DocumentCode :
1409478
Title :
A Tangent Bundle Theory for Visual Curve Completion
Author :
Ben-Yosef, Guy ; Ben-Shahar, Ohad
Author_Institution :
Dept. of Comput. Sci., Ben-Gurion Univ. of the Negev, Beer-Sheva, Israel
Volume :
34
Issue :
7
fYear :
2012
fDate :
7/1/2012 12:00:00 AM
Firstpage :
1263
Lastpage :
1280
Abstract :
Visual curve completion is a fundamental perceptual mechanism that completes the missing parts (e.g., due to occlusion) between observed contour fragments. Previous research into the shape of completed curves has generally followed an “axiomatic” approach, where desired perceptual/geometrical properties are first defined as axioms, followed by mathematical investigation into curves that satisfy them. However, determining psychophysically such desired properties is difficult and researchers still debate what they should be in the first place. Instead, here we exploit the observation that curve completion is an early visual process to formalize the problem in the unit tangent bundle R2 × S1, which abstracts the primary visual cortex (V1) and facilitates exploration of basic principles from which perceptual properties are later derived rather than imposed. Exploring here the elementary principle of least action in V1, we show how the problem becomes one of finding minimum-length admissible curves in R2 × S1. We formalize the problem in variational terms, we analyze it theoretically, and we formulate practical algorithms for the reconstruction of these completed curves. We then explore their induced visual properties vis-à-vis popular perceptual axioms and show how our theory predicts many perceptual properties reported in the corresponding perceptual literature. Finally, we demonstrate a variety of curve completions and report comparisons to psychophysical data and other completion models.
Keywords :
computational geometry; axiomatic approach; geometrical properties; mathematical investigation; minimum-length admissible curves; observed contour fragments; perceptual mechanism; perceptual properties; primary visual cortex; psychophysical data; tangent bundle theory; visual curve completion; Computational modeling; Context; Mathematical model; Observers; Shape; Visual systems; Visualization; Visual completion; curve completion; inpainting.; tangent bundle;
fLanguage :
English
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publisher :
ieee
ISSN :
0162-8828
Type :
jour
DOI :
10.1109/TPAMI.2011.262
Filename :
6112765
Link To Document :
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