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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)
Osteoporosis is a disease characterized by bone volume loss and architectural deterioration. The majority of work aimed at evaluating the structural implications of the disease has been performed based on stereologic analysis of histomorphometric sections. Only recently noninvasive imaging methods have emerged that provide sufficient resolution to resolve(More)
PURPOSE To explore the potential role of micro-magnetic resonance imaging (micro-MRI) for quantifying trabecular and cortical bone structural parameters in renal osteodystrophy (ROD), a multifactorial disorder of bone metabolism, traditionally evaluated by bone biopsy. MATERIALS AND METHODS Seventeen hemodialysis patients (average PTH level = 502 +/- 415(More)
Bone strength depends on trabecular architecture, characterized by interconnected plates and rods. In osteoporosis, the plates become fenestrated, resulting in more rods that deteriorate and become disconnected. In men, hypogonadism is a common cause of osteoporosis. To determine whether male hypogonadism affects trabecular architecture, we selected 10 men(More)
UNLABELLED We evaluated the effect of testosterone treatment on trabecular architecture by microMRI in 10 untreated severely hypogonadal men. After 2 years, microMRI parameters of trabecular connectivity improved significantly, suggesting the possibility that testosterone improves trabecular architecture. INTRODUCTION Osteoporosis, characterized by low(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)
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)
The strength of trabecular bone and its resistance to fracture traditionally have been associated with apparent density. This paradigm assumes that neither the ultrastructural nor microstructural make-up of the bone is altered during aging and osteoporosis. During the past decade there has been growing evidence from both laboratory and clinical studies(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)
Quantitative magnetic resonance imaging (QMRI) allows measurement of two parameters that are related to the integrity of the trabecular bone: R2*, the rate constant of the free induction signal, and trabecular bone volume fraction (BVF), the counterpart of apparent density. In this work, R2* and BVF were measured in 68 women (mean age, 58.2 +/- 9.5 years)(More)