Semivariogram Analysis of Bone Images Implemented on FPGA Architectures

Osteoporotic fractures are a major concern for the healthcare of elderly and female populations. Early diagnosis of patients with a high risk of osteoporotic fractures can be enhanced by introducing second-order statistical analysis of bone image data using techniques such as variogram analysis. Such analysis is computationally intensive thereby creating an impediment for introduction into imaging machines found in common clinical settings. This paper investigates the fast implementation of the semivariogram algorithm, which has been proven to be effective in modeling bone strength, and should be of interest to readers in the areas of computer-aided diagnosis and quantitative image analysis. The semivariogram is a statistical measure of the spatial distribution of data, and is based on Markov Random Fields (MRFs). Semivariogram analysis is a computationally intensive algorithm that has typically seen applications in the geosciences and remote sensing areas. Recently, applications in the area of medical imaging have been investigated, resulting in the need for efficient real time implementation of the algorithm. A semi-variance, γ(h), is defined as the half of the expected squared differences of pixel values between any two data locations with a lag distance of h. Due to the need to examine each pair of pixels in the image or sub-image being processed, the base algorithm complexity for an image window with n pixels is O (n²) Field Programmable Gate Arrays (FPGAs) are an attractive solution for such demanding applications due to their parallel processing capability. FPGAs also tend to operate at relatively modest clock rates measured in a few hundreds of megahertz. This paper presents a technique for the fast computation of the semivariogram using two custom FPGA architectures. A modular architecture approach is chosen to allow for replication of processing units. This allows for high throughput due to concurrent processing of pixel pairs. The current implementation is focused on isotropic semivariogram computations only. The algorithm is benchmarked using VHDL on a Xilinx XUPV5-LX110T development Kit, which utilizes the Virtex5 FPGA. Medical image data from DXA scans are utilized for the experiments. Implementation results show that a significant advantage in computational speed is attained by the architectures with respect to implementation on a personal computer with an Intel i7 multi-core processor.