The enhancement and detection of elongated structures in noisy image data is relevant for many biomedical applications. To handle complex crossing structures in 2D images, 2D orientation scores U:R2×S1¿R were introduced, which already showed their use in a variety of applications. Here we extend this work to 3D orientation scores U:R3×S2¿R . First, we construct the orientation score from a given dataset, which is achieved by an invertible coherent state type of transform. For this transformation we introduce 3D versions of the 2D cake-wavelets, which are complex wavelets that can simultaneously detect oriented structures and oriented edges. For efficient implementation of the different steps in the wavelet creation we use a spherical harmonic transform. Finally, we show some first results of practical applications of 3D orientation scores.
Keywords: Orientation scores; Reproducing kernel spaces; 3D wavelet design; Scale spaces on SE(3); Coherence enhancing Diffusion on SE(3)
|Title of host publication
|Scale Space and Variational Methods in Computer Vision (5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31-June 4, 2015, Proceedings)
|J.-F. Aujol, M. Nikolova, N. Papadakis
|Published - 2015
|Lecture Notes in Computer Science