Uncertainty Quantification for Scale-Space Blob Detection

TL;DR

This paper introduces a novel method for quantifying uncertainty in blob detection within noisy images by representing positional and size uncertainties as regions in a 3D scale space, applicable to astrophysics and deconvolution tasks.

Contribution

It extends blob detection to uncertain images using a total variation-based approach, providing a physically interpretable uncertainty representation in scale space.

Findings

Effective uncertainty regions are obtained from level sets of a total variation minimizer.

The method is demonstrated on astrophysics and deconvolution problems.

Numerical approaches are compared for solving the non-smooth optimization problem.

Abstract

We consider the problem of blob detection for uncertain images, such as images that have to be inferred from noisy measurements. Extending recent work motivated by astronomical applications, we propose an approach that represents the uncertainty in the position and size of a blob by a region in a three-dimensional scale space. Motivated by classic tube methods such as the taut-string algorithm, these regions are obtained from level sets of the minimizer of a total variation functional within a high-dimensional tube. The resulting non-smooth optimization problem is challenging to solve, and we compare various numerical approaches for its solution and relate them to the literature on constrained total variation denoising. Finally, the proposed methodology is illustrated on numerical experiments for deconvolution and models related to astrophysics, where it is demonstrated that it allows to represent the uncertainty in the detected blobs in a precise and physically interpretable way.