Framelet-Based Algorithm for Segmentation of Tubular Structures

Framelets have been used successfully in various problems in image processing, including inpainting, impulse noise removal, super-resolution image restoration, etc. Segmentation is the process of identifying object outlines within images. There are quite a few efficient algorithms for segmentation that depend on the partial differential equation modeling. In this paper, we apply the framelet-based approach to identify tube-like structures such as blood vessels in medical images. Our method iteratively refines a region that encloses the possible boundary or surface of the vessels. In each iteration, we apply the framelet-based algorithm to denoise and smooth the possible boundary and sharpen the region. Numerical experiments of real 2D/3D images demonstrate that the proposed method is very efficient and outperforms other existing methods.

[1]  Michael Unser,et al.  Texture classification and segmentation using wavelet frames , 1995, IEEE Trans. Image Process..

[2]  Laurent Demanet,et al.  Fast Discrete Curvelet Transforms , 2006, Multiscale Model. Simul..

[3]  Serena Morigi,et al.  Segmentation of 3D Tubular Structures by a PDE-Based Anisotropic Diffusion Model , 2008, MMCS.

[4]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[5]  Raymond H. Chan,et al.  Wavelet Algorithms for High-Resolution Image Reconstruction , 2002, SIAM J. Sci. Comput..

[6]  Xavier Bresson,et al.  Fast Global Minimization of the Active Contour/Snake Model , 2007, Journal of Mathematical Imaging and Vision.

[7]  Tony F. Chan,et al.  A logic framework for active contours on multi-channel images , 2005, J. Vis. Commun. Image Represent..

[8]  Jian-Feng Cai,et al.  A framelet-based image inpainting algorithm , 2008 .

[9]  Raymond H. Chan,et al.  Simultaneously inpainting in image and transformed domains , 2009, Numerische Mathematik.

[10]  Serena Morigi,et al.  Composed Segmentation of Tubular Structures by an Anisotropic PDE Model , 2009, SSVM.

[11]  Aichi Chien,et al.  Frame based segmentation for medical images , 2011 .

[12]  Bin Dong,et al.  MRA-based wavelet frames and applications , 2013 .

[13]  Ken Masamune,et al.  A Variational Method for Geometric Regularization of Vascular Segmentation in Medical Images , 2008, IEEE Transactions on Image Processing.

[14]  Joachim Weickert,et al.  Anisotropic diffusion in image processing , 1996 .

[15]  A. Ron,et al.  Affine Systems inL2(Rd): The Analysis of the Analysis Operator , 1997 .

[16]  Arivazhagan Selvaraj,et al.  Texture segmentation using wavelet transform , 2003, Pattern Recognit. Lett..

[17]  Joachim Hornegger,et al.  Semi-automatic level-set based segmentation and stenosis quantification of the internal carotid artery in 3D CTA data sets , 2007, Medical Image Anal..

[18]  Raymond H. Chan,et al.  Inpainting by Flexible Haar-Wavelet Shrinkage , 2008, SIAM J. Imaging Sci..

[19]  Tony F. Chan,et al.  Active contours without edges , 2001, IEEE Trans. Image Process..

[20]  Minh N. Do,et al.  Ieee Transactions on Image Processing the Contourlet Transform: an Efficient Directional Multiresolution Image Representation , 2022 .

[21]  Francis K. H. Quek,et al.  A review of vessel extraction techniques and algorithms , 2004, CSUR.

[22]  Jian-Feng Cai,et al.  Split Bregman Methods and Frame Based Image Restoration , 2009, Multiscale Model. Simul..

[23]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[24]  Knut-Andreas Lie,et al.  Scale Space and Variational Methods in Computer Vision, Second International Conference, SSVM 2009, Voss, Norway, June 1-5, 2009. Proceedings , 2009, SSVM.

[25]  Mila Nikolova,et al.  Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models , 2006, SIAM J. Appl. Math..

[26]  Aly A. Farag,et al.  Cerebrovascular segmentation for MRA data using level sets , 2003, CARS.