Segmentation of medical images using mean value guided contour

HighlightsApplying the mean value theorem in contour repositioning to enhance the accuracy of medical image segmentation.Not using energy minimization makes the proposed model the promising capability in complex geometries, irreducible convergence speed in the saddle and stationary points, recovering boundary ruptures, and the ability to not rounding the edges of the contour.Unlike the standard optimization methods, the user gets rid of numerous parameters that should be manually set during the segmentation.The model runs very fast; e.g., the speed is more than 1400 times faster than Gauss–newton optimization that is one of the methods with best performance. &NA; Partial differential equation‐based (PDE‐based) methods are extensively used in image segmentation, especially in contour models. Difficulties associated with the boundaries, namely troubles with developing initialization, inadequate convergence to boundary concavities, and difficulties connected to saddle points and stationary points of active contours make the contour models suffer from a feeble performance of referring to complex geometries. The present paper is designed to take advantage of mean value theorem rather than minimizing energy function for contours. It is efficiently capable of resolving above‐mentioned problems by applying this theorem to the edge map gradient vectors, which is calculated from the image. Since the contour is computed in a straightforward manner from an edge map instead of force balance equation, it varies from other contour‐based image segmentation methods. To illustrate the ability of the proposed model in complex geometries and ruptures, several experiments were also provided to validate the model. The experiments' results demonstrated that the proposed method, which is called mean value guided contour (MVGC), is capable of repositioning contours into boundary concavities and has suitable forcefulness in complex geometries. Graphical abstract Figure. No caption available.

[1]  Ning Ji-feng,et al.  NGVF: An improved external force field for active contour model , 2007 .

[2]  Michel Couprie,et al.  Segmentation of 4D cardiac MRI: Automated method based on spatio-temporal watershed cuts , 2010, Image Vis. Comput..

[3]  Mikkel B. Stegmann,et al.  Bi-temporal 3D active appearance models with applications to unsupervised ejection fraction estimation , 2005, SPIE Medical Imaging.

[4]  Antonio Boccuto,et al.  Kurzweil - Henstock Integral in Riesz Spaces , 2018 .

[5]  Xuelong Li,et al.  Mean shift based gradient vector flow for image segmentation , 2013, Comput. Vis. Image Underst..

[6]  Yehoshua Y. Zeevi,et al.  Geodesic Active Contours Applied to Texture Feature Space , 2001, Scale-Space.

[7]  Jürgen Weese,et al.  Automated segmentation of the left ventricle in cardiac MRI , 2004, Medical Image Anal..

[8]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[9]  Jerry L. Prince,et al.  Snakes, shapes, and gradient vector flow , 1998, IEEE Trans. Image Process..

[10]  James S. Duncan,et al.  Segmentation of the Left Ventricle From Cardiac MR Images Using a Subject-Specific Dynamical Model , 2010, IEEE Transactions on Medical Imaging.

[11]  Timothy F. Cootes,et al.  Active Appearance Models , 1998, ECCV.

[12]  Alfred M. Bruckstein,et al.  Regularized Laplacian Zero Crossings as Optimal Edge Integrators , 2003, International Journal of Computer Vision.

[13]  Patrick Clarysse,et al.  A dynamic elastic model for segmentation and tracking of the heart in MR image sequences , 2010, Medical Image Anal..

[14]  Denis Friboulet,et al.  Fast automatic myocardial segmentation in 4D cine CMR datasets , 2014, Medical Image Anal..

[15]  John K. Tsotsos,et al.  Efficient and generalizable statistical models of shape and appearance for analysis of cardiac MRI , 2008, Medical Image Anal..

[16]  Jerry L. Prince,et al.  Gradient vector flow: a new external force for snakes , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[17]  Ling Shao,et al.  A review of heart chamber segmentation for structural and functional analysis using cardiac magnetic resonance imaging , 2016, Magnetic Resonance Materials in Physics, Biology and Medicine.

[18]  Marcos Martín-Fernández,et al.  Unsupervised 4D myocardium segmentation with a Markov Random Field based deformable model , 2011, Medical Image Anal..

[19]  Cornelius Rosse,et al.  Hollinshead's Textbook of Anatomy , 1997 .

[20]  Daniel Rueckert,et al.  Segmentation of 4D Cardiac MR Images Using a Probabilistic Atlas and the EM Algorithm , 2003, MICCAI.

[21]  Boying Wu,et al.  Split Bregman method for minimization of improved active contour model combining local and global information dynamically , 2012 .

[22]  Tamás Szirányi,et al.  Harris function based active contour external force for image segmentation , 2012, Pattern Recognit. Lett..

[23]  Carole Le Guyader,et al.  Extrapolation of Vector Fields Using the Infinity Laplacian and with Applications to Image Segmentation , 2009, SSVM.

[24]  Xianghai Wang,et al.  Image segmentation framework using EdgeFlow-Based active contours , 2013 .

[25]  Junbo Wang,et al.  Image Segmentation Framework Using Gradient Guided Active Contours , 2015 .

[26]  Lixiong Liu,et al.  A Novel Method for Segmentation of the Cardiac MR Images using Generalized DDGVF Snake Models with Shape Priors , 2009 .

[27]  Ying Li,et al.  A novel active contour model for image segmentation using distance regularization term , 2013, Comput. Math. Appl..

[28]  Jerry L. Prince,et al.  Generalized gradient vector flow external forces for active contours , 1998, Signal Process..

[29]  J. Steele.  The Cauchy–Schwarz Master Class: References , 2004 .

[30]  Wei Xie,et al.  Active contours driven by divergence of gradient vector flow , 2016, Signal Process..

[31]  Omer Berenfeld,et al.  Automated segmentation and reconstruction of patient-specific cardiac anatomy and pathology from in vivo MRI* , 2012 .

[32]  Nassir Navab,et al.  Segmentation by retrieval with guided random walks: Application to left ventricle segmentation in MRI , 2013, Medical Image Anal..

[33]  Milan Sonka,et al.  3-D active appearance models: segmentation of cardiac MR and ultrasound images , 2002, IEEE Transactions on Medical Imaging.

[34]  Irène Buvat,et al.  Variational Segmentation of Vector-Valued Images With Gradient Vector Flow , 2014, IEEE Transactions on Image Processing.

[35]  Dimitris N. Metaxas,et al.  Metamorphs: Deformable Shape and Appearance Models , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[36]  Daniel Rueckert,et al.  Segmentation of 4D cardiac MR images using a probabilistic atlas and the EM algorithm , 2004, Medical Image Anal..

[37]  J. Dieudonne.  Foundations of Modern Analysis , 1969 .

[38]  Pingkun Yan,et al.  Feature competition and partial sparse shape modeling for cardiac image sequences segmentation , 2015, Neurocomputing.

[39]  J. M. Aldaz,et al.  Advances in operator cauchy-schwarz inequalities and their reverses , 2015 .

[40]  Philip M. Morse,et al.  Methods of Mathematical Physics , 1947, The Mathematical Gazette.

[41]  Xianghua Xie,et al.  MAC: Magnetostatic Active Contour Model , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[42]  Bing Li,et al.  Active Contour External Force Using Vector Field Convolution for Image Segmentation , 2007, IEEE Transactions on Image Processing.

[43]  Chunming Li,et al.  Segmentation of external force field for automatic initialization and splitting of snakes , 2005, Pattern Recognit..

[44]  Simon Baker,et al.  Lucas-Kanade 20 Years On: A Unifying Framework , 2004, International Journal of Computer Vision.

[45]  Dinggang Shen,et al.  Hierarchical active shape models, using the wavelet transform , 2003, IEEE Transactions on Medical Imaging.

[46]  Yunde Jia,et al.  Adaptive diffusion flow active contours for image segmentation , 2013, Comput. Vis. Image Underst..

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

[48]  Hao Wu,et al.  Numerical Conditioning Problems and Solutions for Nonparametric i.i.d. Statistical Active Contours , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[49]  G. Wright,et al.  Automatic functional analysis of left ventricle in cardiac cine MRI. , 2013, Quantitative imaging in medicine and surgery.

[50]  Huaifei Hu,et al.  Hybrid segmentation of left ventricle in cardiac MRI using Gaussian-mixture model and region restricted dynamic programming. , 2013, Magnetic resonance imaging.

[51]  A. Yezzi,et al.  On the relationship between parametric and geometric active contours , 2000, Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154).

[52]  Liang Xiao,et al.  An active contour model driven by anisotropic region fitting energy for image segmentation , 2013, Digit. Signal Process..

[53]  Tony F. Chan,et al.  Image processing and analysis - variational, PDE, wavelet, and stochastic methods , 2005 .

[54]  Juha Koikkalainen,et al.  Statistical shape model of atria, ventricles and epicardium from short- and long-axis MR images , 2004, Medical Image Anal..

[55]  Alejandro F Frangi,et al.  Automatic cardiac LV segmentation in MRI using modified graph cuts with smoothness and interslice constraints , 2014, Magnetic resonance in medicine.