Discrete texture traces: Topological representation of geometric context

Modeling representations of image patches that are quasi-invariant to spatial deformations is an important problem in computer vision. In this paper, we propose a novel concept, the texture trace, that allows sparse patch representations which are quasi-invariant to smooth deformations and robust against occlusions. We first propose a continuous domain model, the profile trace, which is a function only of the topological properties of an image and is by construction invariant to any homeomorphic transformation of the domain. We analyze its theoretical properties and then derive a discrete-domain approximation, the Discrete Texture Trace (DTT). DTTs are designed to be computationally practical and shown by a set of controlled experiments to be quasi-invariant to smooth spatial deformations as well as common image perturbations. We then show how DTTs can be naturally adapted to the incremental tracking problem, yielding highly precise results on par with the state of the art on challenging real data without using heavy machine learning tools. Indeed, we show that with even just using one image at the start of a sequence (i.e. no incremental updating), our method already outperforms four of six state of the art methods of the recent literature on challenging sequences.