Affine transforms between image space and color space for invariant local descriptors

Accurate local region description is a keypoint in many applications and has been the topic of lots of recent papers. Starting from the very accurate SIFT, most of the approaches exploit the local gradient information that suffers from several drawbacks. First it is unstable in case of severe geometry distortions, second it cannot be easily summarized in a compact way and third it is not designed to account vectorial color information. In this paper, we propose an alternative by designing compact descriptors that account both the colors present in the region and their spatial distribution. Each pixel being characterized by five coordinates, two in the image space and three in the color space, we try to evaluate affine transforms that allow to go from the spatial coordinates to the color coordinates and inversely. Obviously such kind of transform does not exist but we show that after applying it to the original coordinates, the resulted positions are both discriminative and invariant to many acquisition conditions. Hence, depending on the original space (image or color) and the destination space (color or image), we design different complementary descriptors. Their discriminative power and invariance properties are assessed and compared with the best color descriptors in the context of region matching and object classification.