Curvature estimation for enhancement of crossing curves

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Abstract

In this paper we describe a method for estimating curvature of elongated structures in images. The curvature estimation is performed on an invertible orientation score, which is a 3D entity obtained from a 2D image by convolution with a rotating kernel. By considering the group structure we can define left-invariant derivatives, which are essential to construct operations on the orientation score that amount to rotationally invariant operations on the corresponding image. The problem of estimating curvature of an oriented structure is stated as a minimization problem, which can be solved by eigenvector analysis of a matrix constructed from the non-symmetric Hessian matrix. The experiments show the method performs well for a wide range of curvatures and noise levels. The method clearly outperforms a related curvature estimation method by Van Ginkel et al. that tends to give estimates that are too small. We show how we can incorporate the curvature estimate in our method for coherence-enhancing diffusion in orientation scores. This method has superior performance in enhancing crossing contours, which is demonstrated on medical images.
Original languageEnglish
Title of host publicationProceedings of the 11th International Conference on Computer Vision (ICCV 2007) 14-21 October 2007, Rio de Janeiro, Brazil
EditorsW. Niessen, C.F. Westin, M. Nielsen
Place of PublicationPiscataway, New Jersey, USA
PublisherInstitute of Electrical and Electronics Engineers
Pages2822-2929
ISBN (Print)978-1-4244-1631-8
DOIs
Publication statusPublished - 2007
Eventconference; ICCV 2007, Rio de Janeiro, Brazil; 2007-10-14; 2007-10-21 -
Duration: 14 Oct 200721 Oct 2007

Conference

Conferenceconference; ICCV 2007, Rio de Janeiro, Brazil; 2007-10-14; 2007-10-21
Period14/10/0721/10/07
OtherICCV 2007, Rio de Janeiro, Brazil

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    Franken, E. M., Duits, R., & Haar Romenij, ter, B. M. (2007). Curvature estimation for enhancement of crossing curves. In W. Niessen, C. F. Westin, & M. Nielsen (Eds.), Proceedings of the 11th International Conference on Computer Vision (ICCV 2007) 14-21 October 2007, Rio de Janeiro, Brazil (pp. 2822-2929). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ICCV.2007.4409145