Optimization in differentiable manifolds in order to determine the method of construction of prehistoric wall paintings

Arabadjis, D; Rousopoulos, P; Papaodysseus, C; Exarhos, M; Panagopoulos, M; Papazoglou-Manioudaki, L

dc.contributor.author	Arabadjis, D	en
dc.contributor.author	Rousopoulos, P	en
dc.contributor.author	Papaodysseus, C	en
dc.contributor.author	Exarhos, M	en
dc.contributor.author	Panagopoulos, M	en
dc.contributor.author	Papazoglou-Manioudaki, L	en
dc.date.accessioned	2014-03-01T01:36:35Z
dc.date.available	2014-03-01T01:36:35Z
dc.date.issued	2011	en
dc.identifier.issn	0162-8828	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21348
dc.subject	fitting prototype curves to drawn borders	en
dc.subject	geometric guides in prehistoric wall paintings	en
dc.subject	minimal parameters set for curve description	en
dc.subject	optimization in differentiable manifolds	en
dc.subject	pattern recognition in paintings	en
dc.subject	Rotation and translation invariant curve fitting	en
dc.subject.classification	Computer Science, Artificial Intelligence	en
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.other	fitting prototype curves to drawn borders	en
dc.subject.other	Functional forms	en
dc.subject.other	General methodologies	en
dc.subject.other	Geometric entities	en
dc.subject.other	Geometric form	en
dc.subject.other	geometric guides in prehistoric wall paintings	en
dc.subject.other	Low average error	en
dc.subject.other	minimal parameters set for curve description	en
dc.subject.other	Wall paintings	en
dc.subject.other	Geometry	en
dc.subject.other	Optimization	en
dc.subject.other	Painting	en
dc.subject.other	Pattern recognition	en
dc.subject.other	Curve fitting	en
dc.title	Optimization in differentiable manifolds in order to determine the method of construction of prehistoric wall paintings	en
heal.type	journalArticle	en
heal.identifier.primary	10.1109/TPAMI.2011.65	en
heal.identifier.secondary	5740922	en
heal.identifier.secondary	http://dx.doi.org/10.1109/TPAMI.2011.65	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	In this paper, a general methodology is introduced for the determination of potential prototype curves used for the drawing of prehistoric wall paintings. The approach includes 1) preprocessing of the wall-paintings contours to properly partition them, according to their curvature, 2) choice of prototype curves families, 3) analysis and optimization in 4-manifold for a first estimation of the form of these prototypes, 4) clustering of the contour parts and the prototypes to determine a minimal number of potential guides, and 5) further optimization in 4-manifold, applied to each cluster separately, in order to determine the exact functional form of the potential guides, together with the corresponding drawn contour parts. The methodology introduced simultaneously deals with two problems: 1) the arbitrariness in data-points orientation and 2) the determination of one proper form for a prototype curve that optimally fits the corresponding contour data. Arbitrariness in orientation has been dealt with a novel curvature based error, while the proper forms of curve prototypes have been exhaustively determined by embedding curvature deformations of the prototypes into 4-manifolds. Application of this methodology to celebrated wall paintings excavated at Tyrins, Greece, and the Greek island of Thera manifests that it is highly probable that these wall paintings were drawn by means of geometric guides that correspond to linear spirals and hyperbolae. These geometric forms fit the drawings' lines with an exceptionally low average error, less than 0.39 mm. Hence, the approach suggests the existence of accurate realizations of complicated geometric entities more than 1,000 years before their axiomatic formulation in the Classical Ages. © 2011 IEEE.	en
heal.publisher	IEEE COMPUTER SOC	en
heal.journalName	IEEE Transactions on Pattern Analysis and Machine Intelligence	en
dc.identifier.doi	10.1109/TPAMI.2011.65	en
dc.identifier.isi	ISI:000294910000009	en
dc.identifier.volume	33	en
dc.identifier.issue	11	en
dc.identifier.spage	2229	en
dc.identifier.epage	2244	en