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TransforMesh: A Topology-Adaptive Mesh-Based Approach to Surface Evolution
"... Abstract. Most of the algorithms dealing with image based 3-D reconstruction involve the evolution of a surface based on a minimization criterion. The mesh parametrization, while allowing for an accurate surface representation, suffers from the inherent problems of not being able to reliably deal wi ..."
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Cited by 48 (8 self)
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Abstract. Most of the algorithms dealing with image based 3-D reconstruction involve the evolution of a surface based on a minimization criterion. The mesh parametrization, while allowing for an accurate surface representation, suffers from the inherent problems of not being able to reliably deal with selfintersections and topology changes. As a consequence, an important number of methods choose implicit representations of surfaces, e.g. level set methods, that naturally handle topology changes and intersections. Nevertheless, these methods rely on space discretizations, which introduce an unwanted precision-complexity trade-off. In this paper we explore a new mesh-based solution that robustly handles topology changes and removes self intersections, therefore overcoming the traditional limitations of this type of approaches. To demonstrate its efficiency, we present results on 3-D surface reconstruction from multiple images and compare them with state-of-the art results. 1
Robust topological operations for dynamic explicit surfaces
- SIAM Journal on Scientific Computing
"... Abstract. We present a solution to the mesh tangling problem in surface tracking. Using an explicit triangle mesh to track the location of a surface as it moves in three dimensions has many potential advantages for accuracy and efficiency, compared to implicit capturing methods such as level sets. H ..."
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Cited by 36 (6 self)
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Abstract. We present a solution to the mesh tangling problem in surface tracking. Using an explicit triangle mesh to track the location of a surface as it moves in three dimensions has many potential advantages for accuracy and efficiency, compared to implicit capturing methods such as level sets. However, particularly when “mesh surgery ” is required for topological changes, this approach is prone to tangling: The mesh may self-intersect or otherwise no longer represent a physical interface. Our new approach uses robust collision testing to determine when a mesh operation—such as motion, adaptive refinement, coarsening, or topological change—will lead to an invalid state; we then either roll back noncritical operations or apply robust collision response algorithms, minimally perturbing the mesh to guarantee validity. We present numerical examples demonstrating the robustness and accuracy of the method.
Deforming Meshes that Split and Merge
"... Figure 1: Dropping viscoelastic balls in an Eulerian fluid simulation. Invisible geometry is quickly deleted, while the visible surfaces retain their details even after translating through the air and splashing on the ground. We present a method for accurately tracking the moving surface of deformab ..."
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Cited by 31 (5 self)
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Figure 1: Dropping viscoelastic balls in an Eulerian fluid simulation. Invisible geometry is quickly deleted, while the visible surfaces retain their details even after translating through the air and splashing on the ground. We present a method for accurately tracking the moving surface of deformable materials in a manner that gracefully handles topological changes. We employ a Lagrangian surface tracking method, and we use a triangle mesh for our surface representation so that fine features can be retained. We make topological changes to the mesh by first identifying merging or splitting events at a particular grid resolution, and then locally creating new pieces of the mesh in the affected cells using a standard isosurface creation method. We stitch the new, topologically simplified portion of the mesh to the rest of the mesh at the cell boundaries. Our method detects and treats topological events with an emphasis on the preservation of detailed features, while simultaneously simplifying those portions of the material that are not visible. Our surface tracker is not tied to a particular method for simulating deformable materials. In particular, we show results from two significantly different simulators: a Lagrangian FEM simulator with tetrahedral elements, and an Eulerian grid-based fluid simulator. Although our surface tracking method is generic, it is particularly well-suited for simulations that exhibit fine surface details and numerous topological events. Highlights of our results include merging of viscoplastic materials with complex geometry, a taffy-pulling animation with many fold and merge events, and stretching and slicing of stiff plastic material.
Physics-inspired topology changes for thin fluid features
, 2010
"... Figure 1: Our algorithm efficiently produces detailed thin sheets and liquid droplets, even with low-resolution fluid simulations — The main corridor in this example is only 30 fluid cells wide. We propose a mesh-based surface tracking method for fluid animation that both preserves fine surface deta ..."
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Cited by 19 (6 self)
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Figure 1: Our algorithm efficiently produces detailed thin sheets and liquid droplets, even with low-resolution fluid simulations — The main corridor in this example is only 30 fluid cells wide. We propose a mesh-based surface tracking method for fluid animation that both preserves fine surface details and robustly adjusts the topology of the surface in the presence of arbitrarily thin features like sheets and strands. We replace traditional re-sampling methods with a convex hull method for connecting surface features during topological changes. This technique permits arbitrarily thin fluid features with minimal re-sampling errors by reusing points from the original surface. We further reduce re-sampling artifacts with a subdivision-based mesh-stitching algorithm, and we use a higher order interpolating subdivision scheme to determine the location of any newly-created vertices. The resulting algorithm efficiently produces detailed fluid surfaces with arbitrarily thin features while maintaining a consistent topology with the underlying fluid simulation.
Topology-Adaptive Mesh Deformation for Surface Evolution, Morphing, and Multi-View Reconstruction
, 2009
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P.: Minimizing the multiview stereo reprojection error for triangular surface meshes
- In: British Machine Vision Conference. (2008
"... This article proposes a variational multi-view stereo vision method based on meshes for recovering 3D scenes (shape and radiance) from images. Our method is based on generative models and minimizes the reprojection error (difference between the observed images and the images synthesized from the rec ..."
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Cited by 16 (4 self)
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This article proposes a variational multi-view stereo vision method based on meshes for recovering 3D scenes (shape and radiance) from images. Our method is based on generative models and minimizes the reprojection error (difference between the observed images and the images synthesized from the reconstruction). Our contributions are twofold. 1) For the first time, we rigor-ously compute the gradient of the reprojection error for non smooth surfaces defined by discrete triangular meshes. The gradient correctly takes into ac-count the visibility changes that occur when a surface moves; this forces the contours generated by the reconstructed surface to perfectly match with the apparent contours in the input images. 2) We propose an original modifica-tion of the Lambertian model to take into account deviations from the constant brightness assumption without explicitly modelling the reflectance properties of the scene or other photometric phenomena involved by the camera model. Our method is thus able to recover the shape and the diffuse radiance of non Lambertian scenes. 1
WOJTAN C.: Tracking surfaces with evolving topology
- ACM Trans. Graph. (SIGGRAPH
, 2012
"... Figure 1: Our method recovers a sequence of high-quality, temporally coherent triangle meshes from any sequence of closed surfaces with arbitrarily changing topology. We reliably extract correspondences from a level set and track textures backwards through a fluid simulation. We present a method for ..."
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Cited by 13 (2 self)
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Figure 1: Our method recovers a sequence of high-quality, temporally coherent triangle meshes from any sequence of closed surfaces with arbitrarily changing topology. We reliably extract correspondences from a level set and track textures backwards through a fluid simulation. We present a method for recovering a temporally coherent, deforming triangle mesh with arbitrarily changing topology from an incoherent sequence of static closed surfaces. We solve this problem using the surface geometry alone, without any prior information like surface templates or velocity fields. Our system combines a proven strategy for triangle mesh improvement, a robust multi-resolution non-rigid registration routine, and a reliable technique for changing surface mesh topology. We also introduce a novel topological constraint enforcement algorithm to ensure that the output and input always have similar topology. We apply our technique to a series of diverse input data from video reconstructions, physics simulations, and artistic morphs. The structured output of our algorithm allows us to efficiently track information like colors and displacement maps, recover velocity information, and solve PDEs on the mesh as a post process.
Incremental free-space carving for real-time 3d reconstruction
, 2010
"... Almost all current multi-view methods are slow, and thus suited to offline reconstruction. This paper presents a set of heuristic space-carving algorithms with a focus on speed over detail. The algorithms discretize space via the 3D Delaunay triangulation, and they carve away the volumes that violat ..."
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Cited by 9 (0 self)
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Almost all current multi-view methods are slow, and thus suited to offline reconstruction. This paper presents a set of heuristic space-carving algorithms with a focus on speed over detail. The algorithms discretize space via the 3D Delaunay triangulation, and they carve away the volumes that violate free-space or visibility constraints. Whereas similar methods exist, our algorithms are fast and fully incremental. They encompass a dynamic event-driven approach to reconstruction that is suitable for integration with online SLAM or Structure-from-Motion. We integrate our algorithms with PTAM [12], and we realize a complete system that reconstructs 3D geometry from video in real-time. Experiments on typical real-world inputs demonstrate online performance with modest hardware. We provide run-time complexity analysis and show that the perevent processing time is independent of the number of images previously processed: a requirement for real-time operation on lengthy image sequences.
Convex Multi-Region Segmentation on Manifolds
"... In this paper, we address the problem of segmenting data defined on a manifold into a set of regions with uniform properties. In particular, we propose a numerical method when the manifold is represented by a triangular mesh. Based on recent image segmentation models, our method minimizes a convex e ..."
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Cited by 5 (0 self)
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In this paper, we address the problem of segmenting data defined on a manifold into a set of regions with uniform properties. In particular, we propose a numerical method when the manifold is represented by a triangular mesh. Based on recent image segmentation models, our method minimizes a convex energy and then enjoys significant favorable properties: it is robust to initialization and avoid the problem of the existence of local minima present in many variational models. The contributions of this paper are threefold: firstly we adapt the convex image labeling model to manifolds; in particular the total variation formulation. Secondly we show how to implement the proposed method on triangular meshes, and finally we show how to use and combine the method in other computer vision problems, such as 3D reconstruction. We demonstrate the efficiency of our method by testing it on various data. 1.
SketchSurfaces: Sketch-Line Initialized Deformable Surfaces for Efficient and Controllable Interactive 3D Medical Image Segmentation
"... Abstract. We present an intuitive, fast and accurate interactive segmentation method for visualizing and analyzing 3D medical images. Our method combines a general deformable subdivision-surface model with a novel sketch-line user initialization process. The model is simply and precisely initialized ..."
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Cited by 3 (1 self)
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Abstract. We present an intuitive, fast and accurate interactive segmentation method for visualizing and analyzing 3D medical images. Our method combines a general deformable subdivision-surface model with a novel sketch-line user initialization process. The model is simply and precisely initialized with a few quick sketch lines drawn across the width of the target object on several key slices of the volume image. The smooth surface constructed using these lines is extremely close to the shape of the object boundary, making the model’s task of snapping to this boundary much simpler and hence more likely to succeed in noisy images with minimal user editing. Our subdivision surface based deformable model provides a foundation for precise user steering/editing capabilities and all of the simple, intuitive user interactions are seamlessly integrated with advanced visualization capabilities. We use our model to segment objects from several 3D medical images to demonstrate its efficiency and accuracy. 1
