Robust topological features for deformation invariant image matching

Abstract

Local photometric descriptors are a crucial low level component of numerous computer vision algorithms. In practice, these descriptors are constructed to be invariant to a class of transformations. However, the development of a descriptor that is simultaneously robust to noise and invariant under general deformation has proven difficult. In this paper, we introduce the Topological-Attributed Relational Graph (T-ARG), a new local photometric descriptor constructed from homology that is provably invariant to locally bounded deformation. This new robust topological descriptor is backed by a formal mathematical framework. We apply T-ARG to a set of benchmark images to evaluate its performance. Results indicate that T-ARG significantly outperforms traditional descriptors for noisy, deforming images.

Automatic non-rigid image registration based on deformation invariant feature and local geometric constraint

“…For instance, the SIFT descriptor [8] and many of its variants [9][10][11] have proven to be invariant under affine transformations. Unfortunately, this class of local descriptors is unable to keep invariant under non-rigid transformation, such as an animal moving its body or a cloth being folded [12]. An interesting exception is [13], that treat an intensity image as a surface embedded in 3D space and using a Geodesic Intensity Histogram (GIH) as a feature point descriptor.…”