Research Martin Styner

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Dissertation Martin Styner, Goal:

Develop and apply a shape description suitable for doing statistical shape analysis in neurological studies of morphological changes in human brains associated with neurological diseases, like schizophrenia, autism, Alzheimer's syndrome and others.

Properties that are required from a shape description suitable for shape analysis :

• An efficient description is needed to cope with the high dimensional feature space.
• The shape features and their changes have to be localized in an anatomically correct way.
• The shape features and their changes should be meaningful and invoke an intuitive understanding of the local and global form.
• The description has to be stable in the presence of shape variability, since I deal with populations of similar shapes.
• The description should offer means to establish an appropriate correspondence.

It is evident that in order to find a the description that is most suitable for a shape analysis, the different properties cannot be achieved achieved simultaneously in one single description. A medial description for example offers meaningful features, but is quite unstable in the presence of shape variability. A sampled description is only efficient if the sampling is low, but the resulting coarse scale description does not guarantee anatomical correctness. A parametrized description is often efficient even at a fine scale, but the features and especially their changes are not intuitive. I thus propose to have two descriptions, each one incorporating some of the desired properties. By combining two descriptions some of the inherent disadvantages can be overcome and all requirements can be met in the combined description. Such a combined description is presented in the next chapter.

The winner:         Combined Boundary Medial Shape Description

This document describes a novel approach that incorporates variability of an object population into the generation of a characteristic 3D shape model. The proposed shape representation is a combination of the fine scale spherical harmonics (SPHARM) boundary description and the coarse scale m-rep description. The medial description is composed of a net of medial samples with fixed graph properties. The medial model is computed automatically from a predefined shape space using pruned 3D Voronoi skeletons to determine the stable medial branching topology. An intrinsic coordinate system and an implicit correspondence between shapes is defined on the medial manifold. Our novel representation describes shape and shape changes in a natural and intuitive fashion.

Additional info: Why shape (why is volume measurement not enough) ? Why medial representations ?
 

Shape descriptions of a human hippocampus
Here are the 3 shape description used in this research 

(A) Description of the object boundary via a parametrized decomposition using spherical harmonics (SPHARM). This shape description is global (changes of parameters cause changes to the whole object). It is a fine scale description since it can be computed to a predefined accuracy.	(B) Description of the medial symmetry axis of the object via Voronoi skeletons. Voronoi skeletons are derived from a regularized inner Voronoi graph. In this visualization the Voronoi faces are colored with the corresponding thickness information (red - green - blue: 4.6mm - 2mm -1.0 mm radius). This is a local, fine scale description.	(C) Description of the medial symmetry axis of the object via m-rep. A m-rep is set of medial atoms (dots) linked in a medial graph, with inter- and intrafigural links (purple lines). The m-rep implies a boundary (blue transparent). It is local, coarse scale description, since the number of samples is low.  The color and radius of the medial atoms correspond to the thickness information

 
 

MAIN  PROBLEM:  How to generate of a stable common m-rep model with fixed medial graph given an object population

Our scheme can be subdivided into 3 steps and is visualized in below Figure :

1. Define a shape space by the average object and the major deformations (from population via PCA, covering 95% variability).
2. Determine an appropriately stable figural/sheet topology in the shape space -> This gives us the figures, or also called medial sheets
3. Determine the appropriate sampling of the medial sheets/figures -> fully determines the medial graph

Click on the images or the links to see the details of the methods:
 

1. Definition of a shape space by the average (green) and the major deformations (covering at least 95% of variability). Here shown is the first (red) and second PCA (orange). We assume that the average model and the eigenmodes describe the biological variability of the population appropriately and span the space of all similar biological shapes. From this shape space, we sample a set of representative shapes, onto which we apply all other routines.

2. Determination of common model topology for the medial manifold on given shape space. Shapes in the shape space are described via pruned Voronoi skeleton. For each skeleton we determine a set of medial sheets, which form the medial topology. The medial sheets are then transformed into a common spatial frame, in which they are compared with each other (spatial match). All non-matching sheets make up the common topology.

3. The common topology and a set of grid parameters (n(i) x m(i) grid points for sheet i) determine the medial model. Grid sampling parameters are optimized for minimal number given a predefined maximal approximation error for all shapes in the given shape space. The sampling algorithm is based on the longest 1D thinning axis of the edge-smoothed 3D medial sheet.

Several experiments have been performed and some results are shown on the results page.
 
 

Scientific contributions of this dissertation

1. In regard to computational geometry issues of Voronoi skeletons, this dissertation presents a general scheme that automatically prunes 3D Voronoi skeletons with good results. Such a scheme did not exist prior to this dissertation. Additionally, my experiments showed that only a very small number of skeletal sheets are necessary to describe even quite complex shapes, which is a surprising and encouraging finding.
2. This work is also the first to compute a common medial branching  topology. This common medial branching is necessary to deal with one of the  major disadvantage of medial descriptions: the  sensitivity of the branching topology to even small shape variations. This works also shows that the complexity of the common branching topology is of the same magnitude as the  individual branching topology.
3. Medial representations are also sensitive to small boundary perturbations. This work presents a medial sampling technique that  together with the m-rep methodology allows to deal with this sensitivity.
4. I presented a new shape description scheme for shape analysis via  incorporating prior statistical knowledge about the object variability. This description scheme allows new insights and paths of exploration in various fields of morphological research. The shape features thereby are meaningful and allow to answer questions that could not be answered before.
5. I have shown a convincing study that shape information has clinical information that is superior to volume measurements. Not only can the clinically important information be better localized, but also effects can be measure that cannot be detected with volume measurements.

Future Work

1. Statistical m-rep model capturing the statistical distribution of the m-rep atom features for an improved fit procedure.
2. Extract m-rep features that are better suited for shape analysis as described by P. Yushkevich on 2D m-reps.
3. More validation of stability of PCA/branching topology/sampling
4. Confirm Asymmetry index significant for m-reps of Boston hippocampus-amygdala data (as seen in SPHARM)
5. Stanley series of hippocampi
6. Improve the tool VSkelTool