An Optimal Scale for Edge Detection
Many problems in early vision are ill posed. Edge detection is a typical example. This paper applies regularization techniques to the problem of edge detection. We derive an optimal filter for edge detection with a size controlled by the regularization parameter $\\ lambda $ and compare it to t...
| Main Authors: | , |
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| Language: | en_US |
| Published: |
2004
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| Online Access: | http://hdl.handle.net/1721.1/6499 |
| _version_ | 1811082241563951104 |
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| author | Geiger, Davi Poggio, Tomaso |
| author_facet | Geiger, Davi Poggio, Tomaso |
| author_sort | Geiger, Davi |
| collection | MIT |
| description | Many problems in early vision are ill posed. Edge detection is a typical example. This paper applies regularization techniques to the problem of edge detection. We derive an optimal filter for edge detection with a size controlled by the regularization parameter $\\ lambda $ and compare it to the Gaussian filter. A formula relating the signal-to-noise ratio to the parameter $\\lambda $ is derived from regularization analysis for the case of small values of $\\lambda$. We also discuss the method of Generalized Cross Validation for obtaining the optimal filter scale. Finally, we use our framework to explain two perceptual phenomena: coarsely quantized images becoming recognizable by either blurring or adding noise. |
| first_indexed | 2024-09-23T11:59:58Z |
| id | mit-1721.1/6499 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:59:58Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/64992019-04-11T05:42:45Z An Optimal Scale for Edge Detection Geiger, Davi Poggio, Tomaso Many problems in early vision are ill posed. Edge detection is a typical example. This paper applies regularization techniques to the problem of edge detection. We derive an optimal filter for edge detection with a size controlled by the regularization parameter $\\ lambda $ and compare it to the Gaussian filter. A formula relating the signal-to-noise ratio to the parameter $\\lambda $ is derived from regularization analysis for the case of small values of $\\lambda$. We also discuss the method of Generalized Cross Validation for obtaining the optimal filter scale. Finally, we use our framework to explain two perceptual phenomena: coarsely quantized images becoming recognizable by either blurring or adding noise. 2004-10-04T15:13:04Z 2004-10-04T15:13:04Z 1988-09-01 AIM-1078 http://hdl.handle.net/1721.1/6499 en_US AIM-1078 2655175 bytes 1034256 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | Geiger, Davi Poggio, Tomaso An Optimal Scale for Edge Detection |
| title | An Optimal Scale for Edge Detection |
| title_full | An Optimal Scale for Edge Detection |
| title_fullStr | An Optimal Scale for Edge Detection |
| title_full_unstemmed | An Optimal Scale for Edge Detection |
| title_short | An Optimal Scale for Edge Detection |
| title_sort | optimal scale for edge detection |
| url | http://hdl.handle.net/1721.1/6499 |
| work_keys_str_mv | AT geigerdavi anoptimalscaleforedgedetection AT poggiotomaso anoptimalscaleforedgedetection AT geigerdavi optimalscaleforedgedetection AT poggiotomaso optimalscaleforedgedetection |