A variational approach to bone segmentation in CT images

We present a variational approach for segmenting bone structures in Computed Tomography (CT) images. We introduce a novel functional on the space of image segmentations, and subsequently minimize this functional through a gradient descent partial differential equation. The functional we propose provides a measure of similarity of the intensity characteristics of the bone and tissue regions through a comparison of their cumulative distribution functions; minimizing this similarity measure therefore yields the maximal separation between the two regions. We perform the minimization of our proposed functional using level set partial differential equations; in addition to numerical stability, this yields topology independence, which is especially useful in the context of CT bone segmentation where a bone region may consist of several disjoint pieces. Finally, we present an extensive validation of our method against expert manual segmentation on CT images of the wrist, ankle, foot, and pelvis.

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

[2]  Tae-Seong Kim,et al.  A density distance augmented Chan-Vese active contour for CT bone segmentation , 2008, 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[3]  Tony F. Chan,et al.  Histogram Based Segmentation Using Wasserstein Distances , 2007, SSVM.

[4]  Jun Xie,et al.  Segmentation of kidney from ultrasound images based on texture and shape priors , 2005, IEEE Transactions on Medical Imaging.

[5]  Kaleem Siddiqi,et al.  Flux Maximizing Geometric Flows , 2001, ICCV.

[6]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

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

[8]  W. Eric L. Grimson,et al.  A shape-based approach to the segmentation of medical imagery using level sets , 2003, IEEE Transactions on Medical Imaging.

[9]  Yan Kang,et al.  A new accurate and precise 3-D segmentation method for skeletal structures in volumetric CT data , 2003, IEEE Transactions on Medical Imaging.

[10]  Anne M.R. Agur,et al.  Grant's Atlas of Anatomy , 1943 .

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

[12]  R. Kohler.  A segmentation system based on thresholding , 1981 .

[13]  Yunmei Chen,et al.  Using Prior Shapes in Geometric Active Contours in a Variational Framework , 2002, International Journal of Computer Vision.

[14]  Michael Unser,et al.  Variational B-Spline Level-Set: A Linear Filtering Approach for Fast Deformable Model Evolution , 2009, IEEE Transactions on Image Processing.

[15]  Ron Kikinis,et al.  Improved watershed transform for medical image segmentation using prior information , 2004, IEEE Transactions on Medical Imaging.

[16]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Rolf Adams,et al.  Seeded Region Growing , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Nikos Paragios,et al.  Shape Priors for Level Set Representations , 2002, ECCV.

[19]  Allen R. Hanson,et al.  Segmenting images using localized histograms and region merging , 1987, International Journal of Computer Vision.

[20]  J. Sethian,et al.  A Fast Level Set Method for Propagating Interfaces , 1995 .

[21]  V. Caselles,et al.  A geometric model for active contours in image processing , 1993 .

[22]  Ron Kimmel,et al.  Numerical geometry of images - theory, algorithms, and applications , 2003 .

[23]  Purang Abolmaesumi,et al.  An estimation/correction algorithm for detecting bone edges in CT images , 2005, IEEE Transactions on Medical Imaging.

[24]  Tao Zhang,et al.  Active contours for tracking distributions , 2004, IEEE Transactions on Image Processing.

[25]  Ross T. Whitaker,et al.  A Level-Set Approach to 3D Reconstruction from Range Data , 1998, International Journal of Computer Vision.

[26]  Xose Manuel Pardo,et al.  A snake for CT image segmentation integrating region and edge information , 2001, Image Vis. Comput..

[27]  Tao Zhang,et al.  Model-based segmentation of medical imagery by matching distributions , 2005, IEEE Transactions on Medical Imaging.

[28]  Benjamin B. Kimia,et al.  Segmentation of carpal bones from CT images using skeletally coupled deformable models , 2003, Medical Image Anal..

[29]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[30]  Anthony J. Yezzi,et al.  A statistical approach to snakes for bimodal and trimodal imagery , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[31]  Randy E. Ellis,et al.  Validation of bone segmentation and improved 3-D registration using contour coherency in CT data , 2006, IEEE Transactions on Medical Imaging.