Generalized Morphological 3D Shape Decomposition Grayscale Interframe Interpolation Method

Authors: Dragos Nicolae VIZIREANU

Abstract:

One of the main image representations in Mathematical Morphology is the 3D Shape Decomposition Representation, useful for Image Compression and Representation,and Pattern Recognition. The 3D Morphological Shape Decomposition representation can be generalized a number of times,to extend the scope of its algebraic characteristics as much as possible. With these generalizations, the Morphological Shape Decomposition 's role to serve as an efficient image decomposition tool is extended to grayscale images.This work follows the above line, and further develops it. Anew evolutionary branch is added to the 3D Morphological Shape Decomposition's development, by the introduction of a 3D Multi Structuring Element Morphological Shape Decomposition, which permits 3D Morphological Shape Decomposition of 3D binary images (grayscale images) into "multiparameter" families of elements. At the beginning, 3D Morphological Shape Decomposition representations are based only on "1 parameter" families of elements for image decomposition.This paper addresses the gray scale inter frame interpolation by means of mathematical morphology. The new interframe interpolation method is based on generalized morphological 3D Shape Decomposition. This article will present the theoretical background of the morphological interframe interpolation, deduce the new representation and show some application examples.Computer simulations could illustrate results.

Keywords: 3D shape decomposition representation, mathematical morphology, gray scale interframe interpolation

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1056635

References:

[1] A.G. Bors, L. Kechagias, I. Pitas, "Binary morphological shape-based interpolation applied to 3-D tooth reconstruction," IEEE Trans. on Medical Imaging, vol. 21, no. 2, pp. 100-109, 2002. ┬® IEEE.
[2] R. Kresch, D. Malah, "Morphological Multi-Structuring-Element Skeleton and its Applications'', Proc. of ISSSE'92, Paris, pp. 166-169, September 1992.
[3] R. Kresch, D. Malah, ``Multi-Parameter Skeleton Decomposition'', Proc. of the Intern. Symp. on Mathematical Morphology ISMM'94, J. Serra and P. Soille (eds.), pp.141- 148, September 1994.
[4] S. Beucher, "Sets, partitions and functions interpolations," in International Symposium on Mathematical Morphology and its Applications to Image and Signal Processing IV, Amsterdam, Netherlands, June 3-5, 1998, pp. 307-314.
[5] (2002/12) Tong-Yee Lee, Chao-Hung Lin, "Feature-guided Shape-based Image Interpolation, IEEE Transactions on Medical Imaging Dec. 2002 (SCI_16,EI) NSC-91-2213-E-006-078, Vol. 21, No. 12, pp. 1479-1489
[6] Vassilios Chatzis and Ioannis Pitas. Interpolation of 3d binary images based on morphological skeletonizations. In Proceedings IEEE International Conference on Multimedia Computing Systems, Florence, Italy, volume II, pages 939-943, June 1999.
[7] E.R. Dougherty and R.A. Lotufo. Hands-on Morphological Image Processingods in Imaging. SPIE Press, Bellingham, WA, 2003.
[8] Marcin Iwanowski and Jean Serra. Morphological interpolation and color images. In Proceedings of International Conference on Image Processing, Vennice, Italy, 1999.
[9] Tong-Yee Lee and Wen-Hsiu Wang. Morphology-based threedimensional interpolation. IEEE Transactions on Medical Imaging, 19(7):711-721, July 2000.
[10] Erik Meijering. A chronology of interpolation. from ancient astronomy to modern signal and image processing. Proceedinig of the IEEE, 90(3):319-342, March 2002.
[11] Jean Serra. Mathematical Morphology, volume II. London : Academic Press, 1988.
[12] Pierre Soille. Morphological Image Analysis: Principles and Applications. Springer-Verlag, 2nd edition edition, 2003.