Building Kernels from Binary Strings for Image Matching

In the statistical learning framework, the use of appropriate kernels may be the key for substantial improvement in solving a given problem. In essence, a kernel is a similarity mea- sure between input points satisfying some mathematical requirements and possibly capturing the domain knowledge. In this paper, we focus on kernels for images: we represent the image informa- tion content with binary strings and discuss various bitwise manipulations obtained using logical operators and convolution with nonbinary stencils. In the theoretical contribution of our work, we show that histogram intersection is a Mercer's kernel and we determine the modifications under which a similarity measure based on the notion of Hausdorff distance is also a Mercer's kernel. In both cases, we determine explicitly the mapping from input to feature space. The presented experimental results support the relevance of our analysis for developing effective trainable systems.