提出通用滤波器可视化工具，可高效分析多种图像处理任务。
The Filter Echo: A General Tool for Filter Visualisation
- 将扩散回声推广为通用滤波器回声，适用于多种非线性滤波场景。
- 压缩后存储量减少20至100倍，显著提升实用性。
- 适合图像处理研究者与工程师快速理解滤波器行为。
为选择合适滤波器或改进现有滤波器，深入理解其内部机制至关重要。扩散回声（diffusion echoes）作为空间自适应脉冲响应，有助于可视化非线性扩散滤波的效果，但学界关注甚少。原因可能有二：一是该概念最初仅针对扩散滤波，显得应用受限；二是扩散回声存储开销大，难以实用。本文解决上述问题，提出滤波器回声（filter echo）作为扩散回声的泛化形式，应用于自适应平滑之外的任务，如图像修复、渗透过程及变分光流计算。我们构建了一个框架，用于可视化和分析不同任务下各类滤波器的回声。此外，提出一种压缩方法，使滤波器回声的存储需求降低20至100倍。
原文摘要 · Abstract (English)
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.
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