With the continuous growth of sensor performances, image analysis and processing algorithms have to cope with larger and larger data volumes. Besides, the informative components of an image might not be the pixels themselves, but rather the objects they belong to. This has led to a wide range of successful multiscale techniques in image analysis and computer vision. Hierarchical representations are thus of first importance, and require efficient algorithms to be computed in order to address real-life applications. Among these hierarchical models, we focus on morphological trees (e.g., min/max-tree, tree of shape, binary partition tree, αtree) that come with interesting properties and already led to appropriate techniques for image processing and analysis, with a growing interest from the image processing community. More precisely, we build upon two recent algorithms for efficient α-tree computation and introduce several improvements to achieve higher performance. We also discuss the impact of the data structure underlying the tree representation, and provide for the sake of illustration several applications where efficient multiscale image representation leads to fast but accurate techniques, e.g. in remote sensing image analysis or video segmentation.
Ray-triangle intersection is an important algorithm, not only in the field of realistic rendering (based on ray tracing) but also in physics simulation, collision detection, modeling, etc. Obviously, the speed of this well-defined algorithm's implementations is important because calls to such a routine are numerous in rendering and simulation applications. Contemporary fast intersection algorithms, which use SIMD instructions, focus on the intersection of ray packets against triangles. For intersection between single rays and triangles, operations such as horizontal addition or dot product are required. The SSE4 instruction set adds the dot product instruction which can be used for this purpose. This paper presents a new modification of the fast ray-triangle intersection algorithms commonly used, which-when implemented on SSE4-outperforms the current state-of-the-art algorithms. It also allows both a single ray and ray packet intersection calculation with the same precomputed data. The speed gain measurements are described and discussed in the paper.
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