TY - JOUR
T1 - Boundaries, shading, and border ownership
T2 - A cusp at their interaction
AU - Lawlor, Matthew
AU - Holtmann-Rice, Daniel
AU - Huggins, Patrick
AU - Ben-Shahar, Ohad
AU - Zucker, Steven W.
N1 - Funding Information:
We thank D. DeCarlo for the use of his program, rtsc , which was used to generate several figures; H. Chen and P. Belhumeur for participation in earlier stages of this research; and J. Koenderink and A. van Doorn for conversations. Portions of this material were presented at the following meetings and appeared in their proceedings: IEEE Conference on Computer Vision and Pattern Recognition, 2001; the Eigth International Conference on Computer Vision, 2001; The Fourth International Workshop on Visual Form, 2001; Workshop on Biologically Motivated Computer Vision, 2002; and the Stockholm Workshop on Computational Vision, 2008. They are brought together here for the first time. Research supported by AFOSR, ARO, DARPA, NGA, ONR and NSF. OBS is partially funded by the Psychobiology Young Investigator grant 207-07-08, the Israel Science Foundation (ISF) Grant No. 1245/08 and the generous support of the Frankel fund, the Paul Ivanier center for Robotics Research and the Zlotowski Center for Neuroscience at Ben-Gurion University.
PY - 2009/1/1
Y1 - 2009/1/1
N2 - The association of borders with "figure" rather than "background" provides a topological organizing principle for early vision. Such global influences have recently been shown to have local effects, with neuronal activity modulated by stimulus properties from well outside the classical receptive field. We extend the theoretical analysis of such phenomena by developing the geometry of interaction between shading, boundaries, and boundary ownership for smooth surfaces. The purely exterior edges of smooth objects enjoy a fold-type relationship between shading and boundary, due to foreshortening, while the background is cut off transversely. However, at cusp points in the image mapping the exterior boundary ends abruptly. Since such singular points are notoriously unstable, we conjecture that this process is regularized by a natural quantization of suggestive contours due to physiological boundary-detection mechanisms. The result extends a theorem about how contours must end to one that characterizes surface (Gaussian) curvature in the neighborhood of where they appear to end. Apparent contours and their interaction with local shading thus provide important monocular shape cues.
AB - The association of borders with "figure" rather than "background" provides a topological organizing principle for early vision. Such global influences have recently been shown to have local effects, with neuronal activity modulated by stimulus properties from well outside the classical receptive field. We extend the theoretical analysis of such phenomena by developing the geometry of interaction between shading, boundaries, and boundary ownership for smooth surfaces. The purely exterior edges of smooth objects enjoy a fold-type relationship between shading and boundary, due to foreshortening, while the background is cut off transversely. However, at cusp points in the image mapping the exterior boundary ends abruptly. Since such singular points are notoriously unstable, we conjecture that this process is regularized by a natural quantization of suggestive contours due to physiological boundary-detection mechanisms. The result extends a theorem about how contours must end to one that characterizes surface (Gaussian) curvature in the neighborhood of where they appear to end. Apparent contours and their interaction with local shading thus provide important monocular shape cues.
KW - Co-circularity
KW - Cusp
KW - Differential geometry
KW - Edge analysis
KW - Long-range horizontal connections
KW - Shading analysis
UR - http://www.scopus.com/inward/record.url?scp=70149106571&partnerID=8YFLogxK
U2 - 10.1016/j.jphysparis.2009.05.005
DO - 10.1016/j.jphysparis.2009.05.005
M3 - Article
AN - SCOPUS:70149106571
SN - 0928-4257
VL - 103
SP - 18
EP - 36
JO - Journal of Physiology Paris
JF - Journal of Physiology Paris
IS - 1-2
ER -