Optimum kernel function design from scale space features for object detection

Scale-space representation of an image is a significant way to generate features for classification. However, for a specific classification task, the entire scale-space may not be useful; only a part of it is typically effective. Toward this end, we design a data dependent classification kernel function, which is a weighted mixture of kernels defined on individual scales. In order to choose the optimum weights in the mixture kernel function (MKF), we propose an optimization criterion that leads to the minimization of Raleigh quotient in the positive orthant. This optimization is in general a difficult, non-convex, quadratically constrained quadratic programming. Utilizing a property of ratio of functions, we reduce the aforementioned optimization into a novel binary search, which is essentially a series of quadratic programming. As an application we choose a significant detection problem in oil sands mining called large lump detection from videos. Employing support vector classifier with our MKF yields encouraging results on these difficult-to-process images and compares favorably against the kernel alignment method as well as Fisher criterion adopted in.