Gaussian Scale-Space Theory
Computational Framework for Segmentation and Grouping
Computational Framework for Segmentation and Grouping
Invertible Apertured Orientation Filters in Image Analysis
International Journal of Computer Vision
The curve indicator random field
The curve indicator random field
Journal of Mathematical Imaging and Vision
A Cortical Based Model of Perceptual Completion in the Roto-Translation Space
Journal of Mathematical Imaging and Vision
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Nonlinear diffusion on the 2D Euclidean motion group
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
International Journal of Computer Vision
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From an image we construct an invertible orientation score, which provides an overview of local orientations in an image. This orientation score is a function on the group SE (2) of both positions and orientations. It allows us to diffuse along multiple local line segments in an image. The transformation from image to orientation score amounts to convolutions with an oriented kernel rotated at multiple angles. Under conditions on the oriented kernel the transform between image and orientation score is unitary. This allows us to relate operators on images to operators on orientation scores in a robust way such that we can deal with crossing lines and orientation uncertainty. To obtain reasonable Euclidean invariant image processing the operator on the orientation score must be both left invariant and non-linear. Therefore we consider non-linear operators on orientation scores which amount to direct products of linear left-invariant scale spaces on SE (2). These linear left-invariant scale spaces correspond to well-known stochastic processes on SE (2) for line completion and line enhancement and are given by group convolution with the corresponding Green's functions. We provide the exact Green's functions and approximations, which we use together with invertible orientation scores for automatic line enhancement and completion.