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

TL;DR

This paper introduces a novel method for optimizing the metric in the LDDMM framework by integrating it with machine learning, specifically kernel methods, to improve registration and classification in biomedical imaging.

Contribution

It presents a new approach to learn the Riemannian metric on diffeomorphisms within a machine learning framework, enhancing registration and predictive modeling in medical imaging.

Findings

Improved registration quality on synthetic data.

Enhanced classification accuracy on schizophrenia subcortical shapes.

Significant ROC AUC improvement in schizophrenia-control prediction.

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.