On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications
This paper investigates the linear degeneracies of projective structure estimation from point and line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) in the case when the scene is a...
| Main Authors: | , |
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| Language: | en_US |
| Published: |
2004
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| Online Access: | http://hdl.handle.net/1721.1/7251 |
| _version_ | 1826206799594782720 |
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| author | Stein, Gideon P. Shashua, Amnon |
| author_facet | Stein, Gideon P. Shashua, Amnon |
| author_sort | Stein, Gideon P. |
| collection | MIT |
| description | This paper investigates the linear degeneracies of projective structure estimation from point and line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) in the case when the scene is a Linear Line Complex (set of lines in space intersecting at a common line) and is 21 when the scene is planar. The LLC situation is only linearly degenerate, and we show that one can obtain a unique solution when the admissibility constraints of the tensor are accounted for. The line configuration described by an LLC, rather than being some obscure case, is in fact quite typical. It includes, as a particular example, the case of a camera moving down a hallway in an office environment or down an urban street. Furthermore, an LLC situation may occur as an artifact such as in direct estimation from spatio-temporal derivatives of image brightness. Therefore, an investigation into degeneracies and their remedy is important also in practice. |
| first_indexed | 2024-09-23T13:38:43Z |
| id | mit-1721.1/7251 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:38:43Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/72512019-04-10T11:52:49Z On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications Stein, Gideon P. Shashua, Amnon This paper investigates the linear degeneracies of projective structure estimation from point and line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) in the case when the scene is a Linear Line Complex (set of lines in space intersecting at a common line) and is 21 when the scene is planar. The LLC situation is only linearly degenerate, and we show that one can obtain a unique solution when the admissibility constraints of the tensor are accounted for. The line configuration described by an LLC, rather than being some obscure case, is in fact quite typical. It includes, as a particular example, the case of a camera moving down a hallway in an office environment or down an urban street. Furthermore, an LLC situation may occur as an artifact such as in direct estimation from spatio-temporal derivatives of image brightness. Therefore, an investigation into degeneracies and their remedy is important also in practice. 2004-10-20T21:04:15Z 2004-10-20T21:04:15Z 1997-12-01 AIM-1620 CBCL-157 http://hdl.handle.net/1721.1/7251 en_US AIM-1620 CBCL-157 15748041 bytes 1226827 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | Stein, Gideon P. Shashua, Amnon On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications |
| title | On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications |
| title_full | On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications |
| title_fullStr | On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications |
| title_full_unstemmed | On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications |
| title_short | On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications |
| title_sort | on degeneracy of linear reconstruction from three views linear line complex and applications |
| url | http://hdl.handle.net/1721.1/7251 |
| work_keys_str_mv | AT steingideonp ondegeneracyoflinearreconstructionfromthreeviewslinearlinecomplexandapplications AT shashuaamnon ondegeneracyoflinearreconstructionfromthreeviewslinearlinecomplexandapplications |