General sweep mathematical morphology

General sweep mathematical morphology provides a new class of morphological operations, which allow one to select varying shapes and orientations of structuring elements during the sweeping process. Such a class holds syntactic characteristics similar to algebraic morphology as well as sweep geometric modeling. The conventional morphology is a subclass of the general sweep morphology. The sweep morphological dilation/erosion provides a natural representation of sweep motion in the manufacturing processes, and the sweep opening/closing provides variant degrees of smoothing in image filtering. The theoretical framework for representation, computation and analysis of sweep morphology is presented in this paper. Its applications to the sweeping with deformations, image enhancement, edge linking, and shortest path planning for rotating objects are also discussed.

[1]  Frank Y. Shih,et al.  Threshold Decomposition of Gray-Scale Morphology into Binary Morphology , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Aly A. Farag,et al.  Edge linking by sequential search , 1995, Pattern Recognit..

[3]  Frank Y. Shih.  Object representation and recognition using mathematical morphology model , 1991, J. Syst. Integr..

[4]  John C. Russ,et al.  The Image Processing Handbook , 2016, Microscopy and Microanalysis.

[5]  Alberto Martelli,et al.  An application of heuristic search methods to edge and contour detection , 1976, CACM.

[6]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[7]  Frank Y. Shih,et al.  Adaptive mathematical morphology for edge linking , 2004, Inf. Sci..

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

[9]  Roland T. Chin,et al.  Analysis of Thinning Algorithms Using Mathematical Morphology , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  M. Carter.  Computer graphics: Principles and practice , 1997 .

[11]  H. Elliott,et al.  Stochastic boundary estimation and object recognition , 1980 .

[12]  Yukinori Kakazu,et al.  RESEARCH ON 3-D GEOMETRIC MODELING BY SWEEP PRIMITIVES , 1982 .

[13]  Requicha,et al.  Solid Modeling: A Historical Summary and Contemporary Assessment , 1982, IEEE Computer Graphics and Applications.

[14]  Aristides A. G. Requicha,et al.  Representation of Tolerances in Solid Modeling: Issues and Alternative Approaches , 1984 .

[15]  G. Arce,et al.  Morphological filters: Statistics and further syntactic properties , 1987 .

[16]  Rafael C. González,et al.  Local Determination of a Moving Contrast Edge , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Shyang Chang,et al.  A shortest path algorithm for a nonrotating object among obstacles of arbitrary shapes , 1993, IEEE Trans. Syst. Man Cybern..

[18]  H. Voelcker,et al.  Solid modeling: current status and research directions , 1983, IEEE Computer Graphics and Applications.

[19]  Warren A. Hunt,et al.  The Role of Solid Modelling in Machining-Process Modelling and NC Verification , 1981 .

[20]  Jarek Rossignac.  CSG-BRep duality and compression , 2002, SMA '02.

[21]  Soo-Chang Pei,et al.  A morphological approach to shortest path planning for rotating objects , 1998, Pattern Recognit..

[22]  P. Eichel,et al.  A method for a fully automatic definition of coronary arterial edges from cineangiograms. , 1988, IEEE transactions on medical imaging.

[23]  Ralph R. Martin,et al.  Sweeping of three-dimensional objects , 1990, Comput. Aided Des..

[24]  Frank Y. Shih,et al.  The efficient algorithms for achieving Euclidean distance transformation , 2004, IEEE Transactions on Image Processing.

[25]  Vadim Shapiro,et al.  Boundary representation deformation in parametric solid modeling , 1998, TOGS.

[26]  ARISTIDES A. G. REQUICHA,et al.  Representations for Rigid Solids: Theory, Methods, and Systems , 1980, CSUR.

[27]  Ja-Ling Wu,et al.  Theoretical aspects of vertically invariant gray-level morphological operators and their application on adaptive signal and image filtering , 1999, IEEE Trans. Signal Process..

[28]  Xinhua Zhuang,et al.  Image Analysis Using Mathematical Morphology , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[29]  Ming C. Leu,et al.  Analysis and modelling of deformed swept volumes , 1994, Comput. Aided Des..

[30]  K. K. Wang,et al.  Geometric Modeling for Swept Volume of Moving Solids , 1986, IEEE Computer Graphics and Applications.

[31]  S. H. Park,et al.  Geometric Representation of Translational Swept Volumes and its Applications , 1986 .

[32]  Rodney A. Brooks,et al.  Symbolic Reasoning Among 3-D Models and 2-D Images , 1981, Artif. Intell..

[33]  Pijush K. Ghosh,et al.  A mathematical model for shape description using Minkowski operators , 1988, Comput. Vis. Graph. Image Process..

[34]  Aldo W. Morales,et al.  Statistical analysis of morphological openings , 1993, IEEE Trans. Signal Process..