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    Groupoids, Frobenius algebras and Poisson sigma models

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    In this paper we discuss some connections between groupoids and Frobenius algebras specialized in the case of Poisson sigma models with boundary. We prove a correspondence between groupoids in the category Set and relative Frobenius algebras in the category Rel, as well as an adjunction between a special type of semigroupoids and relative H*-algebras. The connection between groupoids and Frobenius algebras is made explicit by introducing what we called weak monoids and relational symplectic groupoids, in the context of Poisson sigma models with boundary and in particular, describing such structures in the ex- tended symplectic category and the category of Hilbert spaces. This is part of a joint work with Alberto Cattaneo and Chris Heunen.Comment: 12 pages, 1 figure. To appear in "Mathematical Aspects of Quantum Field Theories". Mathematical Physical Studies, Springer. Proceedings of the Winter School in Mathematical Physics, Les Houges, 201

    Design of an FPGA-based smart camera and its application towards object tracking : a thesis presented in partial fulfilment of the requirements for the degree of Master of Engineering in Electronics and Computer Engineering at Massey University, Manawatu, New Zealand

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    Smart cameras and hardware image processing are not new concepts, yet despite the fact both have existed several decades, not much literature has been presented on the design and development process of hardware based smart cameras. This thesis will examine and demonstrate the principles needed to develop a smart camera on hardware, based on the experiences from developing an FPGA-based smart camera. The smart camera is applied on a Terasic DE0 FPGA development board, using Terasic’s 5 megapixel GPIO camera. The algorithm operates at 120 frames per second at a resolution of 640x480 by utilising a modular streaming approach. Two case studies will be explored in order to demonstrate the development techniques established in this thesis. The first case study will develop the global vision system for a robot soccer implementation. The algorithm will identify and calculate the positions and orientations of each robot and the ball. Like many robot soccer implementations each robot has colour patches on top to identify each robot and aid finding its orientation. The ball is comprised of a single solid colour that is completely distinct from the colour patches. Due to the presence of uneven light levels a YUV-like colour space labelled YC1C2 is used in order to make the colour values more light invariant. The colours are then classified using a connected components algorithm to segment the colour patches. The shapes of the classified patches are then used to identify the individual robots, and a CORDIC function is used to calculate the orientation. The second case study will investigate an improved colour segmentation design. A new HSY colour space is developed by remapping the Cartesian coordinate system from the YC1C2 to a polar coordinate system. This provides improved colour segmentation results by allowing for variations in colour value caused by uneven light patterns and changing light levels
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