Add more description about CPD vs ICP filters (#2472)

* Elaborate difference between ICP and CPD filters.

* longer underline

doc/stages/filters.cpd.rst

@@ -22,6 +22,23 @@ the "moving" points after the calculated transformation has been applied, one
 point view per input.  Any additional information about the cpd registration,
 e.g. the rigid transformation matrix, will be placed in the stage's metadata.
 
+When to use CPD vs ICP
+----------------------
+
+Summarized from the `Non-rigid point set registration: Coherent Point Drift
+<http://graphics.stanford.edu/courses/cs468-07-winter/Papers/nips2006_0613.pdf>`_ paper.
+
+- CPD outperforms the ICP in the presence of noise and outliers by the use of
+  a probabilistic assignment of correspondences between pointsets, which is
+  innately more robust than the binary assignment used in ICP.
+
+- CPD does not work well for large in-plane rotation, such transformation can
+  be first compensated by other well known global registration techniques before
+  CPD algorithm is carried out
+
+- CPD is most effective when estimating smooth non-rigid transformations.
+
+
 .. plugin::
 
 Examples
@@ -67,6 +84,7 @@ The metadata output might start something like:
 .. seealso::
 
     :ref:`filters.transformation` to apply a transform to other points.
+    :ref:`filters.icp` for deterministic binary point pair assignments.
 
 Options
 --------

doc/stages/filters.icp.rst

@@ -4,13 +4,34 @@ filters.icp
 ==============
 
 The **ICP filter** uses the `PCL's Iterative Closest Point (ICP)`_ algorithm to
-calculate a rigid (rotation and translation) transformation that best aligns
+calculate a **rigid** (rotation and translation) transformation that best aligns
 two datasets.  The first input to the ICP filter is considered the "fixed"
 points, and all subsequent points are "moving" points.  The output from the
 change filter are the "moving" points after the calculated transformation has
 been applied, one point view per input.  The transformation matrix is inserted
 into the stage's metadata.
 
+.. note::
+
+    ICP requires that the initial pose of the two point sets to be adequately
+    close, which are not always available, especially when transformation is
+    non-rigid. ICP can handle limited nonrigid transformations but be aware
+    ICP may be unable to escape a local minimum. Consider using CPD instead.
+
+    From :cite:`Xuechen2019`:
+
+    ICP starts with an initial guess of the transformation between the two
+    point sets and then iterates between finding the correspondence under the
+    current transformation and updating the transformation with the newly
+    found correspondence. ICP is widely used because it is rather
+    straightforward and easy to implement in practice; however, its biggest
+    problem is that it does not guarantee finding the globally optimal
+    transformation. In fact, ICP converges within a very small basin in the
+    parameter space, and it easily becomes trapped in local minima. Therefore,
+    the results of ICP are very sensitive to the initialization, especially
+    when high levels of noise and large proportions of outliers exist.
+
+
 .. plugin::
 
 Examples
@@ -51,6 +72,8 @@ The metadata output might start something like:
 .. seealso::
 
     :ref:`filters.transformation` to apply a transform to other points.
+    :ref:`filters.cpd` for the use of a probabilistic assignment of correspondences between pointsets.
+
 
 Options
 --------

doc/stages/references.bib

@@ -20,4 +20,29 @@ @article{Yuille1998
 year = {1988}
 }
 
+@article{Xuechen2019,
+abstract = {The rigid registration of two 3D point sets is a fundamental problem in
+computer vision. The current trend is to solve this problem globally using the
+BnB optimization framework. However, the existing global methods are slow for
+two main reasons: the computational complexity of BnB is exponential to the
+problem dimensionality (which is six for 3D rigid registration), and the bound
+evaluation used in BnB is inefficient. In this paper, we propose two
+techniques to address these problems. First, we introduce the idea of
+translation invariant vectors, which allows us to decompose the search of a 6D
+rigid transformation into a search of 3D rotation followed by a search of 3D
+translation, each of which is solved by a separate BnB algorithm. This
+transformation decomposition reduces the problem dimensionality of BnB
+algorithms and substantially improves its efficiency. Then, we propose a new
+data structure, named 3D Integral Volume, to accelerate the bound evaluation
+in both BnB algorithms. By combining these two techniques, we implement an
+efficient algorithm for rigid registration of 3D point sets. Extensive
+experiments on both synthetic and real data show that the proposed algorithm
+is three orders of magnitude faster than the existing state-of-the-art global
+methods.},
+author = {Xuechen Li and Yinlong Liu and Yiru Wang and Chen Wang and Manning Wang and Zhijian Song},
+title = {{Fast and Globally Optimal Rigid Registration of 3D Point Sets by Transformation Decomposition}},
+year = {2019},
+note = {Available at \url{https://arxiv.org/pdf/1812.11307.pdf}}
+}
+
 %======