Boundary Finding with Parametrically Deformable Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parametrization of closed surfaces for 3-D shape description
Computer Vision and Image Understanding
The nature of statistical learning theory
The nature of statistical learning theory
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Geometry and invariance in kernel based methods
Advances in kernel methods
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
Statistical Shape Analysis Using Fixed Topology Skeletons: Corpus Callosum Study
IPMI '99 Proceedings of the 16th International Conference on Information Processing in Medical Imaging
Small Sample Size Learning for Shape Analysis of Anatomical Structures
MICCAI '00 Proceedings of the Third International Conference on Medical Image Computing and Computer-Assisted Intervention
Three-Dimensional Model-Based Segmentation of Brain MRI
WBIA '98 Proceedings of the IEEE Workshop on Biomedical Image Analysis
Discriminative Analysis for Image-Based Studies
MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part I
Performance Issues in Shape Classification
MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part I
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Regularized tensor factorization for multi-modality medical image classification
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part III
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
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Statistical analysis of anatomical shape differences between two different populations can be reduced to a classification problem, i.e., learning a classifier function for assigning new examples to one of the two groups while making as few mistakes as possible. In this framework, feature vectors representing the shape of the organ are extracted from the input images and are passed to the learning algorithm. The resulting classifier then has to be interpreted in terms of shape differences between the two groups back in the image domain. We propose and demonstrate a general approach for such interpretation using deformations of outline meshes to represent shape differences. Given a classifier function in the feature space, we derive a deformation that corresponds to the differences between the two classes while ignoring shape variability within each class. The algorithm essentially estimates the gradient of the classification function with respect to node displacements in the outline mesh and constructs the deformation of the mesh that corresponds to moving along the gradient vector. The advantages of the presented algorithm include its generality (we derive it for a wide class of non-linear classifiers) as well as its flexibility in the choice of shape features used for classification. It provides a link from the classifier in the feature space back to the natural representation of the original shapes as surface meshes. We demonstrate the algorithm on artificial examples, as well as a real data set of the hippocampus-amygdala complex in schizophrenia patients and normal controls.