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    Improving Shadow Map Filtering with Statistical Analysis
    (The Eurographics Association, 2011) Gumbau, Jesus; Szirmay-Kalos, László; Sbert, Mateu; Sellés, Miguel Chover; N. Avis and S. Lefebvre
    Shadow maps are widely used in real-time applications. Shadow maps cannot be filtered linearly as regular textures, thus undersampling leads to severe aliasing. This problem has been attacked by methods that transform the depth values to allow approximate linear filtering and to approaches based on statistical analysis, which suffer from light bleeding artifacts. In this paper we propose a new statistical filtering method for shadow maps, which approximates the cumulative distribution function (CDF) of depths with a power function. This approximation significantly reduces light bleeding artifacts, maintaining performance and spatial costs. Like existing techniques, the algorithm is easy to implement on the graphics hardware and is fairly scalable.
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    Crystal Scattering Simulation for PET on the GPU
    (The Eurographics Association, 2011) Magdics, Milán; Szirmay-Kalos, László; N. Avis and S. Lefebvre
    This paper presents a fast algorithm to simulate inter-crystal scattering to increase the accuracy of Positron Emission Tomography (PET). Theoretically, inter-crystal scattering computation would require the solution of a particle transport problem, which is quite time consuming. However, most of this calculation can be ported to a pre-processing phase, taking advantage of the fact that the structure of the detector is fixed. Pre-computing the scattering probabilities inside the crystals, the final system response is the convolution of the geometric response obtained with the assumption that crystals are ideal absorbers and the crystal transport probability matrix. This convolution is four-dimensional which poses complexity problems as the complexity of the naive convolution evaluation grows exponentially with the dimension of the domain. We use Monte Carlo method to attack the curse of dimension. We demonstrate that these techniques have just negligible overhead.