Regularization Theory and Shape Constraints
Many problems of early vision are ill-posed; to recover unique stable solutions regularization techniques can be used. These techniques lead to meaningful results, provided that solutions belong to suitable compact sets. Often some additional constraints on the shape or the behavior of the pos...
| Main Authors: | , |
|---|---|
| Language: | en_US |
| Published: |
2004
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.3/5513 |
| _version_ | 1826208298669441024 |
|---|---|
| author | Verri, Alessandro Poggio, Tomaso |
| author_facet | Verri, Alessandro Poggio, Tomaso |
| author_sort | Verri, Alessandro |
| collection | MIT |
| description | Many problems of early vision are ill-posed; to recover unique stable solutions regularization techniques can be used. These techniques lead to meaningful results, provided that solutions belong to suitable compact sets. Often some additional constraints on the shape or the behavior of the possible solutions are available. This note discusses which of these constraints can be embedded in the classic theory of regularization and how, in order to improve the quality of the recovered solution. Connections with mathematical programming techniques are also discussed. As a conclusion, regularization of early vision problems may be improved by the use of some constraints on the shape of the solution (such as monotonicity and upper and lower bounds), when available. |
| first_indexed | 2024-09-23T14:03:16Z |
| id | mit-1721.1/5513 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:03:16Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/55132019-04-12T08:25:06Z Regularization Theory and Shape Constraints Verri, Alessandro Poggio, Tomaso regularization early vision constraints mathematicalsprogramming Many problems of early vision are ill-posed; to recover unique stable solutions regularization techniques can be used. These techniques lead to meaningful results, provided that solutions belong to suitable compact sets. Often some additional constraints on the shape or the behavior of the possible solutions are available. This note discusses which of these constraints can be embedded in the classic theory of regularization and how, in order to improve the quality of the recovered solution. Connections with mathematical programming techniques are also discussed. As a conclusion, regularization of early vision problems may be improved by the use of some constraints on the shape of the solution (such as monotonicity and upper and lower bounds), when available. 2004-08-31T18:12:08Z 2004-08-31T18:12:08Z 1986-09-01 AIM-916 http://hdl.handle.net/1721.3/5513 en_US AIM-916 23 p. 2974510 bytes 1134203 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | regularization early vision constraints mathematicalsprogramming Verri, Alessandro Poggio, Tomaso Regularization Theory and Shape Constraints |
| title | Regularization Theory and Shape Constraints |
| title_full | Regularization Theory and Shape Constraints |
| title_fullStr | Regularization Theory and Shape Constraints |
| title_full_unstemmed | Regularization Theory and Shape Constraints |
| title_short | Regularization Theory and Shape Constraints |
| title_sort | regularization theory and shape constraints |
| topic | regularization early vision constraints mathematicalsprogramming |
| url | http://hdl.handle.net/1721.3/5513 |
| work_keys_str_mv | AT verrialessandro regularizationtheoryandshapeconstraints AT poggiotomaso regularizationtheoryandshapeconstraints |