputs, the name of the class
 that contains its implementation and a name to register it on the server.
 
\end_layout

\begin_layout Standard
In this case, both algorithmic filters (MGAC and MACWE) are wrapped in the
 same class (
\family typewriter
MorphologicalSnakesFilter
\family default
) and they will be called depending on a selection made at runtime by the
 user.
 
\end_layout

\begin_layout Standard
The filter for adding and subtracting segmentations was wrapped in a class
 called 
\family typewriter
SegmentationLogicFilter.
\end_layout

\begin_layout Standard
In case the user needs to call any of VTK's own filters directly from an
 ESPina plug-in, it is possible to do so, but it has to be exposed to the
 server in the same way as user-provided filters.
 That means that an XML file describing the interface of that filter has
 to be included when building the plug-in.
 We used this procedure to enable the use of the filter 
\family typewriter
vtkImageEllipsoidSource
\family default
 to draw the starting mask on the image as the user moves the mouse around
 the screen.
 
\end_layout

\begin_layout Standard
All XML files created for the purposes described in this section can be
 found alongside the code of the plug-in for further reference.
 
\end_layout

\begin_layout Subsection
User Interaction
\end_layout

\begin_layout Standard
The objective of a user when working with this plug-in is to generate a
 segmentation object in ESPina's data model.
 In this model a segmentation is a group of voxels that have been labeled
 as belonging to a structure according to certain taxonomy (e.g.
 a synapse).
 Before starting the process of segmentation the user must choose what kind
 of structure he is going to be labeling using ESPina's taxonomy selector.
 Once a class for the object has been selected, the user must perform the
 following steps to create a valid segmentation using our plug-in: 
\end_layout

\begin_layout Itemize
Select from the drop-down menu what algorithm is going to be used, at this
 point the only alternatives are MACWE or MGAC but more could be added in
 the future.
 
\end_layout

\begin_layout Itemize
Click on the selector tool to get the proper cursor.
 This indicates to the plug-in that the user is starting a new segmentation.
 
\end_layout

\begin_layout Itemize
When moving the cursor over the image a green area will become highlighted
 (a disk if using MGAC and a sphere if using MACWE), this represents the
 initial contour that will be the seed for the iterative growing process.
 
\end_layout

\begin_layout Itemize
At this stage the user can change the radius of the initial mask by holding
 the CTRL key and using the wheel of the mouse.
 
\end_layout

\begin_layout Itemize
Once the user is satisfied with the location of the initial mask he must
 left click to indicate that the evolution process has begun.
 The color of the mask will change from green to dark blue.
 
\end_layout

\begin_layout Itemize
At this point the user can control the growth of the curve by holding the
 CTRL key and using the wheel of the mouse.
 In this way, the user can go forward or backwards (up to the initial seed
 curve) until satisfied with the results.
 
\end_layout

\begin_layout Itemize
If at any moment in this step the user wants to stop this curve's evolution
 and wants to delete it, a right click will delete the current curve and
 send the user back to the last stage in the segmentation process.
\end_layout

\begin_layout Itemize
Once the curve has reached the desired size the user must left click again
 to signal the end of the evolution of this particular curve.
 The color of the curve will change from dark blue to light blue.
 Now the user has a choice, he could repeat the process and grow a new curve
 which when done will be annexed to the existing (light blue) curve or if
 he is satisfied with the current state of the segmentation he will click
 on the "Add Segmentation" button on the tool bar which will add the curve
 to ESPina's model as a completed segmentation.
 
\end_layout

\begin_layout Itemize
When creating additional curves the user has the option of holding the SHIFT
 key when clicking on the image and this will tell the system that the curve
 that is being evolved must be considered as "negative" and thus not annexed
 but subtracted from the current segmentation.
 In this case instead of being dark blue the curve will be colored white.
 
\end_layout

\begin_layout Subsection
Architecture Of The Plug-in
\end_layout

\begin_layout Standard
Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:classdiag"

\end_inset

 presents a schematic representation of the architecture of the plug-in.
 The main class of the system is called 
\family typewriter
MorphologicalSnakes
\family default
, technically it represents the tool bar that is loaded in the ESPina system
 when the plug-in is loaded but it also acts as the main container and controlle
r of the rest of our classes.
 The classes that are located in the top right part of the diagram are the
 ones more related to user interaction:
\end_layout

\begin_layout Itemize

\family typewriter
MorphologicalSnakesSelector
\family default
: is the class tasked with interpreting most of the user input.
 It captures mouse movement to draw the green mask on the image.
 It also captures the wheel movement used to adjust the radius of the initial
 mask as well as for the evolution of the mask.
\end_layout

\begin_layout Itemize

\family typewriter
RadiusAction
\family default
: controls and monitors the radius selection widget.
\end_layout

\begin_layout Itemize

\family typewriter
AlgCBAction
\family default
: controls and monitors the algorithm the user has chosen to control the
 curve evolution.
 
\end_layout

\begin_layout Standard
The classes in the lower part of the diagram are the ones that control the
 segmentation per se:
\end_layout

\begin_layout Itemize

\family typewriter
SegmentationLogicFilter
\family default
: wrapper for the segmentation logic filter implemented in VTK.
\end_layout

\begin_layout Itemize

\family typewriter
SnakesFilterManager
\family default
: it's the class that handles the actual evolution of the curve.
 It calls the corresponding filter to generate every iteration of the evolution
 of the curve.
 It also keeps a history of the previous steps of the evolution, allowing
 the user to go back and forth when interacting with the curve.
\end_layout

\begin_layout Itemize

\family typewriter
MorphologicalSnakesFilter
\family default
: wrapper for MGAC and MACWE filters implemented in VTK.
\end_layout

\begin_layout Itemize
VTK files: already explained in the previous section.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename Images/classdiag.svg
	display false
	width 100text%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Relations between the different classes of the plug-in.
 Yellow classes are exclusively VTK classes and purple classes were made
 to fit into ESPina's model.
 
\begin_inset CommandInset label
LatexCommand label
name "fig:classdiag"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Section
Putting It All Together
\end_layout

\begin_layout Standard
We have already explained the way the algorithms were implemented and also
 how the plug-in was designed.
 The key to putting it all together and actually being able to use the plug-in
 in ESPina is the use of Cmake.
 As explained in the prerequisites section, this is a configurable building
 tool and it is indispensable for building the plug-in.
 One of it greatest strengths is that it allows for expert users to define
 macros and routines specific for their application.
 In this case, since this plug-in is technically a plug-in for ParaView,
 it is built using some macros specifically created for that purpose by
 Kitware to be used in a CMake configuration file.
 Cmake works based on a file that is called CMakeLists.txt which contains
 all the instructions to build a file using CMake.
 For further reference, we recommend going to CMake documentation online
 and consulting the CMakeLists.txt file which is distributed with the codebase
 of the plug-in.
 
\end_layout

\begin_layout Standard
What CMake actually does is generate all the files necessary to build the
 binaries, depending on the toolset that is being used.
 During our work we generated files to be compiled using the standard GNU
 make tool that comes with most modern *NIX systems.
 It can also generate files to be compiled using certain IDEs like Code::Blocks,
 QT Creator and Visual Studio on a Windows environment.
 
\end_layout

\begin_layout Standard
Once a working binary library is compiled, the way to load the plug-in in
 ESPina is to go to the menu: Settings
\begin_inset Formula $\rightarrow$
\end_inset

Manage Plugins
\family roman
\series medium
\shape up
\size normal
\emph off
\bar no
\strikeout off
\uuline off
\uwave off
\noun off
\color none

\begin_inset Formula $\rightarrow$
\end_inset


\family default
\series default
\shape default
\size default
\emph default
\bar default
\strikeout default
\uuline default
\uwave default
\noun default
\color inherit
"Load New..." and then navigate to the compiled binary file.
 After successfully executing these steps, there should be a new tool bar
 on ESPina that allows the user to interact with the plug-in.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename Images/loaded.svg
	display false
	width 100col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
The result of correctly loading the plug-in on ESPina.
 Emphasized in red is the new tool bar.
\begin_inset CommandInset label
LatexCommand label
name "fig:Toolbar_loaded"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Chapter
Results and Discussion
\begin_inset CommandInset label
LatexCommand label
name "chap:Results"

\end_inset


\end_layout

\begin_layout Standard
Since the main objective was to implement the MGAC and MACWE algorithms
 proposed by 
\begin_inset CommandInset citation
LatexCommand citet
key "Marquez_2012"

\end_inset

, we can report that the objective was reached and that both the algorithms
 were successfully implemented, resulting in a tool which allows the users
 to interactively segment an image in 3D.
 In figures 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:ejec1"

\end_inset

 and 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:ejec2"

\end_inset

 we show some snapshots of the segmentation process: the initial seed of
 a curve, the evolution of that curve up to its limits (in this case dictated
 by the size of the initial VOI), the adding of a second curve to that segmentat
ion, and then the generation of the segmentation object in ESPina's model.
 Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:ejec3"

\end_inset

 shows a 3D representation of the segmentation obtained.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename Images/progression/correct/v1.svg
	display false
	width 50page%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Snapshots of the segmentation of a tubular structure.
\begin_inset CommandInset label
LatexCommand label
name "fig:ejec1"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename Images/progression/correct/v2.svg
	display false
	width 50page%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Snapshots of the segmentation of a tubular structure.
\begin_inset CommandInset label
LatexCommand label
name "fig:ejec2"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename Images/progression/correct/v3.svg
	display false
	width 50page%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
3D Views of the final segmentation once added to ESPina's model.
\begin_inset CommandInset label
LatexCommand label
name "fig:ejec3"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
From preliminary testing and evaluation we find that both algorithms work
 as expected, but present some shortcomings on their performance, specially
 the MGAC.
\end_layout

\begin_layout Standard
In figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Evolution"

\end_inset

 we can appreciate the evolution of a similar curve by both algorithms when
 trying to segment the same structure from approximately the same starting
 condition (remember that they cannot start exactly with the same curve
 because MGAC's initial curve is a disk while MACWE's is a sphere).
\end_layout

\begin_layout Standard
As we can see, MGAC grows faster but it's less accurate on the borders,
 it presents a lot of "leaking" in some points.
 MACWE on the other hand evolves more slowly, but is more accurate in keeping
 within the borders of the objective structure.
 It is very hard to show on this report the performance of both algorithms
 in every situation, however, it's clear to that none of the two is right
 for every situation and that the performance of each depends on a lot of
 both external and internal variables.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename Images/progression/comparative/comp.svg
	display false
	width 50page%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
An example of the evolution of a single curve.
 The input image (a), the stop function derived from it (b), and the evolution
 of both algorithms up to thirty iterations.
\begin_inset CommandInset label
LatexCommand label
name "fig:Evolution"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
To go a little more into detail into the factors that seem to be impending
 the performance of the MGAC, we find that it is highly dependent on two
 external factors, one is the selection of the parameters for the algorithm
 and the other is in the selection of the stop criterion used to guide the
 evolution (for example, when images have fuzzy edges, a criterion that
 favors stopping on edges might have some trouble to actually stop the evolution
 in the right area).
 Further ahead we present some ideas about ways to overcome these problems,
 and enhance the results obtained from this approach.
 
\end_layout

\begin_layout Standard
As for MACWE we find that it works pretty well "out-of- the-box", and is
 even capable of overcoming some of the challenges posed by the images on
 which it was tested.
 This appears to be related to the fact that it doesn't rely so heavily
 on external parameters bur rather works with global information directly
 from the image.
 It did run into some situations where the curve instead of growing, disappears
 within a few iterations of the algorithm, this seems to have to do with
 the selection of the initial volume of interest (as discussed in section
 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:ImplementationAlgorithms"

\end_inset

).
 Maybe a more sensible approach would be to modify the selection of the
 VOI so that it is not fixed, but it is always kept at at certain distance
 from the edges of the curve.
 This hypothesis was not tested.
 
\end_layout

\begin_layout Standard
One of the aspects that seems to affect the performance of these algorithms
 is the quality of the image being processed, in this case the main test
 image had some issues regarding the distribution of data on its Z axis.
 This was caused by the fact that the image had a different resolution on
 that axis than on the X and Y axes.
 This resulted in some distortions on the image that made it difficult for
 the curve to stay within certain boundaries, specially on the Z axis.
 The distortions on the image were not evenly distributed along the Z axis,
 while in some areas the discontinuity was barely perceivable in other parts
 of the image we found big leaps from one slice to another, this inconsistency
 had an effect on the performance of the segmentation tool.
 In Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:discontinuity"

\end_inset

 the reader can appreciate the kinds of discontinuity that were present
 in some of the images.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename Images/discontinuidad.png
	display false
	width 100col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
A cross-cut of a stack of images that shows discontinuities on the Z axis
 (a).
 Details of a portion of the cross-cut (b).
 
\begin_inset CommandInset label
LatexCommand label
name "fig:discontinuity"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Section
Possible Improvements And Future Work
\end_layout

\begin_layout Standard
For the improvement of the performance of WGAC, the key areas are the selection
 of the parametric components of the algorithms, as well as the selection
 of a stop criterion function.
 
\end_layout

\begin_layout Standard
Although we found that with the parameters used by the authors in their
 work the results were acceptable, it might be interesting to try to come
 up with this parameters in a more automated fashion, taking into account
 user input as well as any other characteristics of the image that could
 be extracted automatically.
 This could be accomplished in several ways, for example:
\end_layout

\begin_layout Standard
We propose a two stage procedure to obtain a fully automated parameterization
 for the segmentation algorithms.
\end_layout

\begin_layout Standard
The objective of the first stage would be to obtain training data for the
 fully automatic system.
 It would work like this: 
\end_layout

\begin_layout Itemize
The scientist would choose a structure within an image that he wishes to
 label.
\end_layout

\begin_layout Itemize
The system would generate at random a new "individual" represented by the
 different values of the parameters that have to be established.
 
\end_layout

\begin_layout Itemize
The system would run a number of iterations of curve evolution starting
 from a seed selected by the user.
 
\end_layout

\begin_layout Itemize
The user will give a fitness rating to this solution.
\end_layout

\begin_layout Itemize
Depending on the fitness of the individual, it is selected as a viable solution
 or it is evolved using known evolutionary techniques.
\end_layout

\begin_layout Itemize
The process is repeated until a fit enough solution is found.
 
\end_layout

\begin_layout Itemize
All the data generated by the process is stored in a database, relating
 the kind of structure being labeled, the characteristics of the image and
 the corresponding solution.
\end_layout

\begin_layout Standard
Once a suitable database has been populated with the knowledge of the experts
 the second stage would be the training of a machine learning algorithm
 which could be used to do automatic segmentation on an image.
 In this second stage the user would just supply the seed for the structures
 and the system would be able to select the parameters and run the necessary
 iterations based on the training obtained in the first stage.
\end_layout

\begin_layout Standard
As for the selection of the stop criterion function used for the curve evolution
, the one that is being used right now favors stopping in the image borders,
 however, the kind of images that have been used have very fuzzy borders
 so that criteria might not necessarily be the best.
 Could there be another way to select, construct or improve the performance
 of that function?.
 Could this function be derived using user input, including interactive
 information about where the function should stop?.
 We present some alternatives that could be considered to address this issue:
\end_layout

\begin_layout Itemize
From a certain perspective, the stop function is not more than a preprocessing
 step, or filtering, of the initial image to extract from it certain information
 that is useful for the next step of the process.
 Maybe different sets of filters or operations could be identified that
 produce stop criteria that is particularly well suited for certain kinds
 of structures.
 It might be possible to provide the users with a methodology to obtain
 the best possible stop criterion before starting segmentation depending
 on the objective structure.
 
\end_layout

\begin_layout Itemize
Sometimes, user input is indispensable for the proper labeling of an image,
 in those cases, it would be interesting if the user could provide the algorithm
 an aid to use in conjunction with the stop function obtained automatically.
 The main idea would be to provide the user with the tools to set special
 attraction and repulsion areas in the image, to actively aid in the evolution
 of the curve.
\end_layout

\begin_layout Standard
In figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:stopCriterionImage"

\end_inset

 we can better appreciate the aspect the stop criterion function has once
 it has been computed, and how some of the actions just described could
 work, by modifying the aspect of the stop criterion function in some way
 or another.
 The objective would be to obtain a function with very clear dark zones
 (low values) in the parts of the image we would like it to stop.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename Images/stopCriterion.png
	display false
	width 90text%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Visualization of a slice of an image (top) and the stop criterion function
 derived from it (bottom).
\begin_inset CommandInset label
LatexCommand label
name "fig:stopCriterionImage"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Standard
The following ideas are not aimed specifically at improving the performance
 of a specific algorithm but rather of the tool as a whole.
\end_layout

\begin_layout Standard
It appears that the initial shape and size of the curve has an impact on
 the effectiveness of the tool to evolve the curve correctly.
 For example, in our images there are a lot of structures that have a sort
 of tubular shape along the Z axis.
 If the developer knew that kind of details beforehand, with the input of
 the experts, the shape of the initial curve as well as that of the VOI
 could be designed to improve the performance of the algorithm in detecting
 that kind of structure.
 For example, instead of a disk or a sphere like it is being used now, it
 could be useful to use as an initial shape for the curve a "strand" that
 the user could approximate to the position of the structure, going from
 the top slice to the bottom slice.
 A library could be developed with the initial shapes that are found to
 be of use and this could help speed up the process of labeling by allowing
 the user to always start the evolution with the most fitting initial shape
 for the curve.
 
\end_layout

\begin_layout Standard
With regards to the usability of our tool and the value added to the scientists,
 we consider that the next step should be a series of live tests with the
 users to get some data about the increase in efficiency in the segmentation
 process when comparing the status quo with the use of this tool.
 Once that data is available we could do some A/B tests to try out interaction
 alternatives and fine tune the interface of the tool with the aim of maximizing
 the productivity of the experts and allowing them to process as many images
 as possible rapidly and correctly.
 
\end_layout

\begin_layout Standard
On a more practical note, and this work being more of a proof-of-concept
 approach, the particulars of the implementation of the algorithms could
 use some polishing with an eye on improving the computational efficiency
 of the code, in particular aiming to take advantage of multi-threading
 or other possible parallelizations techniques.
 This could also be achieved, with a loss in modularity, by replacing the
 use of some of the more generic VTK filters with some custom made filters
 that combined multiple operations in one.
\end_layout

\begin_layout Chapter
Conclusions
\begin_inset CommandInset label
LatexCommand label
name "chap:Conclusions"

\end_inset


\end_layout

\begin_layout Standard
The extraction of meaningful and useful data from images is a complex and
 time consuming task.
 More specifically the scientists of the Cajal Blue Brain have a clear need
 for a tool that allows them to address the problem of having too many images
 to process and the amount of time it takes to manually label every slice
 of every image.
 This labeling is needed, in the context of the project, to allow the extraction
 of meaningful data from electronic microscopy images of brain tissue that
 would allow to fulfill one of the objectives of the Blue Brain Project
 which is the simulation of a big network of neuronal cells based on modeling
 the interaction of this kind of cells in a real brain.
 
\end_layout

\begin_layout Standard
This problem of labeling the elements in an image is known in the computer
 vision domain as segmentation.
 The application of known segmentation techniques could be a potential solution
 to the problem of the massive labeling needed by the brain scientists of
 the Cajal Blue Brain project.
 In chapter 
\begin_inset CommandInset ref
LatexCommand ref
reference "chap:Previous-Work"

\end_inset

 we gave a very brief overview of the many approaches that have been proposed
 in the literature regarding the segmentation problem.
 One of the most successful of these approaches is known as active contours,
 or Snakes.
 These techniques are based on the evolution of a curve, normally by finding
 the solution of a partial differential equation (PDE).
 The use of PDEs has a number of disadvantages, specially concerning the
 complexity of the calculations involved as well as the numerical stability
 of the methods.
 A recent proposal was made by 
\begin_inset CommandInset citation
LatexCommand citet
key "Marquez_2012"

\end_inset

 to apply a morphological approach to the evolution of the Snakes, avoiding
 the use of PDEs and lowering the computational cost of the solution.
 The algorithms they propose are called Morphological Geodesic Active Contours
 (MGAC) and Morphological Active Contours Without Edges (MACWE).
 An explanation of these algorithm can be found in sections 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Morphological-Geodesic-Active"

\end_inset

 and 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Morphological-ACWB"

\end_inset

.
 
\end_layout

\begin_layout Standard
Our main objective in the present work was to create a tool that allows
 a scientist to interactively segment an image with the aid of the MGAC
 and MACWE algorithms.
 This tool is a plug-in for a software system called ESPina that was developed
 by members of the Cajal Blue Brain Project as an interaction and visualization
 tool for the analysis of neuronal images.
 The plug-in adds a tool bar to ESPina that allows the user to do segmentation
 with the morphological algorithms described earlier.
 This tool was designed to be interactive in order to fully harness the
 input of the experts, who have full control over where the initial curve
 is placed, as well as over the evolution of that curve until they are satisfied
 with the results.
 This process allows for the user to iteratively add together several independen
tly evolved curves into a final labeling of a structure.
 
\end_layout

\begin_layout Standard
In chapter
\begin_inset CommandInset ref
LatexCommand ref
reference "chap:Implementation"

\end_inset

 the interested user can find all the technical details of the way the algorithm
s and the user interaction were implemented.
 The algorithmic part of the implementation was done using VTK, a library
 developed by Kitware for image data processing, analysis and visualization,
 it required the use of some filters that come bundled in VTK's libraries
 and also the development of some new stand-alone filters.
 The user interaction parts of the tool were done complying with ESPina's
 extensibility model.
\end_layout

\begin_layout Standard
The primary result of our work is a tool that allows a user to interactively
 do 3D image segmentation in the ESPina environment, based on morphological
 active contour algorithms.
 The performance of this tool is relatively good, but depends heavily on
 several factors for its accuracy (parameterization, quality of the image,
 shape of initial curve, etc.).
 Seeing these results, we propose several avenues for further development
 of this subject: the use of machine learning techniques for automatic parameter
ization, and a redesign of user input and interactivity being the ones with
 the most potential.
\end_layout

\begin_layout Standard
The objectives of projects Blue Brain and Cajal Blue Brain are large and
 inspiring, and reliable image segmentation techniques are a key part of
 the puzzle these projects are trying to solve.
 This tool aims to take a bold step into solving that problem and we consider
 that it opens up several paths that could eventually lead to a more solid
 solution.
 
\end_layout

\begin_layout Standard
\begin_inset CommandInset bibtex
LatexCommand bibtex
bibfiles "references"
options "bibtotoc,plainnat"

\end_inset


\end_layout

\end_body
\end_document