Abstract
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.
Acknowledgments
Quadratic optimization was performed using PR LOQO optimizer written by Alex Smola.
This research was supported in part by NSF IIS 9610249 grant.M. E. Shenton was supported by NIMH K02, MH 01110 and R01 MH 50747 grants, R. Kikinis was supported by NIH PO1 CA67165, R01RR11747, P41RR13218 and NSF ERC 9731748 grants.
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Golland, P., Grimson, W.E.L., Shenton, M.E., Kikinis, R. (2001). Deformation Analysis for Shape Based Classification. In: Insana, M.F., Leahy, R.M. (eds) Information Processing in Medical Imaging. IPMI 2001. Lecture Notes in Computer Science, vol 2082. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45729-1_54
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DOI: https://doi.org/10.1007/3-540-45729-1_54
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