Sub-Riemannian Snakes on the Projective Line Bundle with Applications to Segmentation of SEM Images

TL;DR

This paper introduces a computationally efficient snake model on the projective line bundle for image segmentation, using a novel symmetric, cusp-free pseudo-distance that improves over previous models.

Contribution

It presents a new pseudo-distance on the projective line bundle that is symmetric, cusp-free, and satisfies the triangle inequality on a large set, enabling efficient geodesic tracking.

Findings

Effective segmentation of SEM images demonstrated

Pseudo-distance is symmetric and cusp-free, unlike previous models

Method reduces computational cost by computing distance maps only where needed

Abstract

Geodesic tracking on the projective line bundle $\R^2 \times P^1 $ has many uses, including the segmentation of objects in images. However, global tracking requires expensive distance map computations. We provide a practical solution to this problem by introducing a snake model on $\R^2 \times P^1$, where we only compute the distance map where needed. Our method introduces a geometric criterion for switching between fast spatial snakes and computing minimizing geodesics of a new projective line bundle model. The new pseudo-distance underlying our geometric model is both symmetric and cusp-free, in contrast to previous geodesic sub-Riemannian models on $\R^2 \times P^1$. Our pseudo-distance satisfies the triangle inequality on a large set that we characterize, and includes a connected-component-informed cost function, which is highly advantageous in applications. Experiments on Scanning Electron Microscopy (SEM) images demonstrate our method's robust, automatic segmentation of overlapping electronic structures.