The complexity of recognizing polyhedral scenes

Kirousis, LM; Papadimitriou, CH

dc.contributor.author	Kirousis, LM	en
dc.contributor.author	Papadimitriou, CH	en
dc.date.accessioned	2014-03-01T01:07:17Z
dc.date.available	2014-03-01T01:07:17Z
dc.date.issued	1988	en
dc.identifier.issn	0022-0000	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9905
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-38249027274&partnerID=40&md5=640ce9b7bbdcbc79f46898d3b72e1c31	en
dc.subject.classification	Computer Science, Hardware & Architecture	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.title	The complexity of recognizing polyhedral scenes	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1988	en
heal.abstract	Given a drawing of straight lines on the plane, we wish to decide whether it is the projection of the visible part of a set of opaque polyhedra. This is the fundamental algorithmic problem that underlies much of the research in computer vision. Although there are extensive literature and reports on empirically successful algorithms for this problem and its many extensions, there has been no definite result concerning its complexity. In this paper we show that, rather surprisingly, this problem is NP-complete, and therefore there is probably no polynomial-time algorithm for solving it. This is true even in the relatively simple case of trihedral scenes (no four planes share a point) without shadows and cracks. Despite this negative result, we present positive results for the important special case of orthohedral scenes (all planes are normal to one of the three axes). © 1988.	en
heal.publisher	ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS	en
heal.journalName	Journal of Computer and System Sciences	en
dc.identifier.isi	ISI:A1988Q490700003	en
dc.identifier.volume	37	en
dc.identifier.issue	1	en
dc.identifier.spage	14	en
dc.identifier.epage	38	en