Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment
Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of a...
| Main Authors: | , , |
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| Language: | en_US |
| Published: |
2004
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| Online Access: | http://hdl.handle.net/1721.1/6557 |
| _version_ | 1826202280030896128 |
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| author | Grimson W. Eric L. Huttenlocher, Daniel P. Jacobs, David W. |
| author_facet | Grimson W. Eric L. Huttenlocher, Daniel P. Jacobs, David W. |
| author_sort | Grimson W. Eric L. |
| collection | MIT |
| description | Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods. |
| first_indexed | 2024-09-23T12:05:01Z |
| id | mit-1721.1/6557 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:05:01Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/65572019-04-11T02:52:21Z Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment Grimson W. Eric L. Huttenlocher, Daniel P. Jacobs, David W. Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods. 2004-10-04T15:31:21Z 2004-10-04T15:31:21Z 1991-08-01 AIM-1250 http://hdl.handle.net/1721.1/6557 en_US AIM-1250 5692320 bytes 2225833 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | Grimson W. Eric L. Huttenlocher, Daniel P. Jacobs, David W. Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment |
| title | Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment |
| title_full | Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment |
| title_fullStr | Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment |
| title_full_unstemmed | Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment |
| title_short | Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment |
| title_sort | affine matching with bounded sensor error a study of geometric hashing and alignment |
| url | http://hdl.handle.net/1721.1/6557 |
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