This paper presents the MOUGH (Mixture of Uniform and Gaussian Hough) Transform for shape-based object detection and tracking. We show that the edgels of a rigid object at a given orientation are approximately distributed according to a Gaussian Mixture Model (GMMs). A variant of the Generalized Hough Transform is proposed, voting using GMMs and optimized via Expectation-Maximization, that is capable of searching images for a mildly-deformable shape, based on a training dataset of (possibly noisy) images with only crude estimates of scale and centroid of the object in each image. Further modifications are proposed to optimize the algorithm for tracking. The method is able to locate and track objects reliably even against complex backgrounds such as dense moving foliage, and with a moving camera. Experimental results indicate that the algorithm is superior to previously-published variants of the Hough transform and to Active Shape Models in tracking pedestrians from a side view.