Hardware efficient PDE solvers in quantized image processing - Strzodka, Robert (2004)
Performance and accuracy of scientific computations are competing aspects. A close interplay between the design of computational schemes and their implementation can improve both aspects by making better use of the available resources. The thesis describes the design of robust schemes under strong quantization and their hardware efficient implementation on data-stream-based architectures for PDE based image processing. The strong quantization improves execution time, but renders traditional error estimates useless. The precision of the number formats is too small to control the quantitative error in iterative schemes. Instead, quantized schemes which preserve the qualitative behavior of the continuous models are constructed. In particular for the solution of the quantized anisotropic diffusion model one can derive a quantized scale-space with almost identical properties to the continuous one. Thus the image evolution is accurately reconstructed despite the inability to control the error in the long run, which is difficult even for high precision computations ...
Keywords: Hochschulschrift; Programmierbare logische Anordnung; Grafik-Hardware; Numerisches Verfahren; Partielle Differentialgleichung; Bildverarbeitung