Combining Geometric and Topological Information for Boundary Estimation

TL;DR

This paper introduces a novel boundary estimation method that combines geometric and topological information, improving initialization and accuracy for complex object structures in images.

Contribution

It presents a topologically-guided initialization technique for active contour models, enhancing boundary estimation for objects with complex topologies.

Findings

Improved boundary estimation accuracy in complex topologies

Effective initialization reduces sensitivity of active contours

Successful application to real-world medical images

Abstract

A fundamental problem in computer vision is boundary estimation, where the goal is to delineate the boundary of objects in an image. In this paper, we propose a method which jointly incorporates geometric and topological information within an image to simultaneously estimate boundaries for objects within images with more complex topologies. We use a topological clustering-based method to assist initialization of the Bayesian active contour model. This combines pixel clustering, boundary smoothness, and potential prior shape information to produce an estimated object boundary. Active contour methods are knownto be extremely sensitive to algorithm initialization, relying on the user to provide a reasonable starting curve to the algorithm. In the presence of images featuring objects with complex topological structures, such as objects with holes or multiple objects, the user must initialize separate curves for each boundary of interest. Our proposed topologically-guided method can provide an interpretable, smart initialization in these settings, freeing up the user from potential pitfalls associated with objects of complex topological structure. We provide a detailed simulation study comparing our initialization to boundary estimates obtained from standard segmentation algorithms. The method is demonstrated on artificial image datasets from computer vision, as well as real-world applications to skin lesion and neural cellular images, for which multiple topological features can be identified.