Joint graph cut and relative fuzzy connectedness image segmentation algorithm

We introduce an image segmentation algorithm, called GC(sum)(max), which combines, in novel manner, the strengths of two popular algorithms: Relative Fuzzy Connectedness (RFC) and (standard) Graph Cut (GC). We show, both theoretically and experimentally, that GC(sum)(max) preserves robustness of RFC with respect to the seed choice (thus, avoiding "shrinking problem" of GC), while keeping GC's stronger control over the problem of "leaking though poorly defined boundary segments." The analysis of GC(sum)(max) is greatly facilitated by our recent theoretical results that RFC can be described within the framework of Generalized GC (GGC) segmentation algorithms. In our implementation of GC(sum)(max) we use, as a subroutine, a version of RFC algorithm (based on Image Forest Transform) that runs (provably) in linear time with respect to the image size. This results in GC(sum)(max) running in a time close to linear. Experimental comparison of GC(sum)(max) to GC, an iterative version of RFC (IRFC), and power watershed (PW), based on a variety medical and non-medical images, indicates superior accuracy performance of GC(sum)(max) over these other methods, resulting in a rank ordering of GC(sum)(max)>PW∼IRFC>GC.

[1]  Timothy F. Cootes,et al.  Comparing Active Shape Models with Active Appearance Models , 1999, BMVC.

[2]  Richard M. Leahy,et al.  Surface-based labeling of cortical anatomy using a deformable atlas , 1997, IEEE Transactions on Medical Imaging.

[3]  Andrew Blake,et al.  "GrabCut" , 2004, ACM Trans. Graph..

[4]  Andrew F. Laine,et al.  Improving statistics for hybrid segmentation of high-resolution multichannel images , 2002, SPIE Medical Imaging.

[5]  Gilles Aubert,et al.  Some Remarks on the Equivalence between 2D and 3D Classical Snakes and Geodesic Active Contours , 2004, International Journal of Computer Vision.

[6]  Supun Samarasekera,et al.  Fuzzy Connectedness and Object Definition: Theory, Algorithms, and Applications in Image Segmentation , 1996, CVGIP Graph. Model. Image Process..

[7]  Guido Gerig,et al.  Multiscale medial shape-based analysis of image objects , 2003, Proc. IEEE.

[8]  Jitendra Malik,et al.  Normalized Cuts and Image Segmentation , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Leo Grady,et al.  A Seeded Image Segmentation Framework Unifying Graph Cuts And Random Walker Which Yields A New Algorithm , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[10]  S. L. Free,et al.  Cerebellar volumes in newly diagnosed and chronic epilepsy , 2002, Journal of Neurology.

[11]  Vladimir Kolmogorov,et al.  "GrabCut": interactive foreground extraction using iterated graph cuts , 2004, ACM Trans. Graph..

[12]  Jayaram K. Udupa,et al.  Synergistic arc-weight estimation for interactive image segmentation using graphs , 2010, Comput. Vis. Image Underst..

[13]  Dzung L. Pham,et al.  Spatial Models for Fuzzy Clustering , 2001, Comput. Vis. Image Underst..

[14]  Andrew Blake,et al.  Geodesic star convexity for interactive image segmentation , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[15]  Andrew Mehnert,et al.  Relaxed image foresting transforms for interactive volume image segmentation , 2010, Medical Imaging.

[16]  Baba C. Vemuri,et al.  Shape Modeling with Front Propagation: A Level Set Approach , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Jayaram K. Udupa,et al.  Oriented active shape models , 2006, SPIE Medical Imaging.

[18]  Jayaram K. Udupa,et al.  Cloud bank: A multiple clouds model and its use in MR brain image segmentation , 2009, 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[19]  Jayaram K. Udupa,et al.  User-Steered Image Segmentation Paradigms: Live Wire and Live Lane , 1998, Graph. Model. Image Process..

[20]  Olga Veksler,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Demetri Terzopoulos,et al.  United Snakes , 1999, Medical Image Anal..

[22]  Filip Malmberg Image Foresting Transform: On-the-Fly Computation of Segmentation Boundaries , 2011, SCIA.

[23]  Camille Couprie,et al.  Power Watershed: A Unifying Graph-Based Optimization Framework , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  Jayaram K. Udupa,et al.  Region-Based Segmentation: Fuzzy Connectedness, Graph Cut and Related Algorithms , 2010 .

[25]  Jayaram K. Udupa,et al.  Affinity functions in fuzzy connectedness based image segmentation I: Equivalence of affinities , 2010, Comput. Vis. Image Underst..

[26]  Luciano da Fontoura Costa,et al.  Erratum to multiscale skeletons by image foresting transform and its applications to neuromorphometry: [Pattern Recognition 35(7) (2002) 1571-1582] , 2003, Pattern Recognit..

[27]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[28]  P H Ellaway,et al.  An Investigation of Motor Function in Schizophrenia using Transcranial Magnetic Stimulation of the Motor Cortex , 1996, British Journal of Psychiatry.

[29]  Joakim Lindblad,et al.  A graph-based framework for sub-pixel image segmentation , 2011, Theor. Comput. Sci..

[30]  Jayaram K. Udupa,et al.  Image segmentation by combining the strengths of Relative Fuzzy Connectedness and Graph Cut , 2012, 2012 19th IEEE International Conference on Image Processing.

[31]  Jayaram K. Udupa,et al.  Hybrid Segmentation of Anatomical Data , 2001, MICCAI.

[32]  Jorge Stolfi,et al.  The image foresting transform: theory, algorithms, and applications , 2004 .

[33]  Vladimir Kolmogorov,et al.  An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision , 2004, IEEE Trans. Pattern Anal. Mach. Intell..

[34]  Alexandre X. Falcão,et al.  Links Between Image Segmentation Based on Optimum-Path Forest and Minimum Cut in Graph , 2009, Journal of Mathematical Imaging and Vision.

[35]  Jayaram K. Udupa,et al.  A framework for comparing different image segmentation methods and its use in studying equivalences between level set and fuzzy connectedness frameworks , 2011, Comput. Vis. Image Underst..

[36]  Jayaram K. Udupa,et al.  Fuzzy Connectedness Image Segmentation in Graph Cut Formulation: A Linear-Time Algorithm and a Comparative Analysis , 2012, Journal of Mathematical Imaging and Vision.

[37]  Guillermo Sapiro,et al.  Interactive Image Segmentation via Adaptive Weighted Distances , 2007, IEEE Transactions on Image Processing.

[38]  Vladimir Kolmogorov,et al.  What energy functions can be minimized via graph cuts? , 2002, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[39]  Jayaram K. Udupa,et al.  Iterative relative fuzzy connectedness for multiple objects with multiple seeds , 2007, Comput. Vis. Image Underst..

[40]  Guillermo Sapiro,et al.  Distancecut: Interactive Segmentation and Matting of Images and Videos , 2007, 2007 IEEE International Conference on Image Processing.

[41]  Jayaram K. Udupa,et al.  Comparison of fuzzy connectedness and graph cut segmentation algorithms , 2011, Medical Imaging.

[42]  Guillermo Sapiro,et al.  Distancecut: Interactive Real-Time Segmentation and Matting of Images and Videos (PREPRINT) , 2007 .

[43]  Leo Grady,et al.  Random Walks for Image Segmentation , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[44]  Discriminant Subspace,et al.  PATTERN ANALYSIS AND MACHINE INTELLIGENCE A publication of the IEEE Computer Society , 2007 .

[45]  Alexandre X. Falcão,et al.  Interactive volume segmentation with differential image foresting transforms , 2004, IEEE Transactions on Medical Imaging.

[46]  Jayaram K. Udupa,et al.  Scale-Based Fuzzy Connected Image Segmentation: Theory, Algorithms, and Validation , 2000, Comput. Vis. Image Underst..

[47]  C VemuriBaba,et al.  Shape Modeling with Front Propagation , 1995 .