Template Matching via Densities on the Roto-Translation Group

TL;DR

This paper introduces a novel template matching method using orientation scores and Lie group geometry to detect objects with orientation patterns, achieving high accuracy and efficiency in medical and camera images.

Contribution

It develops a new template matching framework on the roto-translation group SE(2) using wavelet transforms and spline-based templates, incorporating geometric priors for improved detection.

Findings

Achieved 99.83% success in optic nerve head detection

Achieved 99.32% success in fovea detection

Achieved 95.86% success in pupil detection

Abstract

We propose a template matching method for the detection of 2D image objects that are characterized by orientation patterns. Our method is based on data representations via orientation scores, which are functions on the space of positions and orientations, and which are obtained via a wavelet-type transform. This new representation allows us to detect orientation patterns in an intuitive and direct way, namely via cross-correlations. Additionally, we propose a generalized linear regression framework for the construction of suitable templates using smoothing splines. Here, it is important to recognize a curved geometry on the position-orientation domain, which we identify with the Lie group SE(2): the roto-translation group. Templates are then optimized in a B-spline basis, and smoothness is defined with respect to the curved geometry. We achieve state-of-the-art results on three different applications: detection of the optic nerve head in the retina (99.83% success rate on 1737 images), of the fovea in the retina (99.32% success rate on 1616 images), and of the pupil in regular camera images (95.86% on 1521 images). The high performance is due to inclusion of both intensity and orientation features with effective geometric priors in the template matching. Moreover, our method is fast due to a cross-correlation based matching approach.