The knowledge of thresholding and gradient at different tissue interfaces is of paramount interest in image segmentation and other imaging methods and applications. Most thresholding and gradient selection methods primarily focus on image histograms and therefore, fail to harness the information generated by intensity patterns in an image. We present a new thresholding and gradient optimization method which accounts for spatial arrangement of intensities forming different objects in an image. Specifically, we recognize object class uncertainty, a histogram-based feature, and formulate an energy function based on its correlation with image gradients that characterizes the objects and shapes in a given image. Finally, this energy function is used to determine optimum thresholds and gradients for various tissue interfaces. The underlying theory behind the method is that objects manifest themselves with fuzzy boundaries in an acquired image and that, in a probabilistic sense; intensities with high class uncertainty are associated with high image gradients generally indicating object/tissue interfaces. The new method simultaneously determines optimum values for both thresholds and gradient parameters at different object/tissue interfaces. The method has been applied on several 2D and 3D medical image data sets and it has successfully determined both thresholds and gradients for different tissue interfaces even when some of the thresholds are almost impossible to locate in their histograms. The accuracy and reproducibility of the method has been examined using 3D multi-row detector computed tomography images of two cadaveric ankles each scanned thrice with repositioning the specimen between two scans.

Osteoporosis is a common bone disease that increases risk of low-trauma fractures associated with substantial morbidity, mortality, and financial costs. Clinically, osteoporosis is defined by low bone mineral density (BMD). BMD explains approximately 60-70% of the variance in bone strength. The remainder is due to the cumulative and synergistic effects of other factors, including trabecular and cortical bone micro-architecture. In vivo quantitative characterization of trabecular bone (TB) micro-architecture with high accuracy, reproducibility, and sensitivity to bone strength will improve our understanding of bone loss mechanisms and etiologies benefitting osteoporotic diagnostics and treatment monitoring processes. The overall aim of the Ph.D. research is to design, develop and evaluate new 3-D imaging processing algorithms to characterize the quality of TB micro-architectural in terms of topology, orientation, thickness and spacing, and to move the new technology from investigational research into the clinical arena. Two algorithms regarding to this purpose were developed and validated in detail - (1) star-line-based TB thickness and marrow spacing computation algorithm, and (2) tensor scale (t-scale) based TB topology and orientation computation algorithm. The TB thickness and marrow spacing algorithm utilizes a star-line tracing technique that effectively accounts for partial voluming effects of in vivo imaging with voxel size comparable to TB thickness and also avoids the problem of digitization associated with conventional algorithms. Accuracy of the method was examined on computer-generated phantom images while the robustness of the method was evaluated on human ankle specimens in terms of stability across a wide range of resolutions, repeat scan reproducibility under in vivo condition, and correlation between thickness values computed at ex vivo and in vivo resolutions. Also, the sensitivity of the method was examined by its ability to predict bone strength of cadaveric specimens. Finally, the method was evaluated in an in vivo human study involving forty healthy young-adult volunteers and ten athletes. The t-scale based TB topology and orientation computation algorithm provides measures characterizing individual trabeculae on the continuum between perfect plate and perfect rod as well as individual trabecular orientation. Similar to the TB thickness and marrow spacing computation algorithm, accuracy was examined on computer-generated phantoms while robustness of the algorithm across ex vivo and in vivo resolution, repeat scan reproducibility, and the sensitivity to experimental mechanical bone strength were evaluated in a cadaveric ankle study. And the application of the algorithm was evaluated in a human study involving forty healthy young-adult volunteers and ten patients with SSRI treatment. Beside these two algorithms, an image thresholding algorithm based on the class uncertainty theory is developed to segment TB structure in CT images. Although the algorithm was developed for this specific application, it also works effectively for general 2-D and 3-D images. Moreover, the class uncertainty theory can be utilized as adaptive information in more sophisticated image processing algorithms such as Snakes, ASMs and graph search.