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Turk,
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ItemVessel Segmentation Using a Shape Driven Flow(Georgia Institute of Technology, 2004-09) Nain, Delphine ; Yezzi, Anthony ; Turk, GregWe present a segmentation method for vessels using an implicit deformable model with a soft shape prior. Blood vessels are challenging structures to segment due to their branching and thinning geometry as well as the decrease in image contrast from the root of the vessel to its thin branches. Using image intensity alone to deform a model for the task of segmentation often results in leakages at areas where the image information is ambiguous. To address this problem, we combine image statistics and shape information to derive a region-based active contour that segments tubular structures and penalizes leakages. We present results on synthetic and real 2D and 3D datasets.
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ItemVector Field Design on Surfaces(Georgia Institute of Technology, 2004) Zhang, Eugene ; Mischaikow, Konstantin Michael ; Turk, GregVector field design on surfaces is necessary for many graphics applications: example-based texture synthesis, non-photorealistic rendering, and fluid simulation. A vector field design system should allow a user to create a large variety of complex vector fields with relatively little effort. In this paper, we present a vector field design system for surfaces that allows the user to control the number of singularities in the vector field and their placement. Our system combines basis vector fields to make an initial vector field that meets the user's specifications. The initial vector field often contains unwanted singularities. Such singularities cannot always be eliminated, due to the Poincar'e-Hopf index theorem. To reduce the effect caused by these singularities, our system allows a user to move a singularity to a more favorable location or to cancel a pair of singularities. These operations provide topological guarantees for the vector field in that they only affect the user-specified singularities. Other editing operations are also provided so that the user may change the topological and geometric characteristics of the vector field. We demonstrate our vector field design system for several applications: example-based texture synthesis, painterly rendering of images, and pencil sketch illustrations of smooth surfaces.
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ItemFeature-Based Surface Parameterization and Texture Mapping(Georgia Institute of Technology, 2003) Zhang, Eugene ; Mischaikow, Konstantin Michael ; Turk, GregSurface parameterization is necessary for many graphics tasks: texture-preserving simplification, remeshing, surface painting, and pre-computation of solid textures. The stretch caused by a given parameterization determines the sampling rate on the surface. In this paper, we propose an automatic parameterization method that segments a surface into patches that are then flattened with little stretch. We observe that many objects consist of regions of relative simple shapes, each of which has a natural parameterization. Therefore, we propose a three-stage feature based patch creation method for manifold mesh surfaces. The first two stages, genus reduction and feature identification, are performed with the help of distance-based Morse functions. In the last stage, we create one or two patches for each feature region based on a covariance matrix of the feature's surface points. To reduce the stretch during patch unfolding, we notice that the stretch is a 2x2 tensor which in ideal situations is the identity. Therefore, we propose to use the Green-Lagrange tensor to measure and to guide the optimization process. Furthermore, we allow the boundary vertices of a patch to be optimized by adding scaffold triangles. We demonstrate our feature identification and patch unfolding methods for several textured models. Finally, to evaluate the quality of a given parameterization, we propose an image-based error measure that takes into account stretch, seams, smoothness, packing efficiency and visibility.
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ItemReconstructing Surfaces by Volumetric Regularization(Georgia Institute of Technology, 2000) Dinh, Huong Quynh ; Turk, Greg ; Slabaugh, Gregory G.We present a new method of surface reconstruction that generates smooth and seamless models from sparse, noisy, and non-uniform range data. Data acquisition techniques from computer vision, such as stereo range images and space carving, produce three dimensional point sets that are imprecise and non-uniform when compared to laser or optical range scanners. Traditional reconstruction algorithms designed for dense and precise data cannot be used on stereo range images and space carved volumes. Our method constructs a three dimensional implicit surface, formulated as a summation of weighted radial basis functions. We achieve three primary advantages over existing algorithms: (1) the implicit functions we construct estimate the surface well in regions where there is little data; (2) the reconstructed surface is insensitive to noise in data acquisition because we can allow the surface to approximate, rather than exactly interpolate, the data; and (3) the reconstructed surface is locally detailed, yet globally smooth, because we use radial basis functions that achieve multiple orders of smoothness.
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ItemImage-Driven Mesh Optimization(Georgia Institute of Technology, 2000) Lindstrom, Peter ; Turk, GregWe describe a method of improving the appearance of a low vertex count mesh in a manner that is guided by rendered images of the original, detailed mesh. This approach is motivated by the fact that greedy simplification methods often yield meshes that are poorer than what can be represented with a given number of vertices. Our approach relies on edge swaps and vertex teleports to alter the mesh connectivity, and uses the downhill simplex method to simultaneously improve vertex positions and surface attributes. Note that this is not a simplification method--the vertex count remains the same throughout the optimization. At all stages of the optimization the changes are guided by a metric that measures the differences between rendered versions of the original model and the low vertex count mesh. This method creates meshes that are geometrically faithful to the original model. Moreover, the method takes into account more subtle aspects of a model such as surface shading or whether cracks are visible between two interpenetrating parts of the model.