In this study, we address the problem of lesion classification in radiographic scans. We adapt image kernel functions to be applicable for high-resolution, grayscale images to improve the classification accuracy of a support vector machine. We take existing kernel functions inspired by the histogram of oriented gradients, and derive an approximation that can be evaluated in linear time of the image size instead of the original quadratic complexity, enabling highresolution input. Moreover, we propose a new variant inspired by the matched filter, to better utilize intensity space. The new kernels are improved to be scale-invariant and combined with a Gaussian kernel built from handcrafted image features. We introduce a simple multiple kernel learning framework that is robust when one of the kernels, in the current case the image feature kernel, dominates the others. The combined kernel is input to a support vector classifier. We tested our method on lesion classification both in chest radiographs and digital tomosynthesis scans. The radiographs originated from a database including 364 patients with lung nodules and 150 healthy cases. The digital tomosynthesis scans were obtained by simulation using 91 CT scans from the LIDC-IDRI database as input. The new kernels showed good separation capability: ROC AuC was in [0.827, 0.853] for the radiograph database and 0.763 for the tomosynthesis scans. Adding the new kernels to the image-feature-based classifier significantly improved accuracy: AuC increased from 0.958 to 0.967 and from 0.788 to 0.801 for the two applications.