Exploring the representation capabilities of the HOG descriptor

Object recognition strategies are increasingly based on regional descriptors such as SIFT or HOG at a sparse set of points or on a dense grid of points. Despite their success on databases such as PASCAL and CALTECH, the capability of such a representation in capturing the essential object content of the image is not well-understood: How large is the equivalence class of images sharing the same HOG descriptor? Are all these images from the same object category, and if not, do the non-category images resemble random images which cannot generically arise from imaged scenes? How frequently do images from two categories share the same HOG-based representation? These questions are increasingly more relevant as very large databases such as ImageNet and LabelMe are being developed where the current object recognition strategies show limited success. We examine these questions by introducing the metameric class of moments of HOG which allows for a target image to be morphed into an impostor image sharing the HOG representation of a source image while retaining the initial visual appearance. We report that two distinct images can be made to share the same HOG representation when the overlap between HOG patches is minimal, and the success of this method falls with increasing overlap. This paper is therefore a step in the direction of developing a sampling theorem for representing images by HOG features.