Computer-aided diagnosis of medical images has emerged as an important tool to objectively improve the performance, accuracy and consistency for clinical workflow. To computerize the medical image diagnostic recognition problem, there are three fundamental problems: where to look (i.e., where is the region of interest from the whole image/volume), image feature description/encoding, and similarity metrics for classification or matching. In this paper, we exploit the motivation, implementation and performance evaluation of task-driven iterative, discriminative image patch mining; covariance matrix based descriptor via intensity, gradient and spatial layout; and log-Euclidean distance kernel for support vector machine, to address these three aspects respectively. To cope with often visually ambiguous image patterns for the region of interest in medical diagnosis, discovery of multilabel selective discriminative patches is desired. Covariance of several image statistics summarizes their second order interactions within an image patch and is proved as an effective image descriptor, with low dimensionality compared with joint statistics and fast computation regardless of the patch size. We extensively evaluate two extended Gaussian kernels using affine-invariant Riemannian metric or log-Euclidean metric with support vector machines (SVM), on two medical image classification problems of degenerative disc disease (DDD) detection on cortical shell unwrapped CT maps and colitis detection on CT key images. The proposed approach is validated with promising quantitative results on these challenging tasks. Our experimental findings and discussion also unveil some interesting insights on the covariance feature composition with or without spatial layout for classification and retrieval, and different kernel constructions for SVM. This will also shed some light on future work using covariance feature and kernel classification for medical image analysis.