A New Fuzzy Skeletonization Algorithm and Its Applications to Medical Imaging

Skeletonization provides a simple yet compact representation of an object and is widely used in medical imaging applications including volumetric, structural, and topological analyses, object representation, stenoses detection, path-finding etc. Literature of three-dimensional skeletonization is quite matured for binary digital objects. However, the challenges of skeletonization for fuzzy objects are mostly unanswered. Here, a framework and an algorithm for fuzzy surface skeletonization are developed using a notion of fuzzy grassfire propagation which will minimize binarization related data loss. Several concepts including fuzzy axial voxels, local and global significance factors are introduced. A skeletal noise pruning algorithm using global significance factors as significance measures of individual branches is developed. Results of application of the algorithm on several medical objects have been illustrated. A quantitative comparison with an ideal skeleton has demonstrated that the algorithm can achieve sub-voxel accuracies at various levels of noise and downsampling. The role of fuzzy skeletonization in thickness computation at relatively low resolution has been demonstrated.

[1]  Punam K. Saha,et al.  Three‐dimensional digital topological characterization of cancellous bone architecture , 2000 .

[2]  Bidyut Baran Chaudhuri,et al.  Detection of 3-D Simple Points for Topology Preserving Transformations with Application to Thinning , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Bidyut Baran Chaudhuri,et al.  A new shape preserving parallel thinning algorithm for 3D digital images , 1997, Pattern Recognit..

[4]  Punam K. Saha,et al.  Fuzzy Distance Transform: Theory, Algorithms, and Applications , 2002, Comput. Vis. Image Underst..

[5]  Zhengrong Liang,et al.  Automatic centerline extraction for virtual colonoscopy , 2002, IEEE Transactions on Medical Imaging.

[6]  Gabriella Sanniti di Baja.  Well-Shaped, Stable, and Reversible Skeletons from the (3, 4)-Distance Transform , 1994, J. Vis. Commun. Image Represent..

[7]  Azriel Rosenfeld,et al.  Image enhancement and thresholding by optimization of fuzzy compactness , 1988, Pattern Recognit. Lett..

[8]  T. Saito,et al.  A sequential thinning algorithm for three dimensional digital pictures using the Euclidean distance transformation , 1995 .

[9]  Punam K. Saha,et al.  Measurement of trabecular bone thickness in the limited resolution regime of in vivo MRI by fuzzy distance transform , 2004, IEEE Transactions on Medical Imaging.

[10]  Gabriella Sanniti di Baja,et al.  A Width-Independent Fast Thinning Algorithm , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Paul A. Yushkevich,et al.  Segmentation, registration, and measurement of shape variation via image object shape , 1999, IEEE Transactions on Medical Imaging.

[12]  King-Sun Fu,et al.  A parallel thinning algorithm for 3-D pictures , 1981 .

[13]  Sankar K. Pal.  Fuzzy skeletonization of an image , 1989, Pattern Recognit. Lett..

[14]  Gabriella Sanniti di Baja,et al.  Distance-Driven Skeletonization in Voxel Images , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Stina Svensson.  Aspects on the reverse fuzzy distance transform , 2008, Pattern Recognit. Lett..

[16]  Gabriella Sanniti di Baja,et al.  Discrete 3D Tools Applied to 2D Grey-Level Images , 2005, ICIAP.

[17]  Punam K. Saha,et al.  Volumetric Topological Analysis: A Novel Approach for Trabecular Bone Classification on the Continuum Between Plates and Rods , 2010, IEEE Transactions on Medical Imaging.

[18]  Milan Sonka,et al.  A Fully Parallel 3D Thinning Algorithm and Its Applications , 1996, Comput. Vis. Image Underst..

[19]  Ronald M. Summers,et al.  Grey-Scale Skeletonization of Small Vessels in Magnetic Resonance Angiography , 2000, IEEE Trans. Medical Imaging.