Computational anatomy atlas using multilayer perceptron with Lipschitz regularization

TL;DR

This paper introduces a novel method for creating computational anatomy atlases using multilayer perceptrons with Lipschitz regularization to generate smooth, implicit 3D organ models, demonstrated on human ventricles.

Contribution

It proposes a new approach for atlas generation with implicit representations and Lipschitz regularization, improving smoothness and memory efficiency over traditional explicit models.

Findings

Successful implicit modeling of ventricles

Enhanced smoothness of 3D geometries

Open code and data availability

Abstract

A computational anatomy atlas is a set of internal organ geometries. It is based on data of real patients and complemented with virtual cases by using a some numerical approach. Atlases are in demand in computational physiology, especially in cardiological and neurophysiological applications. Usually, atlas generation uses explicit object representation, such as voxel models or surface meshes. In this paper, we propose a method of atlas generation using an implicit representation of 3D objects. Our approach has two key stages. The first stage converts voxel models of segmented organs to implicit form using the usual multilayer perceptron. This stage smooths the model and reduces memory consumption. The second stage uses a multilayer perceptron with Lipschitz regularization. This neural network provides a smooth transition between implicitly defined 3D geometries. Our work shows examples of models of the left and right human ventricles. All code and data for this work are open.