Computer Vision, Graphics, and Image Processing
Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow
IEEE Transactions on Pattern Analysis and Machine Intelligence
Signal Processing for Computer Vision
Signal Processing for Computer Vision
The Möbius Strip Parameterization for Line Extraction
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Analysis of multiple orientations
IEEE Transactions on Image Processing
3D-orientation space: filters and sampling
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Estimation of curvature based shape properties of surfaces in 3D grey-value images
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
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
A comparison of the cingulum tract in ALS-B patients and controls using kernel matching
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
Curvature of n-dimensional space curves in grey-value images
IEEE Transactions on Image Processing
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In this paper we present a framework to construct a continuous orientation representation in arbitrary dimensions. Existing methods for 2D (doubling the angle) and 3D (Knutsson mapping) were found ad hoc. We show how they can be put in a general framework to derive suitable representations for filtering in spaces of arbitrary dimension. The dimensionality of the derived representation is shown to be minimal. Connections with the gradient structure tensor and Knutsson mapping are shown, like the fact that angle doubling works in each pair-cone of the Knutsson mapping. Finally, using projection operators we show how angles between vectors in the base space are related to vectors in the mapped spaces and in particular how to achieve preservation of isotropy.