A New Multiphase Segmentation Method Using Eigenvectors Based on K Real Numbers

In this paper, a new multiphase segmentation which has two stages is proposed. At the first stage, independent from the kind of image, k equidistant real numbers within [0, 1] interval are set as the labels of k main regions. At the second stage, two factors are used, which consist of the intensity function for distinguishing similar regions, as well as the eigenvector of Hessian matrix for distinguishing similar ridges with an auxiliary parameter for controlling the influence of this factor in different images. Also, an iterative algorithm is applied for gradually growing the region. Numerical experiences are given to illustrate the effectiveness of the proposed methods.

[1]  Rangachar Kasturi,et al.  Machine vision , 1995 .

[2]  Tony F. Chan,et al.  Mumford and Shah Model and Its Applications to Image Segmentation and Image Restoration , 2015, Handbook of Mathematical Methods in Imaging.

[3]  R. Sivakumar.  DENOISING OF COMPUTER TOMOGRAPHY IMAGES USING CURVELET TRANSFORM , 2007 .

[4]  G. McLachlan,et al.  The EM Algorithm and Extensions: Second Edition , 2008 .

[5]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[6]  E. Forgy,et al.  Cluster analysis of multivariate data : efficiency versus interpretability of classifications , 1965 .

[7]  Raymond H. Chan,et al.  A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford-Shah Model and Thresholding , 2013, SIAM J. Imaging Sci..

[8]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[9]  J. A. Hartigan,et al.  A k-means clustering algorithm , 1979 .

[10]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[11]  Luc Florack,et al.  Image Structure , 1997, Computational Imaging and Vision.

[12]  J. Bezdek,et al.  FCM: The fuzzy c-means clustering algorithm , 1984 .

[13]  Guillermo Sapiro,et al.  Geodesic Active Contours , 1995, International Journal of Computer Vision.

[14]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[15]  Nasser Aghazadeh,et al.  A multistep segmentation algorithm for vessel extraction in medical imaging , 2014, ArXiv.

[16]  Gabriele Steidl,et al.  A new fuzzy c-means method with total variation regularization for segmentation of images with noisy and incomplete data , 2012, Pattern Recognit..

[17]  Michael K. Ng,et al.  A Multiphase Image Segmentation Method Based on Fuzzy Region Competition , 2010, SIAM J. Imaging Sci..

[18]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .