Which geometric model for the curvature of 2-D shape contours?

Which geometric model for the curvature of 2-D shape contours? Spatial Vision , Vol. 20, No. 3, pp. 219 – 264 (2007)  VSP 2007. Also available online - www.brill.nl/sv Which geometric model for the curvature of 2-D shape contours? BIRGITTA DRESP 1 , ∗ , CHIARA SILVESTRI 2 and RENÉ MOTRO 3 1 LMGC, UMR 5508 CNRS, Université Montpellier, II-CC 048-Place Eugène Bataillon, 34095 Montpellier Cedex 5, France 2 Dipartimento Costruzione dell’Architettura, Istituto Universitario Architettura, Venezia, Italy 3 Equipe SLA, Ecole Nationale Supérieure d’Architecture de Montpellier, 179, rue de l’Espérou, 34093 Montpellier Cedex 5, France Received 19 April 2006; accepted 5 October 2006 Abstract —We investigated the geometric representations underlying the perception of 2-D contour curvature. 88 arcs representing lower and upper halves of concentric circles, or halves of ellipses derived mathematically through planar projection by affinity with the circles, a special case of Newton’s transform, were generated to produce curved line segments with negative and positive curvature and varying sagitta (sag) and/or aspect ratio. Aspect ratio is defined here as the ratio between the sagitta and the chord-length of a given arc. The geometric properties of the arcs suggest a regrouping into four structural models. The 88 stimuli were presented in random order to 16 observers http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Spatial Vision (continued as Seeing & Perceiving from 2010) Brill

Which geometric model for the curvature of 2-D shape contours?

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Publisher
BRILL
Copyright
© 2007 Koninklijke Brill NV, Leiden, The Netherlands
ISSN
0169-1015
eISSN
1568-5683
D.O.I.
10.1163/156856807780421165
Publisher site
See Article on Publisher Site

Abstract

Spatial Vision , Vol. 20, No. 3, pp. 219 – 264 (2007)  VSP 2007. Also available online - www.brill.nl/sv Which geometric model for the curvature of 2-D shape contours? BIRGITTA DRESP 1 , ∗ , CHIARA SILVESTRI 2 and RENÉ MOTRO 3 1 LMGC, UMR 5508 CNRS, Université Montpellier, II-CC 048-Place Eugène Bataillon, 34095 Montpellier Cedex 5, France 2 Dipartimento Costruzione dell’Architettura, Istituto Universitario Architettura, Venezia, Italy 3 Equipe SLA, Ecole Nationale Supérieure d’Architecture de Montpellier, 179, rue de l’Espérou, 34093 Montpellier Cedex 5, France Received 19 April 2006; accepted 5 October 2006 Abstract —We investigated the geometric representations underlying the perception of 2-D contour curvature. 88 arcs representing lower and upper halves of concentric circles, or halves of ellipses derived mathematically through planar projection by affinity with the circles, a special case of Newton’s transform, were generated to produce curved line segments with negative and positive curvature and varying sagitta (sag) and/or aspect ratio. Aspect ratio is defined here as the ratio between the sagitta and the chord-length of a given arc. The geometric properties of the arcs suggest a regrouping into four structural models. The 88 stimuli were presented in random order to 16 observers

Journal

Spatial Vision (continued as Seeing & Perceiving from 2010)Brill

Published: Jan 1, 2007

Keywords: GEOMETRIC CUES; PERCEPTUAL LEARNING; SHAPE PERCEPTION; PSYCHOMETRIC FUNCTION; 2-D CONTOUR CURVATURE; LAWS OF SENSATION

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