Multi-scale Anisotropic Fourth-Order Diffusion Improves Ridge and Valley Localization

Shekoufeh Gorgi Zadeh, Stephan Didas, Maximilian Wintergerst, and Thomas Schultz
In: Journal of Mathematical Imaging and Vision (2017)
 

Abstract

Ridge and valley enhancing filters are widely used in applications such as vessel detection in medical image computing. When images are degraded by noise or include vessels at different scales, such filters are an essential step for meaningful and stable vessel localization. In this work, we propose a novel multi-scale anisotropic fourth-order diffusion equation that allows us to smooth along vessels, while sharpening them in the orthogonal direction. The proposed filter uses a fourth-order diffusion tensor whose eigentensors and eigenvalues are determined from the local Hessian matrix, at a scale that is automatically selected for each pixel. We discuss efficient implementation using a fast explicit diffusion scheme and demonstrate results on synthetic images and vessels in fundus images. Compared to previous isotropic and anisotropic fourth-order filters, as well as established second-order vessel enhancing filters, our newly proposed one better restores the centerlines in all cases.

Images

Additional Material

  • PDF (PDF document, 3.6 MB)

Bibtex

@ARTICLE{GorgiZadeh:JMIV17,
    author = {Gorgi Zadeh, Shekoufeh and Didas, Stephan and Wintergerst, Maximilian and Schultz, Thomas},
     title = {Multi-scale Anisotropic Fourth-Order Diffusion Improves Ridge and Valley Localization},
   journal = {Journal of Mathematical Imaging and Vision},
      year = {2017},
      note = {First online April 11, 2017},
  abstract = {Ridge and valley enhancing filters are widely used in applications such as vessel detection in
              medical image computing. When images are degraded by noise or include vessels at different scales,
              such filters are an essential step for meaningful and stable vessel localization. In this work, we
              propose a novel multi-scale anisotropic fourth-order diffusion equation that allows us to smooth
              along vessels, while sharpening them in the orthogonal direction. The proposed filter uses a
              fourth-order diffusion tensor whose eigentensors and eigenvalues are determined from the local
              Hessian matrix, at a scale that is automatically selected for each pixel. We discuss efficient
              implementation using a fast explicit diffusion scheme and demonstrate results on synthetic images
              and vessels in fundus images. Compared to previous isotropic and anisotropic fourth-order filters,
              as well as established second-order vessel enhancing filters, our newly proposed one better restores
              the centerlines in all cases.},
       doi = {10.1007/s10851-017-0729-1}
}