# The Shape of Sight: A Homological Framework for Unifying Visual Perception

arXiv: https://arxiv.org/abs/1802.04723 · HTML: https://mlsanity.com/paper/1802.04723/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2018.

## Built on by (most cited first, 5 of 5)

- [Beyond Joint Demosaicking and Denoising: An Image Processing Pipeline for a Pixel-bin Image Sensor](https://mlsanity.com/paper/2104.09398/) (2021)
- [A self-supervised and adversarial approach to hyperspectral demosaicking and RGB reconstruction in surgical imaging](https://mlsanity.com/paper/2407.19282/) (2024)
- [PyNET-QxQ: An Efficient PyNET Variant for QxQ Bayer Pattern Demosaicing in CMOS Image Sensors](https://mlsanity.com/paper/2203.04314/) (2022)
- [How to Best Combine Demosaicing and Denoising?](https://mlsanity.com/paper/2408.06684/) (2024)
- [ISP meets Deep Learning: A Survey on Deep Learning Methods for Image Signal Processing](https://mlsanity.com/paper/2305.11994/) (2023)

## Abstract (arXiv)

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 (Heven) 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 (Hodd) 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.