Sublabel-Accurate Relaxation of Nonconvex Energies

We propose a novel spatially continuous framework for convex relaxations based on functional lifting. Our method can be interpreted as a sublabel-accurate solution to multilabel problems. We show that previously proposed functional lifting methods optimize an energy which is linear between two labels and hence require (often infinitely) many labels for a faithful approximation. In contrast, the proposed formulation is based on a piecewise convex approximation and therefore needs far fewer labels. In comparison to recent MRF-based approaches, our method is formulated in a spatially continuous setting and shows less grid bias. Moreover, in a local sense, our formulation is the tightest possible convex relaxation. It is easy to implement and allows an efficient primal-dual optimization on GPUs. We show the effectiveness of our approach on several computer vision problems

High performance computing for a 3-D optical diffraction tomographic application in fluid velocimetry

Optical Diffraction Tomography has been recently introduced in fluid velocimetry to provide three dimensional information of seeding particle locations. In general, image reconstruction methods at visible wavelengths have to account for diffraction. Linear approximation has been used for three-dimensional image reconstruction, but a non-linear and iterative reconstruction method is required when multiple scattering is not negligible. Non-linear methods require the solution of the Helmholtz equation, computationally highly demanding due to the size of the problem. The present work shows the results of a non-linear method customized for spherical particle location using GPU computing and a made-to-measure storing format

Implementation of the conjugate gradient algorithm for heterogeneous systems

Lattice QCD calculations require significant computational effort, with the dominant fraction of resources typically spent in the numerical inversion of the Dirac operator. One of the simplest methods to solve such large and sparse linear systems is the conjugate gradient (CG) approach. In this work we present an implementation of CG that can be executed on different devices, including CPUs, GPUs, and FPGAs. This is achieved by using the SYCL/DPC++ framework, which allows the execution of the same source code on heterogeneous systems

Implementation of the conjugate gradient algorithm for heterogeneous systems

Lattice QCD calculations require significant computational effort, with the dominant fraction of resources typically spent in the numerical inversion of the Dirac operator. One of the simplest methods to solve such large and sparse linear systems is the conjugate gradient (CG) approach. In this work we present an implementation of CG that can be executed on different devices, including CPUs, GPUs, and FPGAs. This is achieved by using the SYCL/DPC++ framework, which allows the execution of the same source code on heterogeneous systems

Sparse approximate inverse preconditioners on high performance GPU platforms

Simulation with models based on partial differential equations often requires the solution of (sequences of) large and sparse algebraic linear systems. In multidimensional domains, preconditioned Krylov iterative solvers are often appropriate for these duties. Therefore, the search for efficient preconditioners for Krylov subspace methods is a crucial theme. Recent developments, especially in computing hardware, have renewed the interest in approximate inverse preconditioners in factorized form, because their application during the solution process can be more efficient. We present here some experiences focused on the approximate inverse preconditioners proposed by Benzi and Tůma from 1996 and the sparsification and inversion proposed by van Duin in 1999. Computational costs, reorderings and implementation issues are considered both on conventional and innovative computing architectures like Graphics Programming Units (GPUs)