In this paper, we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field. Our method uses Lagrangian marker particles to rebuild the level set in regions which are under-resolved. This is often the case for flows undergoing stretching and tearing. The overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method. Our method compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution. The method is presented in three spatial dimensions.

In this paper, we present an efficient semi-Lagrangian based particle level set method for the accurate capturing of interfaces. This method retains the robust topological properties of the level set method without the adverse effects of numerical dissipation. Both the level set method and the particle level set method typically use high order accurate numerical discretizations in time and space, e.g. TVD RungeKutta and HJ-WENO schemes. We demonstrate that these computationally expensive schemes are not required. Instead, fast, low order accurate numerical schemes suffice. That is, the addition of particles to the level set method not only removes the difficulties associated with numerical diffusion, but also alleviates the need for computationally expensive high order accurate schemes. We use an efficient, first order accurate semi-Lagrangian advection scheme coupled with a first order accurate fast marching method to evolve the level set function. To accurately track the underlying flow characteristics, the particles are evolved with a second order accurate method. Since we avoid complex high order accurate numerical methods, extending the algorithm to arbitrary data structures becomes more feasible, and we show preliminary results obtained with an octree-based adaptive mesh.

We present a new method for the animation and rendering of photorealistic water effects. Our method is designed to produce visually plausible three dimensional effects, for example the pouring of water into a glass (see figure 1) and the breaking of an ocean wave, in a manner which can be used in a computer animation environment. In order to better obtain photorealism in the behavior of the simulated water surface, we introduce a new "thickened" front tracking technique to accurately represent the water surface and a new velocity extrapolation method to move the surface in a smooth, water-like manner. The velocity extrapolation method allows us to provide a degree of control to the surface motion, e.g. to generate a windblown look or to force the water to settle quickly. To ensure that the photorealism of the simulation carries over to the final images, we have integrated our method with an advanced physically based rendering system.

In the last few years, a variety of multicore architectures have been used to parallelize image processing applications. In this paper, we focus on assessing the parallel speed-ups of different Canny edge detection parallelization strategies on the Tile64, a tiled multicore architecture developed by the Tilera Corporation. Included in these strategies are different ways Canny edge detection can be parallelized, as well as differences in data management. The two parallelization strategies examined were loop-level parallelism and domain decomposition. Loop-level parallelism is achieved through the use of OpenMP, 1 and it is capable of parallelization across the range of values over which a loop iterates. Domain decomposition is the process of breaking down an image into subimages, where each subimage is processed independently, in parallel. The results of the two strategies show that for the same number of threads, programmer implemented, domain decomposition exhibits higher speed-ups than the compiler managed, loop-level parallelism implemented with OpenMP.

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