Modeling Multigrid Algorithms for Variational Imaging

Abstract

UML-based modeling is becoming increasingly popular in many software development projects. One of the key aspects is the possibility to support automatic code generation from UML models while keeping the easy to use modeling abstraction for the software developer. The framework Syntony has been developed to generate discrete-event simulations from standard-compliant UML models in order to support simulation based performance evaluation of systems. In this work, we discuss the extension of Syntony to include automatic code generation in the context of large scale continuous simulations that require the numerical solution of partial differential equations (PDE). We choose variational imaging as an example field, and multigrid as numerical solver. Multigrid algorithms exhibit a fixed sequential structure, where the single steps are problem dependent. Typically, they are implemented in C++, and may depend on special hardware since most of their applications require the solution of large numerical systems and therefore high computational performance. Using Syntony, we provide a modeling framework that can be extended to cover new applications by providing the basic modules and data structures in C++ and modeling the high-level algorithms and classes in UML class and activity diagrams. We evaluate the applicability of our approach in a case study for image denoising. The generated code is a fully working application that computes a denoised output image from a given input image using the methods specified in the UML model. The key benefit lies in the abstraction from low level programming for building complex denoising algorithms. In addition, we show that the code generation and compilation process runs significantly faster than the compilation of the entire framework. We also show that the run-time overhead introduced by the generated code is neglible.