{"type":"ScholarlyArticle","title":"The Stereo Matching Problem From the Topological Viewpoint","authors":[{"name":"A. Peter Blicher","slug":"a-peter-blicher","given":"A. Peter","family":"Blicher","affiliation":""}],"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.","doi":null,"url":"https://ijcai.org/proceedings/1983/242","pdf":"https://ijcai.org/proceedings/1983/0242.pdf","markdown":"https://ijcai.org/proceedings/1983/242.md","bibtex":"https://ijcai.org/proceedings/1983/bibtex/242","volume":{"slug":"1983","title":"Proceedings of the Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1983","url":"https://ijcai.org/proceedings/1983/","year":1983,"location":"Karlsruhe, West Germany","dates":"","editors":"Alan Bundy","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Vision","track":"Vision","number":242,"pages":{"first":1046,"last":1048},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}