Automatic classification of deformable shapes
This work addresses shape classification for medical imaging applications, specifically in cardiology, but appears incremental as it builds on existing diffeomorphic methods.
The paper tackles the problem of automatically classifying deformable 3D shapes by using optimized diffeomorphic registration to generate feature vectors and augmenting small classes with interpolation and perturbations, achieving classification invariant to rigid motions and testing on a cardiology dataset of mitral valve surfaces.
Let $\mathcal{D}$ be a dataset of smooth 3D-surfaces, partitioned into disjoint classes $\mathit{CL}_j$, $j= 1, \ldots, k$. We show how optimized diffeomorphic registration applied to large numbers of pairs $S,S' \in \mathcal{D}$ can provide descriptive feature vectors to implement automatic classification on $\mathcal{D}$, and generate classifiers invariant by rigid motions in $\mathbb{R}^3$. To enhance accuracy of automatic classification, we enrich the smallest classes $\mathit{CL}_j$ by diffeomorphic interpolation of smooth surfaces between pairs $S,S' \in \mathit{CL}_j$. We also implement small random perturbations of surfaces $S\in \mathit{CL}_j$ by random flows of smooth diffeomorphisms $F_t:\mathbb{R}^3 \to \mathbb{R}^3$. Finally, we test our automatic classification methods on a cardiology data base of discretized mitral valve surfaces.