Piecewise Affine Transformations

Package for smooth deformation of complex shapes.

Installation

Pkg.add("PiecewiseAffineTransforms")

Usage Overview

Piecewise affine transformation resembles ordinary affine transformation, but instead of warping single region linearly, it splits down area under the question into a set of triangles and warps each such triangle separately.

Let's say, we have an image of a face and want to warp it to have different expression (destination image is here only for demonstration, we will not use it):

using PiecewiseAffineTransforms

src_img = ...
dst_img = ...

(full version of code is available in examples/ex.jl)

Source image	Destination image

We will also assume that both faces are annotated with corresponding shape landmarks:

src_shape = ... # should be a Nx2 matrix of Float64,
                #  where N is a number of landmarks
dst_shape = ...

First of all, we need to split the shapes into triangles, i.e. triangulate them:

trigs = delaunayindexes(src_shape)  # Tx3 matrix of Int, where T is
                                    #  a number of resuling triangles
# needs ImageView installed (Pkg.add("ImageView"))
triplot(src_img, src_shape, trigs)
triplot(dst_img, dst_shape, trigs)

WARNING: Triangulation is based on VoronoiDelaunay.jl, which currently has a bug resulting in one lost triangle from time to time. To overcome this, just get good sample of triangulation and save it for future use.

Source shape	Destination shape

Warping src_image from src_shape to dst_shape may be as simple as calling this:

@time warped = pa_warp(src_img, src_shape, dst_shape, trigs)
# 1.44 seconds

But if you are going to repeat warping to dst_shape for many source images or just many times, it's worth to prepare warp by creating PAWarpParams object and using it for all future transformation to dst_shape:

@time pa_params = pa_warp_params(dst_shape, trigs, (480, 640))
# 5.92 seconds
@time warped = pa_warp(pa_params, src_img, src_shape)
# 0.075 seconds

But anyway, they both give (almost) the same result:

Original image	Warped image

Acknowledgement

Code for prepared warp was mostly extracted from ICAAM project by Luca Vezzaro.