A New Morphological 3D Shape Decomposition: Grayscale Interframe Interpolation Method

One of the main image representations in Mathematical Morphology is the 3D Shape Decomposition Representation, useful for Image Compression, 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 was extended to discrete images and grayscale images. This work follows the above line, and further develops it. A new 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 iamges) 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 interframe interpolation by means of mathematical morphology. The new interframe interpolation method, called 3D Shape Decomposition interpolation is based on 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.