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(Updated 09/12/2006)

Objective:

We have developed a novel multiscale shape representation and segmentation algorithm based on the spherical wavelet transform. Our work is motivated by the need to compactly and accurately encode variations at multiple scales in the shape representation in order to drive the segmentation and shape analysis of deep brain structures, such as the caudate nucleus or the hippocampus. Our proposed shape representation can be optimized to compactly encode shape variations in a population at the needed scale and spatial locations, enabling the construction of more descriptive, non-global, non-uniform shape probability priors to be included in the segmentation and shape analysis framework. In particular, this representation addresses the shortcomings of techniques that learn a global shape prior at a single scale of analysis and cannot represent fine, local variations in a population of shapes in the presence of a limited dataset.

Progress:

• We developed a multiscale representation of 3D surfaces using conformal mappings and spherical wavelets. We then learned a prior probability distribution over the wavelet coefficients to model shape variations at different scales and spatial locations in a training set. This novel multiscale shape prior was shown to encode more descriptive and localized shape variations than the Active Shape Models (ASM) prior for a given training set size. The results were published in [1] on a prostate dataset.

• We have replicated our results from [1] on the left caudate nucleus dataset from the Brockton dataset (Harvard, Core 3). Additionally, one of the nice application of our technique is the automatic discovery of uncorrelated shape variations in a dataset, at various scales. The visualization of resulting bands on the mean shape can in itself be interesting for shape analysis (see Figure) by indicating which surface patches co-vary across the training set. For example at scale 1, bands 1 and 2 indicate two uncorrelated shape processes in the caudate data that make sense anatomically: the variation of the head and of the body. It is also interesting that bands have compact spatial support, though this is not a constraint of our technique.

Figure 1: 2 examples bands discovered by the prior color-coded on the mean shape of the 29 left caudates from the Harvard Brockton dataset. The color shows the cumulative value of the wavelet bases that belong to that band. Higher value (light-blue to red) areas represent surface locations with correlated variations across shapes

• Segmentation: Based on our representation, we derived a parametric active surface evolution using the multiscale prior coefficients as parameters for our optimization procedure to naturally include the prior for segmentation. Additionally, the optimization method can be applied in a coarse-to-fine manner. In [2] we report results on the caudate nucleus in the Brockton dataset (Harvard, Core 3). Our validation shows that our algorithm is computationally efficient and outperforms the Active Shape Model (ASM) algorithm, by capturing finer shape details.

Ongoing:

• Classification: We are collaborating with Martin Styner (UNC, Core 1) to include our shape features in the UNC shape analysis pipeline. We obtained interesting preliminary results that have been verified by Jim Levitt (Harvard PNL, Core 3). See Caudate and Corpus Callosum Analysis. We have also discussed our results with Martin Styner during a UNC site visit (see June 8-9, 2006, Georgia Tech visit to UNC: Shape Analysis Discussion). A scientific paper is being prepared with our results.
• ITK Filter: We are developing an ITK Filter for the Spherical wavelet transform (See ITK Spherical Wavelet Transform Filter)

References:

• [1] Nain D, Haker S, Bobick A, Tannenbaum A. Multiscale 3D Shape Analysis using Spherical Wavelets. Proc MICCAI, Oct 26-29 2005; p 459-467 [1]

• [2] Nain D, Haker S, Bobick A, Tannenbaum A. Shape-driven 3D Segmentation using

Spherical Wavelets. Proc MICCAI, Oct 2-5, 2006. To Appear.

Key Investigators:

• Georgia Tech: Delphine Nain, Aaron Bobick, Allen Tannenbaum, Yi Gao and Xavier Le Faucheur
• Harvard SPL: Steve Haker

Collaborators

• Core 1: Martin Styner (UNC)
• Core 2: Jim Miller (GE), Luis Ibanez (Kitware)
• Core 3: James Levitt, Marc Niethammer, Sylvain Bouix, Martha Shenton (Harvard PNL)

Links:

• Caudate and Corpus Callosum Analysis.
• June 8-9, 2006, Georgia Tech visit to UNC: Shape Analysis Discussion
• ITK Spherical Wavelet Transform Filter
• Georgia Tech Summary Page