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| Format: | Preprint |
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2018
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| Online Access: | https://arxiv.org/abs/1802.04723 |
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| _version_ | 1866917098776690688 |
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| author | Li, Xin |
| author_facet | Li, Xin |
| contents | Visual perception, the brain's construction of a stable world from sensory data, faces several long-standing, fundamental challenges. While often studied separately, these problems have resisted a single, unifying computational framework. In this perspective, we propose a homological framework for visual perception. We argue that the brain's latent representations are governed by their topological parity. This parity interpretation functionally separates homological structures into two distinct classes: 1) Even-dimensional homology ($H_{even}$) acts as static, integrative scaffolds. These structures bind context and content into ``wholes'' or ``what'', serving as the stable, resonant cavities for perceptual objects; 2) Odd-dimensional homology ($H_{odd}$) acts as dynamic, recurrent flows. These structures represent paths, transformations, and self-sustaining ``traces'' or ``where'' that navigate the perceptual landscape. This scaffold-and-flow model is supported by the ventral-dorsal pathway separation and provides a unified solution to three core problems in visual perception. Homological parity hypothesis recasts visual perception not as a linear computation, but as a dynamic interaction between stable, integrative structures and the recurrent, self-sustaining flows that run on them. This perspective offers a new mathematical foundation for linking neural dynamics to perception and cognition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1802_04723 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The Shape of Sight: A Homological Framework for Unifying Visual Perception Li, Xin Computer Vision and Pattern Recognition Visual perception, the brain's construction of a stable world from sensory data, faces several long-standing, fundamental challenges. While often studied separately, these problems have resisted a single, unifying computational framework. In this perspective, we propose a homological framework for visual perception. We argue that the brain's latent representations are governed by their topological parity. This parity interpretation functionally separates homological structures into two distinct classes: 1) Even-dimensional homology ($H_{even}$) acts as static, integrative scaffolds. These structures bind context and content into ``wholes'' or ``what'', serving as the stable, resonant cavities for perceptual objects; 2) Odd-dimensional homology ($H_{odd}$) acts as dynamic, recurrent flows. These structures represent paths, transformations, and self-sustaining ``traces'' or ``where'' that navigate the perceptual landscape. This scaffold-and-flow model is supported by the ventral-dorsal pathway separation and provides a unified solution to three core problems in visual perception. Homological parity hypothesis recasts visual perception not as a linear computation, but as a dynamic interaction between stable, integrative structures and the recurrent, self-sustaining flows that run on them. This perspective offers a new mathematical foundation for linking neural dynamics to perception and cognition. |
| title | The Shape of Sight: A Homological Framework for Unifying Visual Perception |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/1802.04723 |