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The fast radial symmetry (FRS) transform has been very popular for detecting interest points based on local radial symmetry1. Although FRS delivers good performance at a relatively low computational cost and is very well suited for a variety of real-time computer vision applications, it is not invariant to perspective distortions. Moreover, even perfectly (radially) symmetric visual patterns in the real world are perceived by us after a perspective projection. In this paper, we propose a systematic extension to the FRS transform to make it invariant to (bounded) cases of perspective projection — we call this transform the generalized FRS or GFRS transform. We show that GFRS inherits the basic characteristics of FRS and retains its computational efficiency. We demonstrate the wide applicability of GFRS by applying it to a variety of natural images to detect radially symmetric patterns that have undergone significant perspective distortions. Subsequently, we build a nucleus detector based on the GFRS transform and apply it to the important problem of digital histopathology. We demonstrate superior performance over state-of-the-art nuclei detection algorithms, validated using ROC curves. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]