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Investigations on conic invariants with application to object recognition and motion analysis
Abstract
Understanding the geometry of conics provides a framework for using conics in computer vision. The geometric and algebraic invariants of conics have immediate applications in object recognition. A geometric invariant of three coplanar conic is presented. The algebraic invariants of families of any number of coplanar conics is developed by associating the family of conics with a $\lambda$-matrix. A case is presented where the previously used invariants of two conics fail to discriminate between two families of conics, but the new invariants do discriminate. A distance measure for the invariants is defined and the response of the invariants to synthetic noise is determined. The invariants are used to recognize tracked vehicles in real images. The geometry of conics under the plane plus parallax framework is used to determine epipolar geometry and define the relative 3D conic projective structure. The relative 3D conic projective structure is invariant to camera motion and may be used to conduct motion segmentation. The stability of the epipoles and the relative 3D conic projective structure under synthetic noise is investigated. The invariants of families of coplanar conics is extended to invariants of families of space conics. The representation and geometry of space conics is presented and used to derive the location of the point corresponding to the center of a conic in a second image when the epipolar geometry is known. This location may be used as a correspondence condition or as a location predictor in conic detection.
Subject Area
Computer science
Recommended Citation
Heisterkamp, Douglas R, "Investigations on conic invariants with application to object recognition and motion analysis" (1997). ETD collection for University of Nebraska-Lincoln. AAI9805508.
https://digitalcommons.unl.edu/dissertations/AAI9805508