Skeletonisation Scale-Spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909525531951104 |
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| author | Gierke, Julia Peter, Pascal |
| author_facet | Gierke, Julia Peter, Pascal |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_03450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Skeletonisation Scale-Spaces Gierke, Julia Peter, Pascal Image and Video Processing 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. |
| title | Skeletonisation Scale-Spaces |
| topic | Image and Video Processing |
| url | https://arxiv.org/abs/2503.03450 |