2009
DOI: 10.1007/s11263-009-0213-5
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Crossing-Preserving Coherence-Enhancing Diffusion on Invertible Orientation Scores

Abstract: Many image processing problems require the enhancement of crossing elongated structures. These problems cannot easily be solved by commonly used coherenceenhancing diffusion methods. Therefore, we propose a method for coherence-enhancing diffusion on the invertible orientation score of a 2D image. In an orientation score, the local orientation is represented by an additional third dimension, ensuring that crossing elongated structures are separated from each other. We consider orientation scores as functions o… Show more

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Cited by 89 publications
(177 citation statements)
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References 38 publications
(40 reference statements)
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“…Methods that deal with crossings by applying coherenceenhancing diffusion via 2D orientation scores have been developed for 2D data [37,64]. Here, we propose an extension Fig.…”
Section: Background and Related Methodsmentioning
confidence: 99%
“…Methods that deal with crossings by applying coherenceenhancing diffusion via 2D orientation scores have been developed for 2D data [37,64]. Here, we propose an extension Fig.…”
Section: Background and Related Methodsmentioning
confidence: 99%
“…This brain-inspired method is based on the theory of best-fit exponential curves in the roto-translation group SE (2) developed by Duits, Franken and Janssen [15]- [17], and, importantly, does not rely on explicit segmentation of the blood vessels. 2D images are lifted to 3D functions called "orientation scores" by adding an orientation dimension to the domain [18].…”
Section: Measurement Of Retinal Vascular Tortuositymentioning
confidence: 99%
“…. , a 2d ) T and/or conductivity matrix D. We will use ideas similar to our previous work on adaptive diffusions on invertible orientation scores [17], [12], [11], [13] (where we employed evolution equations for the 2D-Euclidean motion group). We use the absolute value to adapt the diffusion and convection to avoid oscillations.…”
Section: Setting Up the Equationsmentioning
confidence: 99%
“…Akin to our framework of linear evolutions on orientation scores, cf. [13,17], this means that we enforce horizontal diffusion and convection, i.e. transport and diffusion only takes place along so-called horizontal curves in H r which are curves t → (p(t), q(t), s(t)) ∈ H r , with s(t) ∈ (0, 1), along which connection between (p(0), q(0), s(0)) and (p(t), q(t), s(t)) and the actual horizontal…”
Section: Convection and Diffusion Along Horizontal Curvesmentioning
confidence: 99%