Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Two-dimensional directional wavelets and the scale-angle representation
Signal Processing
Signal Processing for Computer Vision
Signal Processing for Computer Vision
Coherence-Enhancing Diffusion Filtering
International Journal of Computer Vision
Invertible Orientation Bundles on 2D Scalar Images
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
International Journal of Computer Vision
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Image and Vision Computing
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
From tensor-driven diffusion to anisotropic wavelet shrinkage
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Line Enhancement and Completion via Linear Left Invariant Scale Spaces on SE(2)
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Scale Spaces on the 3D Euclidean Motion Group for Enhancement of HARDI Data
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Crossing-Preserving Coherence-Enhancing Diffusion on Invertible Orientation Scores
International Journal of Computer Vision
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Continuous orientation representation for arbitrary dimensions: a generalized knutsson mapping
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
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Linear and nonlinear diffusion equations are usually considered on an image, which is in fact a function on the translation group. In this paper we study diffusion on orientation scores, i.e. on functions on the Euclidean motion group SE(2). An orientation score is obtained from an image by a linear invertible transformation. The goal is to enhance elongated structures by applying nonlinear left-invariant diffusion on the orientation score of the image. For this purpose we describe how we can use Gaussian derivatives to obtain regularized left-invariant derivatives that obey the non-commutative structure of the Lie algebra of SE(2). The Hessian constructed with these derivatives is used to estimate local curvature and orientation strength and the diffusion is made nonlinearly dependent on these measures. We propose an explicit finite difference scheme to apply the nonlinear diffusion on orientation scores. The experiments show that preservation of crossing structures is the main advantage compared to approaches such as coherence enhancing diffusion.