Count on me: learning to count on a single image

Individuating and locating repetitive patterns in still images is a fundamental task in image processing, typically achieved by means of correlation strategies. In this paper we provide a solid solution to this task using a differential geometry approach, operating on Lie algebra, and exploiting a mixture of templates. The proposed method asks the user to locate few instances of the target patterns (seeds), that become visual templates used to explore the image. We propose an iterative algorithm to locate patches similar to the seeds working in three steps: first clustering the detected patches to generate templates of different classes, then looking for the affine transformations, living on a Lie algebra, that best link the templates and the detected patches, and finally detecting new patches with a convolutional strategy. The process ends when no new patches are found. We will show how our method is able to process heterogeneous unstructured images with multiple visual motifs and extremely crowded scenarios with high precision and recall, outperforming all the state of the art methods.