A Computer Vision Problem in Flatland

SIAM Journal on Applied Algebra and Geometry 2026

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Authors: Sameer Agarwal, Erin Connelly, Annalisa Crannell, Timothy Duff, Rekha R. Thomas
DOI: 10.1137/25m1727552
Cited by: 0
References: 21

Abstract

Abstract. When is it possible to project two sets of labeled points of equal cardinality lying in a pair of projective planes to the same image on a projective line? We give a complete answer to this question, obtaining the following results. We first show that such a pair of projections exist if and only if the two point sets are themselves images of a common point set in projective space. Moreover, we find that for generic pairs of point sets, a common projection exists if and only if their cardinality is at most seven. In these cases, we give an explicit description of the loci of projection centers that enable a common image.

Fields of Study & Subjects

Medical Image Segmentation Techniques Advanced Vision and Imaging Advanced Image and Video Retrieval Techniques

Publication details

Journal / source
SIAM Journal on Applied Algebra and Geometry
Volume
10
Issue
1
Pages
14–45
Publication date
2 January 2026
Language
EN