Invertible Orientation Scores of 3D Images

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1 Invertible Orientation Scores of 3D Images Michiel Janssen Supervisors/Collaborators: Remco Duits Guido Janssen Gonzalo Sanguinetti Jorg Portegies Marcel Breeuwer Javier Olivan Bescos Project: ERC Lie Analysis 1

2 Orientation Scores - Background Elongated structures appear in medical images Retina Muscle Cells Vessels in prostate Methods for detection and enhancement often fail at crossings/bifurcations etc. 15-Apr-15 2

3 Orientation Scores - Background To cope with crossings/bifurcations orientation scores (OS) were introduced Orientation Orientation Score Filter Image x y In the OS crossing structures are disentangled 15-Apr-15 Image OS Image OS 3

4 Orientation Scores - Applications 2D Retinal Vessel Tracking in Orientation Scores Crossing-Preserving Coherence Enhancing Diffusion via Invertible Orientation Scores Image OS Noise Reduction Erik Bekkers Remco Duits Bart ter Haar Romeny Tos Berendschot, A Multi-Orientation Analysis Approach to Retinal Vessel Tracking 15-Apr-15 4

5 Can we extend this work to 3D orientation scores? 15-Apr-15 5

6 3D Orientation Scores Glyph Visualization 15-Apr-15 6

7 Processing via Orientation Scores Image Score Processed image Processed Score

8 Processing via Orientation Scores Image Score Processed image Processed Score

9 Orientation Score Transformation Using Cake-Wavelets 2D All frequencies covered Inverse DFT Stable reconstruction possible from a single scale transformation 3D Antisymmetrize Wavelets and method for efficient computation of wavelets via a spherical harmonic transform. Accepted for oral presentation 15-Apr-15 at conference SSVM! Funk- Transform Inverse DFT 9

10 Orientation Score Transformation Convenient encoding of oriented structures and edges Real: Structure Detectors Imaginary: Edge Detectors 15-Apr-15 10

11 Wavelet Design Using 3D Generalized Zernike Basis For controlling wavelet shape and stability of rec. we need an analytical description in both domains Previously spectral decomposition of harmonic oscillator/ft: Expanding wavelet in 3D Generalized Zernike basis: Analytic description in spatial and Fourier domain! 15-Apr-15 11

12 Orientation Scores Image Score Processed image Processed Score

13 Theory Model orientation score 2D as function on the roto-translation group 3D Left-Invariant Derivatives (2D) Exponential Curves (2D) 13

14 Overview Data-Adaptive Processing via Orientation Scores

15 Structure Tensor Approach for Images Orientation estimation by spectral decomp. of a structure tensor Eigenvector with smallest eigenvalue minimizes

16 Reformulation Structure Tensor Approach for Images Reformulate structure tensor to exp curve fitting problem In exponential curves are straight curves We need to fit We define as the exp curve starting at position with the same spatial velocity as Rewrite directional derivative as time derivative over exponential curves

17 Structure Tensor in Orientation Scores Exponential curve fitting problem in orientation scores In we define as the exp curve starting at position and orientation with the same spatial and angular velocity as

18 Exponential Curve Fits in SE(3) Works similar for the case SE(3) Structure Tensor Minimizes first order variation Hessian Minimizes second Order Variation 18

19 Overview Data-Adaptive Processing via Orientation Scores

20 Data-Adaptive Enhancements Image Score Processed Processed Score image Level set in Data Not adaptive Data + Noise Adaptive 20

21 Application in 3D Vessel Analysis Vesselness Vesselness Vesselness via OS (preserves bifurcations) Vessel Segmentation Next Challenge : In collaboration with Philips 15-Apr-15 21

22 Conclusion Main Results 3D Cake-Wavelets for invertible transform M.H.J. Janssen, R. Duits, M. Breeuwer, Invertible Orientation Scores of 3D Images, Accepted conference paper SSVM 2015, LNCS, Locally adaptive frames (Exp. Curve fit) R. Duits, M.H.J. Janssen, J. Hannink and G.R. Sanguinetti, Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging, Submitted to JMIV, Preprint on Arxiv, 2015 Enhancements expressed in locally adaptive frames Future work Other operators (e.g. crossing preserving vesselness) Sub-Riemannian wavefront propagation in SE(3) 15-Apr Application in 3D vessel detection/enhancement

23 Questions? 15-Apr-15 23