An improved multi-scale autoconvolution transform

Affine invariant feature computing method is an important part of statistical pattern recognition due to the robustness, repeatability, distinguishability and wildly applicability of affine invariant feature. Multi-Scale Autoconvolution (MSA) is a transformation proposed by Esa Rathu which can get complete affine invariant feature. Rathu proved that the linear relationship of any four non-colinear points is affine invariant. The transform is based on a probabilistic interpretation of the image function. The performance of MSA transform is better on image occlusion and noise, but it is sensitive to illumination variation. Aim at this problem, an improved MSA transform is proposed in this paper by computing the map of included angle between N-domain vectors. The proposed method is based on the probabilistic interpretation of N-domain vectors included angle map. N-domain vectors included angle map is built through computing the vectors included angle where the vectors are composed of the image point and its N-domain image points. This is due to that the linear relationship of included angles between vectors composed of any four non-colinear points is an affine invariance. This paper proves the method can be derived in mathematical aspect. The transform values can be used as descriptors for affine invariant pattern classification. The main contribution of this paper is applying the N-domain vectors included angle map while taking the N-domain vector included angle as the probability of the pixel. This computing method adapts the illumination variation better than taking the gray value of the pixel as the probability. We illustrate the performance of improved MSA transform in various object classification tasks. As shown by a comparison with the original MSA transform based descriptors and affine invariant moments, the proposed method appears to be better to cope with illumination variation, image occlusion and image noise.