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arXiv · 1808.04439

Image Registration and Predictive Modeling: Learning the Metric on the Space of Diffeomorphisms

Ayagoz Mussabayeva·Alexey Kroshnin·Anvar Kurmukov·Yulia Dodonova·Li Shen·Shan Cong·Lei Wang·Boris A. Gutman
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Abstract

We present a method for metric optimization in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, by treating the induced Riemannian metric on the space of diffeomorphisms as a kernel in a machine learning context. For simplicity, we choose the kernel Fischer Linear Discriminant Analysis (KLDA) as the framework. Optimizing the kernel parameters in an Expectation-Maximization framework, we define model fidelity via the hinge loss of the decision function. The resulting algorithm optimizes the parameters of the LDDMM norm-inducing differential operator as a solution to a group-wise registration and classification problem. In practice, this may lead to a biology-aware registration, focusing its attention on the predictive task at hand such as identifying the effects of disease. We first tested our algorithm on a synthetic dataset, showing that our parameter selection improves registration quality and classification accuracy. We then tested the algorithm on 3D subcortical shapes from the Schizophrenia cohort Schizconnect. Our Schizpohrenia-Control predictive model showed significant improvement in ROC AUC compared to baseline parameters.

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Ayagoz Mussabayeva, Alexey Kroshnin, Anvar Kurmukov, Yulia Dodonova, Li Shen, Shan Cong, Lei Wang, Boris A. Gutman. 2018-08-10. Image Registration and Predictive Modeling: Learning the Metric on the Space of Diffeomorphisms. https://arxiv.org/abs/1808.04439

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