### Abstract

Original language | English |
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Title of host publication | Geometric Methods in Computer Vision II : San Diego, CA, July 11, 1993 |

Editors | B.C. Vemuri |

Place of Publication | Bellingham |

Publisher | SPIE |

Pages | 64-74 |

Publication status | Published - 1993 |

### Publication series

Name | Proceedings of SPIE |
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Volume | 2031 |

ISSN (Print) | 0277-786X |

### Fingerprint

### Cite this

*Geometric Methods in Computer Vision II : San Diego, CA, July 11, 1993*(pp. 64-74). (Proceedings of SPIE; Vol. 2031). Bellingham: SPIE.

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*Geometric Methods in Computer Vision II : San Diego, CA, July 11, 1993.*Proceedings of SPIE, vol. 2031, SPIE, Bellingham, pp. 64-74.

**Affine and projective differential geometric invariants of space curves.** / Salden, A.H.; Haar Romenij, ter, B.M.; Viergever, M.A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Affine and projective differential geometric invariants of space curves

AU - Salden, A.H.

AU - Haar Romenij, ter, B.M.

AU - Viergever, M.A.

PY - 1993

Y1 - 1993

N2 - A space curve, e.g., a parabolic line on a 2-dimensional surface in 3-dimensional Euclidean space, induces a plane curve under projective mapping. But 2-dimensional scalar input images of such an object are, normally, spatio-temporal slices through a luminance field caused by the interaction of an external field and that object. Consequently, the question arises how to obtain from those input images a consistent description of the space curve under projective transformations. By means of classical scale space theory, algebraic invariance theory, and classical differential geometry a new method of shape description for space curves from one or multiple views is proposed in terms of complete and irreducible sets of affine and projective differential geometric invariants. The method is based on defining implicitly connections for the observed curves that are highly correlated to the projected space curves. These projected curves are assumed to reveal themselves as coherent structures in the scale space representation of the differential structure of the input images. Several applications to stereo, optic flow, texture analysis, and image matching are briefly indicated.

AB - A space curve, e.g., a parabolic line on a 2-dimensional surface in 3-dimensional Euclidean space, induces a plane curve under projective mapping. But 2-dimensional scalar input images of such an object are, normally, spatio-temporal slices through a luminance field caused by the interaction of an external field and that object. Consequently, the question arises how to obtain from those input images a consistent description of the space curve under projective transformations. By means of classical scale space theory, algebraic invariance theory, and classical differential geometry a new method of shape description for space curves from one or multiple views is proposed in terms of complete and irreducible sets of affine and projective differential geometric invariants. The method is based on defining implicitly connections for the observed curves that are highly correlated to the projected space curves. These projected curves are assumed to reveal themselves as coherent structures in the scale space representation of the differential structure of the input images. Several applications to stereo, optic flow, texture analysis, and image matching are briefly indicated.

M3 - Conference contribution

T3 - Proceedings of SPIE

SP - 64

EP - 74

BT - Geometric Methods in Computer Vision II : San Diego, CA, July 11, 1993

A2 - Vemuri, B.C.

PB - SPIE

CY - Bellingham

ER -