提出骨架尺度空间，让形状简化更稳定且可分级。
Skeletonisation Scale-Spaces
- 通过逐步剪枝骨架实现形状的层次化简化
- 新方法满足尺度空间特性，对噪声更鲁棒
- 适合需要稳定形状描述的应用如医学图像分析
中轴变换是形状识别中的经典工具，它用包含所有最大内切圆中心的骨架来等价描述二值对象。尽管该描述在诸多应用中有用，但对噪声敏感：边界微小扰动可能导致骨架大幅扩展。剪枝可缓解此问题，通过移除不必要部分来净化骨架。本文将此原则推广为骨架稀疏化：我们证明，依次移除骨架部分可实现形状的分层简化，且符合尺度空间特性。为此，我们构建了连续与离散理论框架，涵盖结构化陈述与简化性质，并保证不变性。文中展示了两种概念验证应用：骨架剪枝与形状压缩。
原文摘要 · Abstract (English)
The medial axis transform is a well-known tool for shape recognition. Instead of the object contour, it equivalently describes a binary object in terms of a skeleton containing all centres of maximal inscribed discs. While this shape descriptor is useful for many applications, it is also sensitive to noise: Small boundary perturbations can result in large unwanted expansions of the skeleton. Pruning offers a remedy by removing unwanted skeleton parts. In our contribution, we generalise this principle to skeleton sparsification: We show that subsequently removing parts of the skeleton simplifies the associated shape in a hierarchical manner that obeys scale-space properties. To this end, we provide both a continuous and discrete theory that incorporates architectural and simplification statements as well as invariances. We illustrate how our skeletonisation scale-spaces can be employed for practical applications with two proof-of-concept implementations for pruning and compression.
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