---
title: "The Stereo Matching Problem From the Topological Viewpoint"
authors:
  - "A. Peter Blicher"
doi: ""
url: "https://ijcai.org/proceedings/1983/242"
pdf: "https://ijcai.org/proceedings/1983/0242.pdf"
venue: "Proceedings of the Eighth International Joint Conference on Artificial Intelligence"
year: 1983
pages: "1046-1048"
track: "Vision"
keywords:
---

# The Stereo Matching Problem From the Topological Viewpoint

A. Peter Blicher

*Proceedings of the Eighth International Joint Conference on Artificial Intelligence*, pages 1046-1048.

## Abstract

A unifying abstract mathematical structure is presented for a number of vision problems, notably stereo, motion stereo, optic flow, and matching. Ideas from modern di!Terential topology are presented and applied to the general matching problem, a common approach to stereo matching, defined as follows. Given 2 picture functions F1 , F2 : M 2 -+ R", one finds regions K 1 ,K2 C M 2 and a 1-1 matching function g": K 1 -+ K 2 such that Ft = F2 o g". It is shown that generically for monochromepictures (n = 1) there is a large infinity of solutions, but for 2 or more colors (n2) the solution is unique. The paper is offered partially in the hope of introducingvision workers to this type of mathematics and persuading them of its utility.