The recently proposed tracking-learning-detection (TLD) method has become a popular visual tracking algorithm as it was shown to provide promising longterm tracking results. On the other hand, the high computational cost of the algorithm prevents it being used at higher resolutions and frame rates. In this paper, we describe the design and implementation of a heterogeneous CPU-GPU TLD (H-TLD) solution using OpenMP and CUDA. Leveraging the advantages of the heterogeneous architecture, serial parts are run asynchronously on the CPU while the most computationally costly parts are parallelized and run on the GPU. Design of the solution ensures keeping data transfers between CPU and GPU at a minimum and applying stream compaction and overlapping data transfer with computation whenever such transfers are necessary. The workload is balanced for a uniform work distribution across the GPU multiprocessors. Results show that 10.25 times speed-up is achieved at 1920 Â 1080 resolution compared to the baseline TLD. The source code has been made publicly available to download from the following address: http://gpuresearch.ii. metu.edu.tr/codes/.

Symmetry group is an important construct to understand the behaviour of a pure mathematical or a physical system including system of differential equations. We develop a framework that could learn continuous group symmetries governed by a given set of linear differential equations. The key idea in the proposed method is to build the symmetry group G by learning relevant exp() map, which is a crucial object in the study of Lie groups. exp() for G is learned in an implicit manner in terms of the vector fields spanning the associated Lie algebra g. In our experiments, we validate integrity of these learned vector fields by showing their generalization to various solution domains other than the one in which the model is trained. We also demonstrate the construction of a foreknown canonical vector field associated with G, which should remain in the span of g, from learned ones. These learned symmetries reveal the knowledge regarding global solution for a given set of differential equations as discussed in the article. The framework presents an optimal way to transform one solution for that set of differential equations to its another solution as well. This work is also an important step towards learning continuous group symmetries in other topological spaces as well as finding solutions without solving differential equations each time a new set of initial/boundary conditions are specified.