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. The semivariogram is a plot of semivariances for different lag distances between pixels. 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, but they can perform tens of thousands of calculations per clock cycle while operating in the low range of power. This paper presents a technique for the fast computation of the semivariogram using two custom FPGA architectures. The design consists of several modules dedicated to the constituent computational tasks. 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. Anisotropic semivariogram implementation is anticipated to be an extension of the current architecture, ostensibly based on refinements to the current modules. The algorithm is benchmarked using VHDL on a Xilinx XUPV5-LX110T development Kit, which utilizes the Virtex5 FPGA. Medical image data from MRI scans are utilized for the experiments. Computational speedup is measured with respect to Matlab implementation on a personal computer with an Intel i7 multi-core processor. Preliminary simulation results indicate that a significant advantage in speed can be attained by the architectures, making the algorithm viable for implementation in medical devices

Date Published: 27 February 2015
PDF: 10 pages
Proc. SPIE 9400, Real-Time Image and Video Processing 2015, 940005 (27 February 2015); doi: 10.1117/12.2077851

Published in SPIE Proceedings Vol. 9400:
Real-Time Image and Video Processing 2015
Nasser Kehtarnavaz; Matthias F. Carlsohn, Editor(s)