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This paper describes the theory and algorithms of distance transform for fuzzy subsets, called fuzzy distance transform (FDT). The notion of fuzzy distance is formulated by first defining the length of a path on a fuzzy subset and then finding the infimum of the lengths of all paths between two points. The length of a path π in a fuzzy subset of the… (More)

Cancellous bone consists of a network of bony struts and plates that provide mechanical strength to much of the skeleton at minimum weight. It has been shown that loss in bone mass is accompanied by architectural changes that relate to both scale and topology of the network. In this paper, the concept of three-dimensional (3D) digital topology is presented… (More)

Recently, imaging techniques have become available which permit nondestructive analysis of the three-dimensional (3-D) architecture of trabecular bone (TB), which forms a network of interconnected plates and rods. Most osteoporotic fractures occur at locations rich in TB, which has spurred the search for architectural parameters as determinants of bone… (More)

After bone mineral density, orientation is the major determinant of trabecular bone strength and is thus of significant interest in understanding the clinical implications of osteoporotic bone loss. The methods used to measure orientation and anisotropy of the trabecular bone have largely relied on deriving global measures along test lines, computing the… (More)

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