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arXiv Computer Vision By Faian Conrad

Existence of Minimizers for the Gaussian Mumford-Shah Model via Covariance Floors on the Value Distribution

Read the original on arXiv Computer Vision →

The paper investigates the Gaussian Mumford–Shah model, which segments images by minimizing a Gaussian negative log‑likelihood plus a perimeter penalty. It shows that the energy can become unbounded below if a region’s covariance degenerates, but imposing a quantitative covariance floor (or equivalently a uniform Hölder continuity condition on the histogram’s one‑dimensional marginals) guarantees a lower bound and ensures the existence of a minimizer. The authors argue that such covariance floors are generic for noisy images, cannot be scale‑independent, and use the theory to prove convergence of practical regularized models and numerical methods.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Computer Vision.

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