Guillaume Charpiat's Projects in Images

Shape statistics and shape priors


Images are zoomed when clicked.


Aim : to express statistics on a set of shapes
Application : shape prior for image segmentation
Method : compute mean shape + characteristic modes of deformation
Difficulties : automatic alignment of shapes, defining mean and modes


Boletus example

Some of the examples of mushrooms (Boletus):
boletus example boletus example boletus example boletus example

The mean (in red) of all mushrooms (other colors) is computed while aligning them automatically:
boletus mean
And characteristic modes of deformations (in purple) around the mean shape (in blue) are computed:
boletus shape statistics boletus shape statistics boletus shape statistics boletus shape statistics boletus shape statistics


Segmentation of an image with different shape priors (color information is not sufficient to know where boundaries of mushrooms are). A particular color-based criterion is used as an segmentation energy, which is decreased by gradient descent with respect to the red shape:
Without shape prior boletus segmentation boletus segmentation boletus segmentation boletus segmentation boletus segmentation | boletus segmentation
Rigid prior (the mean boletus)
(translation, rotation and scaling only) 		boletus initialisation boletus rigid shape prior segmentation boletus rigid shape prior segmentation boletus rigid shape prior segmentation boletus rigid shape prior segmentation
Statistical shape prior
(mean + modes of variation) 		boletus segmentation (same rigid evolution first) boletus statistical shape prior segmentation | boletus segmentation
Initial-
-isation 		Evo- -lu- -tion Conver-
-gence 		| Click for
the movie




Starfish example

The set of 12 starfish given as a training set:
star example star example star example star example star example star example
star example star example star example star example star example star example


The mean of the set of shapes is computed (in blue), as well as characteristic modes of deformations (purple vector fields):
starfish shape statistics starfish shape statistics starfish shape statistics starfish shape statistics starfish shape statistics starfish shape statistics


Segmentation of an occluded starfish:
Without shape prior starfish segmentation starfish segmentation starfish segmentation starfish segmentation starfish segmentation
Rigid shape prior

(mean shape
up to translations,
rotations and scalings) 		starfish segmentation starfish segmentation starfish segmentation starfish segmentation starfish segmentation
Initial-
-isation 		Evo- -lu- -tion Conver-
-gence


Segmentation of a starfish image:
starfish segmentation starfish segmentation starfish segmentation starfish segmentation starfish segmentation
No shape prior
(2 different initialisations) 		Rigid prior
(mean shape) 		Rigid prior
(mean shape)
+ small deformations
allowed 		Statistical prior:
mean shape
+ characteristic
modes of
deformation only




Other examples of mean shapes

A set of fish (in the middle: the mean shape; around it : some examples from the training set of fish):
fish mean shape

Corpus callosum:
corpus callosum mean shape





Associated publications:
Related project:


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