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 percent success rate on 1,737 images), of the fovea in the retina (99.32 percent success rate on 1,616 images), and of the pupil in regular camera images (95.86 percent on 1,521 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.

This paper presents a supervised retinal vessel segmentation by incorporating vessel filtering and wavelet transform features from orientation scores (OSs), and green intensity. Through an anisotropic wavelet-type transform, a 2D image is lifted to a 3D orientation score in the Lie-group domain of positions and orientations R²⋊S¹. Elongated structures are disentangled into their corresponding orientation planes and enhanced via multi-orientation vessel filtering. In addition, scale-selective OSs (in the domain of positions, orientations and scales R²⋊S¹×R⁺) are obtained by adding a scale adaptation to the wavelet transform. Features are optimally extracted by taking maximum orientation responses at multiple scales, to represent vessels of changing calibers. Finally, we train a Random Forest classifier for vessel segmentation. Extensive validations show that our method achieves a competitive segmentation, and better vessel preservation with less false detections compared with the state-of-the-art methods.