Fractal Analysis of Bone Images
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
3D shape from focus using LULU operators and discrete pulse transform in the presence of noise
Journal of Visual Communication and Image Representation
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The aim of this paper is to find a relationship between alternating sequential filters (ASF) and the morphological sampling theorem (MST) developed by Haralick et al. (1987). The motivation behind this approach is to take advantage of the computational efficiency offered by the MST to implement morphological operations. First, we show alternative proofs for opening and closing in the sampled and unsampled domain using the basis functions. These proofs are important because they show that it possible to obtain any level of a morphological pyramid in one step rather than the traditional two-step procedure. This decomposition is then used to show the relationship of the open-closing in the sampled and unsampled domain. An upper and a lower bound, for the above relationships, are presented. Under certain circumstances, an equivalence is shown for open-closing between the sampled and the unsampled domain. An extension to more complicated algorithms using a union of openings and an intersection of closings is also proposed. Using the Hausdorff metric, it is shown that a morphologically reconstructed image cannot have a better accuracy than twice the radius of the reconstruction structuring element. Binary and gray scale examples are presented