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 measure 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 information content with binary strings and discuss various bitwise manipulations obtained using logical operators and convolution with non-binary 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.