Uncertainty Quantification for Scale-Space Blob Detection

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 th...

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Bibliographic Details
Published in:Journal of mathematical imaging and vision Vol. 66; no. 4; pp. 697 - 717
Main Authors: Parzer, Fabian, Kirisits, Clemens, Scherzer, Otmar
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2024
Springer Nature B.V
Subjects:
Applications of Mathematics
Computer Science
Computer vision
Convex analysis
Image analysis
Image Processing and Computer Vision
Mathematical Methods in Physics
Optimization
Signal,Image and Speech Processing
Uncertainty
Uncertainty quantification
Scale space
Total variation regularization
Blob detection
ISSN:0924-9907, 1573-7683
Online Access:Get full text
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Summary: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.
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ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-024-01194-x