The geometry of fractal sets
Computer Vision, Graphics, and Image Processing
Practical numerical algorithms for chaotic systems
Practical numerical algorithms for chaotic systems
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multiscanning Approach Based on Morphological Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Properties of the Multiscale Morphological Dilation-Erosion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer rendering of stochastic models
Communications of the ACM
MiniMax Methods for Image Reconstruction
MiniMax Methods for Image Reconstruction
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological pyramids with alternating sequential filters
IEEE Transactions on Image Processing
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Abstract: Osteoporosis, an age related bone disorder, is a major health concern in the United States and worldwide. Most of the current techniques to monitor bone condition use bone mass measurements. However, bone mass measurements do not completely describe the mechanisms to distinguish between osteoporotic and normal subjects. Structural parameters such as trabecular connectivity have been proposed as features for assessing bone conditions. As such structure can be seen as an important feature in assessing bone condition. In this article, the trabecular structure is characterized with the aid of the fractal dimension. Existent fractal dimension estimation approaches assume the image to be a fractional Brownian motion process. Also, these methods fail when applied to small image samples. A new approach called continuous alternating sequential filter pyramid-based fractal dimension estimation is presented. This approach assumes only the self-similarity property of fractals, and is applicable to small image sizes, as such it is less constrained. Experimental results demonstrate the efficacy of the fractal dimension model in discriminating normal from osteoporosis cases. The methodology was employed on animal models of osteoporosis and on human data.