Runtime analysis of spatial structure: a CUDA implementation of Minkowski functionals

A known limitation of GPGPU applied to spatially discretised simulation models is the frequency of device-host data transfers necessary to capture events of interest or otherwise provide sufficiently dense data for the robust analysis of evolving state. To reduce this burden, run-time analysis tools executing on the GPU are developed to characterise the spatio-temporal evolution of structure within 3D scalar fields. The Minkowski Functionals (Matheron, 1967) are fundamentally important measures of spatial structure and are used in diverse science and engineering domains (e.g. geoscience, materials science, cosmology and healthcare). The 3D Minkowski Functionals (henceforth MF's) consist of four measures: Volume, Surface-area, Integral Mean Curvature and Total (Gaussian) Curvature. These measures together describe the geometric and topological properties of objects in 3D space. MF’s are computed efficiently from a binary image (where each binary element defines set membership: object vs. background) this image being determined from one or more scalar fields using, in many cases, a simple threshold operation. From the binary image a Binary Pattern Frequency Distribution is determined: this compactly represents the spatial structure information as 256 patterns and has the advantage of being additive such that an image can be subdivided, BPFD's calculated independently for the parts and then summed to give the complete information.

Interested in characterising spatial structure inherent in 3D scalar fields from simulated or imaged data? This poster presents an accelerated solution of the widely used Minkowski Functionals using both OpenACC and CUDA on commodity GPUs. Methods to minimise the memory footprint and hence reduce data transfer costs are presented. Based on measurement frequency an OpenACC rather than a CUDA solution might be appropriate. Next steps highlight the additional methods to further enhance and fine tune the performance of the CUDA solution. Minkowski Functionals have been widely applied in Cosmology, Material Science, Engineering, Microbial Ecology and Healthcare.