A Survey on Skeletons in Digital Image Processing

An image is digitized to convert it to a form which can be stored in a computer's memory or on some form of storage media such as a hard disk or CD-ROM. Once the image has been digitized, it can be operated upon by various image processing operations like enhancement, restoration, reconstruction, compression. An image defined in the "real world" is considered to be a function of two real variables, for example, a(x,y) with a as the amplitude (e.g. brightness) of the image at the real coordinate position (x,y). An image may be considered to contain sub-images sometimes referred to as regions-of-interest, ROIs, or simply regions. This concept reflects the fact that images frequently contain collections of objects each of which can be the basis for a region. In a sophisticated image processing system it should be possible to apply specific image processing operations to selected regions. Thus one part of an image (region) might be processed to suppress motion blur while another part might be processed to improve color rendition. For performing image processing operations ,the basic structure called skeleton is much more essential and highly adaptive tool. Skeletons are important shape descriptors in object representation and recognition. A skeleton that captures essential topology and shape information of the object in a simple form is extremely useful in solving various problems such as character recognition, 3D model matching and retrieval, and medical image analysis. Medical imaging systems. Due to its compact shape representation, image skeleton has been studied for a long time in computer vision, pattern recognition, and optical character recognition. It is a powerful tool for intermediate representation for a number of geometric operations on solid models. Many image processing applications depend on the skeletons.

[1]  Martin D. Levine,et al.  3D part segmentation using simulated electrical charge distributions , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[2]  Geoff Wyvill,et al.  The 'thermodynamics' of shape , 2001, Proceedings International Conference on Shape Modeling and Applications.

[3]  Ross T. Whitaker,et al.  Partitioning 3D Surface Meshes Using Watershed Segmentation , 1999, IEEE Trans. Vis. Comput. Graph..

[4]  Anne Verroust-Blondet,et al.  Extracting skeletal curves from 3D scattered data , 2000, The Visual Computer.

[5]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[6]  Marco Attene,et al.  Re-meshing techniques for topological analysis , 2001, Proceedings International Conference on Shape Modeling and Applications.

[7]  Tamal K. Dey,et al.  Approximate medial axis as a voronoi subcomplex , 2002, SMA '02.

[8]  Stephen M. Pizer,et al.  Zoom-Invariant Vision of Figural Shape: Effects on Cores of Image Disturbances , 1998, Comput. Vis. Image Underst..

[9]  Nancy M. Amato,et al.  Approximate convex decomposition , 2004, SCG '04.

[10]  Son Tran,et al.  Efficient 3D binary image skeletonization , 2005, 2005 IEEE Computational Systems Bioinformatics Conference - Workshops (CSBW'05).

[11]  Franz Aurenhammer,et al.  A Novel Type of Skeleton for Polygons , 1995, J. Univers. Comput. Sci..

[12]  Dominique Attali,et al.  Computing and Simplifying 2D and 3D Continuous Skeletons , 1997, Comput. Vis. Image Underst..

[13]  Gilles Bertrand,et al.  A simple parallel 3D thinning algorithm , 1990, [1990] Proceedings. 10th International Conference on Pattern Recognition.

[14]  Philip M. Hubbard,et al.  Approximating polyhedra with spheres for time-critical collision detection , 1996, TOGS.

[15]  Dominique Attali Squelettes et graphes de Voronoï 2D et 3D. (2D and 3D skeletons and Voronoi graphs) , 1995 .

[16]  Antoine Vigneron,et al.  Motorcycle Graphs and Straight Skeletons , 2002, SODA '02.

[17]  V. Ralph Algazi,et al.  Continuous skeleton computation by Voronoi diagram , 1991, CVGIP Image Underst..

[18]  Franz Aurenhammer,et al.  Straight Skeletons for General Polygonal Figures in the Plane , 1996, COCOON.

[19]  David Eppstein,et al.  Raising roofs, crashing cycles, and playing pool: applications of a data structure for finding pairwise interactions , 1998, SCG '98.

[20]  Steve Capell,et al.  Interactive skeleton-driven dynamic deformations , 2002, ACM Trans. Graph..

[21]  Benjamin B. Kimia,et al.  Computation of the shock scaffold for unorganized point clouds in 3D , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[22]  Stephen M. Pizer,et al.  Object representation by cores: Identifying and representing primitive spatial regions , 1995, Vision Research.

[23]  Gunilla Borgefors,et al.  Distance transformations in digital images , 1986, Comput. Vis. Graph. Image Process..

[24]  Per-Erik Danielsson,et al.  Finding the Minimal Set of Maximum Disks for Binary Objects , 1997, CVGIP Graph. Model. Image Process..

[25]  Mie Sato,et al.  Penalized-Distance Volumetric Skeleton Algorithm , 2001, IEEE Trans. Vis. Comput. Graph..

[26]  Benjamin B. Kimia,et al.  3D Object Recognition Using Shape Similarity-Based Aspect Graph , 2001, ICCV.

[27]  Tamal K. Dey,et al.  Approximate medial axis as a voronoi subcomplex , 2002, SMA '02.

[28]  Nina Amenta,et al.  Finding Alpha-Helices in Skeletons , 2002 .

[29]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[30]  Ayellet Tal,et al.  Hierarchical mesh decomposition using fuzzy clustering and cuts , 2003, ACM Trans. Graph..

[31]  Edward R. Dougherty,et al.  An introduction to morphological image processing , 1992 .

[32]  Jean-Daniel Boissonnat,et al.  Stability and Computation of Medial Axes - a State-of-the-Art Report , 2009, Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration.

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

[34]  Gérard G. Medioni,et al.  Part decomposition and description of 3D shapes , 1994, Proceedings of 12th International Conference on Pattern Recognition.

[35]  R. Brubaker Models for the perception of speech and visual form: Weiant Wathen-Dunn, ed.: Cambridge, Mass., The M.I.T. Press, I–X, 470 pages , 1968 .

[36]  André Lieutier,et al.  Any open bounded subset of Rn has the same homotopy type than its medial axis , 2003, SM '03.

[37]  Olaf Kübler,et al.  Hierarchic Voronoi skeletons , 1995, Pattern Recognit..

[38]  Hans-Peter Seidel,et al.  Linear one-sided stability of MAT for weakly injective 3D domain , 2004, Comput. Aided Des..

[39]  B. Kimia,et al.  3D object recognition using shape similiarity-based aspect graph , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[40]  Stephen M. Pizer,et al.  M-Reps: A New Object Representation for Graphics , 1999 .

[41]  Tiow Seng Tan,et al.  Decomposing polygon meshes for interactive applications , 2001, I3D '01.

[42]  Giuseppe Patanè,et al.  Shape-Covering for Skeleton Extraction , 2002, Int. J. Shape Model..

[43]  Dinesh Manocha,et al.  Exact computation of the medial axis of a polyhedron , 2004, Comput. Aided Geom. Des..

[44]  Arie E. Kaufman,et al.  Alias-Free Voxelization of Geometric Objects , 1999, IEEE Trans. Vis. Comput. Graph..

[45]  Jen-Hui Chuang,et al.  Skeletonization of Three-Dimensional Object Using Generalized Potential Field , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

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

[47]  David H. Eberly,et al.  Zoom-Invariant Vision of Figural Shape: The Mathematics of Cores , 1996, Comput. Vis. Image Underst..

[48]  Pedro V. Sander,et al.  Multi-Chart Geometry Images , 2003, Symposium on Geometry Processing.

[49]  Markus Ilg,et al.  Voronoi skeletons: theory and applications , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[50]  Carol O'Sullivan,et al.  Sphere-tree construction using dynamic medial axis approximation , 2002, SCA '02.

[51]  Marko Subasic,et al.  Level Set Methods and Fast Marching Methods , 2003 .

[52]  Azriel Rosenfeld,et al.  Digital topology: Introduction and survey , 1989, Comput. Vis. Graph. Image Process..

[53]  Seth J. Teller,et al.  Assisted articulation of closed polygonal models , 1998, SIGGRAPH '98.

[54]  Ali Shokoufandeh,et al.  Shock Graphs and Shape Matching , 1998, International Journal of Computer Vision.

[55]  Tsai-Yen Li,et al.  Automatically generating virtual guided tours , 1999, Proceedings Computer Animation 1999.

[56]  Sunghee Choi,et al.  The power crust , 2001, SMA '01.

[57]  Tosiyasu L. Kunii,et al.  Surface coding based on Morse theory , 1991, IEEE Computer Graphics and Applications.

[58]  Damian J. Sheehy,et al.  Shape Description By Medial Surface Construction , 1996, IEEE Trans. Vis. Comput. Graph..

[59]  Dominique Attali,et al.  Using polyballs to approximate shapes and skeletons , 1994, Proceedings of 12th International Conference on Pattern Recognition.

[60]  Adam Krzyzak,et al.  Piecewise Linear Skeletonization Using Principal Curves , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[61]  Tosiyasu L. Kunii,et al.  Constructing a Reeb graph automatically from cross sections , 1991, IEEE Computer Graphics and Applications.

[62]  Szymon Rusinkiewicz,et al.  Modeling by example , 2004, SIGGRAPH 2004.

[63]  Taku Komura,et al.  Topology matching for fully automatic similarity estimation of 3D shapes , 2001, SIGGRAPH.

[64]  Arthur W. Toga,et al.  Efficient Skeletonization of Volumetric Objects , 1999, IEEE Trans. Vis. Comput. Graph..

[65]  Sunghee Choi,et al.  The power crust, unions of balls, and the medial axis transform , 2001, Comput. Geom..

[66]  Tamal K. Dey,et al.  Shape Segmentation and Matching with Flow Discretization , 2003, WADS.

[67]  Ming Ouhyoung,et al.  Skeleton Extraction of 3D Objects with Visible Repulsive Force , 2003 .

[68]  Azriel Rosenfeld,et al.  Sequential Operations in Digital Picture Processing , 1966, JACM.

[69]  Jacques-Olivier Lachaud,et al.  Delaunay conforming iso-surface, skeleton extraction and noise removal , 2001, Comput. Geom..

[70]  Deborah Silver,et al.  Curve-Skeleton Properties, Applications, and Algorithms , 2007, IEEE Trans. Vis. Comput. Graph..