Similarity Limits of Orientation Changes in Affine Transformations With Applications to Planar Pattern Matching

Juan Zha, Tian Xie


Besides descriptor designing, factoring out the categorical effects of affine transformations is also an effective way to match features. This paper proposed and demonstrated a hypothesis that any coplanar orientations have limited geometrical changes when observed in the camera screen under given ranges of 3D affine transformations. Confirmatory experiments are accomplished by Matlab simulations focusing on specific influences of 3D affine transformations on similarity biases between concerned orientation changes. Statistical analyses and results show that rotations about plane axes mainly affect the geometrical biases of orientation changes. A set of fit limits standing for the biggest influences of most affine transformations in specified ranges are numerically approximated by total sample space distribution and experimental extreme values. We use these Similarity Limits of Orientation Changes(SLOC) as optimization constraints in matching problems, and an application example of planar pattern matching is given. The effectiveness and efficiency of SLOC are proved by the experimental results in Mikolajczyk and HPatches testbed.

affine transformation; geometrical orientations; hypothesis testing; planar pattern matching; similarity bias

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DOI: 10.5566/ias.2734

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Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)