A cortical-inspired multi-orientation geometry model for retinal image analysis
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1
Eindhoven University of Technology, Department of Biomedical Engineering, Netherlands
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2
Eindhoven University of Technology, Department of Mathematics and Computer Science, Netherlands
Hubel and Wiesel [1] discovered that the primary visual cells in cat’s striate cortex have a strong directional preference, which relates to the orientation-selective property of the receptive fields in V1. See Figure 1, a so-called cortical hypercolum can be interpreted as a “visual pixel”, neatly decomposed into a complete set of orientations. Motivated by the orientation-selective cells, so-called orientation scores are constructed by lifting all elongated structures (in 2D images) along an extra orientation dimension [2], see Figure 2. Similar to the perceptual organization of orientation in the visual cortex, a 2D orientation score is an object that maps each 2D position and orientation angle (x,y,θ) to a complex scalar. So the original 2D image domain can be extended to the score domain. A great advantage is that it can deal with multiple orientations per position, and the extra dimension enables new techniques for e.g. geometric reasoning and crossing preserving enhancement..
Since we do not want to tamper data-evidence before subsequent image processing operations take place, invertibility of our transformation between image and score is key in our multi-orientation mathematical modeling. We can now disentangle the elongated structures involved in a crossing session for a crossing preserving flow. Based on the invertible orientation score framework, Bekkers et al. [3] developed a fully automatic multi-orientation vessel tracking algorithm which outperforms other state-of-the-art tracking/detection algorithms.
Moreover, synaptic physiological studies of horizontal pathways in cats’ striate cortex show that neurons with aligned receptive field sites excite each other [4]. Therefore, the visual system not only constructs the aforementioned score of local orientations, but also accounts for context and alignment by excitation and inhibition a priori, which can be modeled by left-invariant PDE’s and ODE’s for contour enhancement and contour completion directly on the score [5-8]. Figure 3 shows the stochastic contour enhancement kernel of linear left-invariant diffusion, which is obtained based on the modeling of Brownian motion in the Euclidean rotation-translation group (SE(2)).
In Figure 4 we see that by applying left-invariant diffusion on the invertible orientation score of a 2D image, the elongated structures can be excellently enhanced without destroying the separated crossing parts in the score domain. Therefore, this step is necessary as a pre-enhancing step for the subsequent tracking/detection. As a proof of concept, we show examples of tracking on left-invariantly diffused invertible orientation scores on cases in retinal image vessel tracking where standard ETOS-tracking [3] without left-invariant diffusion fails, see Figure 5.
References
[1] D.H. Hubel and T.N. Wiesel. Receptive fields of single neurons in the cat’s striate cortex. The Journal of Physiology, 148:574–591, 1959.
[2] R. Duits, M. Felsberg, G. Granlund, and B. M. ter Haar Romeny. Image analysis and reconstruction using a wavelet transform constructed from a reducible representation of the Euclidean motion group. International Journal of Computer Vision, 79(1):79–102, 2007.
[3] E.J. Bekkers, R. Duits, T. Berendschot, and B. ter Haar Romeny. A multi-orientation analysis approach to retinal vessel tracking. Journal of Mathematical Imaging and Vision, pages 1–28, 2014.
[4] W. H. Bosking, Y. Zhang, B. Schofield, and D. Fitzpatrick. Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. The Journal of Neuroscience, 17(6):2112–2127, March 1997.
[5] D. Barbieri, G. Citti, G. Cocci, and A. Sarti. A cortical-inspired geometry for contour perception and motion integration. Journal of Mathematical Imaging and Vision, 2014. Accepted and published digitally online.
[6] G. Citti and A. Sarti. A cortical based model of perceptional completion in the roto-translation space. Journal of Mathematical Imaging and Vision, 24(3):307–326, 2006.
[7] J. Zhang, R. Duits and B. M. ter Haar Romeny, Numerical Approaches for Linear Left-invariant Diffusions on SE(2), their Comparison to Exact Solutions, and their Applications in Retinal Imaging. Submitted to NM-TMA. arXiv:1403.3320v4[math.NA], http://arxiv.org/pdf/1403.3320v4.pdf
[8] R. Duits and E.M. Franken. Left-invariant parabolic evolutions on SE(2) and contour enhancement via invertible orientation scores, part I: Linear left-invariant diffusion equations on SE(2). Quarterly of Appl.Math., A.M.S., 68:255–292, 2010.
Keywords:
Visual Cortex,
orientation scores,
elongated structures,
crossing preserving,
Retina,
vessel tracking,
coherence-enhancing diffusion,
enhancement
Conference:
Neuroinformatics 2014, Leiden, Netherlands, 25 Aug - 27 Aug, 2014.
Presentation Type:
Poster, not to be considered for oral presentation
Topic:
Neuroimaging
Citation:
Zhang
J,
Duits
R and
Ter Haar Romeny
B
(2014). A cortical-inspired multi-orientation geometry model for retinal image analysis.
Front. Neuroinform.
Conference Abstract:
Neuroinformatics 2014.
doi: 10.3389/conf.fninf.2014.18.00089
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Received:
28 Apr 2014;
Published Online:
04 Jun 2014.
*
Correspondence:
Prof. Bart Ter Haar Romeny, Eindhoven University of Technology, Department of Biomedical Engineering, Eindhoven, 5600MB, Netherlands, B.M.terhaarRomeny@tue.nl