%0 Journal Article
%J Graphical Models
%D 2011
%T Dimension-independent simplification and refinement of Morse complexes
%A Čomić,Lidija
%A De Floriani, Leila
%K Morse complexes
%K Morse theory
%K Refinement
%K shape modeling
%K simplification
%K Topological representations
%X Ascending and descending Morse complexes, determined by a scalar field f defined over a manifold M, induce a subdivision of M into regions associated with critical points of f, and compactly represent the topology of M. We define two simplification operators on Morse complexes, which work in arbitrary dimensions, and we define their inverse refinement operators. We describe how simplification and refinement operators affect Morse complexes on M, and we show that these operators form a complete set of atomic operators to create and update Morse complexes on M. Thus, any operator that modifies Morse complexes on M can be expressed as a suitable sequence of the atomic simplification and refinement operators we have defined. The simplification and refinement operators also provide a suitable basis for the construction of a multi-resolution representation of Morse complexes.
%B Graphical Models
%V 73
%P 261 - 285
%8 2011/09//
%@ 1524-0703
%G eng
%U http://www.sciencedirect.com/science/article/pii/S1524070311000154
%N 5
%R 10.1016/j.gmod.2011.05.001
%0 Conference Paper
%B Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
%D 2011
%T Simplifying morphological representations of 2D and 3D scalar fields
%A Čomić,Lidija
%A De Floriani, Leila
%A Iuricich,Federico
%K morphological representations
%K Morse complexes
%K multi-dimensional data sets
%K simplification
%X We describe a dual graph-based representation for the ascending and descending Morse complexes of a scalar field, and a compact and dimension-independent data structure based on it, which assumes a discrete representation of the field as a simplicial mesh. We present atomic dimension-independent simplification operators on the graph-based representation. Based on such operators, we have developed a simplification algorithm, which allows generalization of the ascending and descending Morse complexes at different levels of resolution. We show here the results of our implementation, discussing the computation times and the size of the resulting simplified graphs, also in comparison with the size of the original full-resolution graph.
%B Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
%S GIS '11
%I ACM
%C New York, NY, USA
%P 437 - 440
%8 2011///
%@ 978-1-4503-1031-4
%G eng
%U http://doi.acm.org/10.1145/2093973.2094042
%R 10.1145/2093973.2094042
%0 Journal Article
%J ACM transactions on graphics
%D 2005
%T Mesh saliency
%A Lee,Chang Ha
%A Varshney, Amitabh
%A Jacobs, David W.
%K perception
%K saliency
%K simplification
%K viewpoint selection
%K visual attention
%X Research over the last decade has built a solid mathematical foundation for representation and analysis of 3D meshes in graphics and geometric modeling. Much of this work however does not explicitly incorporate models of low-level human visual attention. In this paper we introduce the idea of mesh saliency as a measure of regional importance for graphics meshes. Our notion of saliency is inspired by low-level human visual system cues. We define mesh saliency in a scale-dependent manner using a center-surround operator on Gaussian-weighted mean curvatures. We observe that such a definition of mesh saliency is able to capture what most would classify as visually interesting regions on a mesh. The human-perception-inspired importance measure computed by our mesh saliency operator results in more visually pleasing results in processing and viewing of 3D meshes. compared to using a purely geometric measure of shape. such as curvature. We discuss how mesh saliency can be incorporated in graphics applications such as mesh simplification and viewpoint selection and present examples that show visually appealing results from using mesh saliency.
%B ACM transactions on graphics
%V 24
%P 659 - 666
%8 2005/07//
%@ 0730-0301
%G eng
%U http://doi.acm.org/10.1145/1073204.1073244
%N 3
%R 10.1145/1073204.1073244
%0 Journal Article
%J IEEE Transactions on Visualization and Computer Graphics
%D 2003
%T Modeling and Rendering of Points with Local Geometry
%A Kalaiah,Aravind
%A Varshney, Amitabh
%K differential geometry
%K per-pixel shading.
%K point sample rendering
%K simplification
%X We present a novel rendering primitive that combines the modeling brevity of points with the rasterization efficiency of polygons. The surface is represented by a sampled collection of Differential Points (DP), each with embedded curvature information that captures the local differential geometry in the vicinity of that point. This is a more general point representation that, for the cost of a few additional bytes, packs much more information per point than the traditional point-based models. This information is used to efficiently render the surface as a collection of local geometries. To use the hardware acceleration, the DPs are quantized into $\big. 256\bigr.$ different types and each sampled point is approximated by the closest quantized DP and is rendered as a normal-mapped rectangle. The advantages to this representation are: 1) The surface can be represented more sparsely compared to other point primitives, 2) it achieves a robust hardware accelerated per-pixel shading—even with no connectivity information, and 3) it offers a novel point-based simplification technique that factors in the complexity of the local geometry. The number of primitives being equal, DPs produce a much better quality of rendering than a pure splat-based approach. Visual appearances being similar, DPs are about two times faster and require about 75 percent less disk space in comparison to splatting primitives.
%B IEEE Transactions on Visualization and Computer Graphics
%V 9
%P 30 - 42
%8 2003///
%@ 1077-2626
%G eng
%N 1
%R http://doi.ieeecomputersociety.org/10.1109/TVCG.2003.1175095
%0 Conference Paper
%B Proceedings of the seventeenth annual symposium on Computational geometry
%D 2001
%T Efficient perspective-accurate silhouette computation and applications
%A Pop, Mihai
%A Duncan,Christian
%A Barequet,Gill
%A Goodrich,Michael
%A Huang,Wenjing
%A Kumar,Subodh
%K rendering
%K silhouette
%K simplification
%X Silhouettes are perceptually and geometrically salient features of geo metric models. Hence a number of graphics and visualization applications need to find them to aid further processing. The efficient computation of silhouettes, especially in the context of perspective projection, is known to be difficult. This paper presents a novel efficient and practical algorithm to compute silhouettes from a sequence of viewpoints under perspective projection. Parallel projection is a special case of this algorithm. Our approach is based on a point-plane duality in three dimensions, which allows an efficient computation of the \emph{changes} in the silhouette of a polygonal model between consecutive frames. In addition, we present several applications of our technique to problems from computer graphics and medical visualization. We also provide experimental data that show the efficiency of our approach. million vertices on an SGI Onyx workstation.
%B Proceedings of the seventeenth annual symposium on Computational geometry
%S SCG '01
%I ACM
%C New York, NY, USA
%P 60 - 68
%8 2001///
%@ 1-58113-357-X
%G eng
%U http://doi.acm.org/10.1145/378583.378618
%R 10.1145/378583.378618