Zero-Crossings on Lines of Curvature
We investigate the relations between the structure of the image and events in the geometry of the underlying surface. We introduce some elementary differential geometry and use it to define a coordinate system on the object based on the lines of curvature. Using this coordinate system we can...
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| Language: | en_US |
| Published: |
2004
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| Online Access: | http://hdl.handle.net/1721.1/6388 |
| _version_ | 1811088364847235072 |
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| author | Yuille, A. |
| author_facet | Yuille, A. |
| author_sort | Yuille, A. |
| collection | MIT |
| description | We investigate the relations between the structure of the image and events in the geometry of the underlying surface. We introduce some elementary differential geometry and use it to define a coordinate system on the object based on the lines of curvature. Using this coordinate system we can prove results connecting the extrema, ridges and zero-crossings in the image to geometrical features of the object. We show that extrema of the image typically correspond to points on the surface with zero Gaussian curvature and that parabolic lines often give rise to ridges, or valleys, in the image intensity. We show that directional zero-crossings of the image along the lines of curvature generally correspond to extrema of curvature along such lines. |
| first_indexed | 2024-09-23T14:01:02Z |
| id | mit-1721.1/6388 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:01:02Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/63882019-04-12T08:30:30Z Zero-Crossings on Lines of Curvature Yuille, A. We investigate the relations between the structure of the image and events in the geometry of the underlying surface. We introduce some elementary differential geometry and use it to define a coordinate system on the object based on the lines of curvature. Using this coordinate system we can prove results connecting the extrema, ridges and zero-crossings in the image to geometrical features of the object. We show that extrema of the image typically correspond to points on the surface with zero Gaussian curvature and that parabolic lines often give rise to ridges, or valleys, in the image intensity. We show that directional zero-crossings of the image along the lines of curvature generally correspond to extrema of curvature along such lines. 2004-10-04T14:54:40Z 2004-10-04T14:54:40Z 1984-12-01 AIM-718 http://hdl.handle.net/1721.1/6388 en_US AIM-718 2749048 bytes 2139271 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | Yuille, A. Zero-Crossings on Lines of Curvature |
| title | Zero-Crossings on Lines of Curvature |
| title_full | Zero-Crossings on Lines of Curvature |
| title_fullStr | Zero-Crossings on Lines of Curvature |
| title_full_unstemmed | Zero-Crossings on Lines of Curvature |
| title_short | Zero-Crossings on Lines of Curvature |
| title_sort | zero crossings on lines of curvature |
| url | http://hdl.handle.net/1721.1/6388 |
| work_keys_str_mv | AT yuillea zerocrossingsonlinesofcurvature |