The Filter Echo: A General Tool for Filter Visualisation

Fuente: arXiv
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Main Authors: Gaa, Daniel, Weickert, Joachim, Farag, Iva, Çiçek, Özgün
Format: Preprint
Published: 2025
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author Gaa, Daniel
Weickert, Joachim
Farag, Iva
Çiçek, Özgün
author_facet Gaa, Daniel
Weickert, Joachim
Farag, Iva
Çiçek, Özgün
contents To select suitable filters for a task or to improve existing filters, a deep understanding of their inner workings is vital. Diffusion echoes, which are space-adaptive impulse responses, are useful to visualise the effect of nonlinear diffusion filters. However, they have received little attention in the literature. There may be two reasons for this: Firstly, the concept was introduced specifically for diffusion filters, which might appear too limited. Secondly, diffusion echoes have large storage requirements, which restricts their practicality. This work addresses both problems. We introduce the filter echo as a generalisation of the diffusion echo and use it for applications beyond adaptive smoothing, such as image inpainting, osmosis, and variational optic flow computation. We provide a framework to visualise and inspect echoes from various filters with different applications. Furthermore, we propose a compression approach for filter echoes, which reduces storage requirements by a factor of 20 to 100.
format Preprint
id arxiv_https___arxiv_org_abs_2509_11932
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Filter Echo: A General Tool for Filter Visualisation
Gaa, Daniel
Weickert, Joachim
Farag, Iva
Çiçek, Özgün
Image and Video Processing
To select suitable filters for a task or to improve existing filters, a deep understanding of their inner workings is vital. Diffusion echoes, which are space-adaptive impulse responses, are useful to visualise the effect of nonlinear diffusion filters. However, they have received little attention in the literature. There may be two reasons for this: Firstly, the concept was introduced specifically for diffusion filters, which might appear too limited. Secondly, diffusion echoes have large storage requirements, which restricts their practicality. This work addresses both problems. We introduce the filter echo as a generalisation of the diffusion echo and use it for applications beyond adaptive smoothing, such as image inpainting, osmosis, and variational optic flow computation. We provide a framework to visualise and inspect echoes from various filters with different applications. Furthermore, we propose a compression approach for filter echoes, which reduces storage requirements by a factor of 20 to 100.
title The Filter Echo: A General Tool for Filter Visualisation
topic Image and Video Processing
url https://arxiv.org/abs/2509.11932