Space-optimized texture atlases

Texture atlas parameterization provides an effective way to map a variety of colour and data attributes from 2D texture domains onto polygonal surface meshes. Most of the existing literature focus on how to build seamless texture atlases for continuous photometric detail, but little e ort has been devoted to devise e cient techniques for encoding self-repeating, uncontinuous signals such as building facades. We present a perception-based scheme for generating space-optimized texture atlases speci cally designed for intentionally non-bijective parameterizations. Our scheme combines within-chart tiling support with intelligent packing and perceptual measures for assigning texture space in accordance to the amount of information contents of the image and on its saliency. We demonstrate our optimization scheme in the context of real-time navigation through a gigatexel urban model of an European city. Our scheme achieves signi cant compression ratios and speed-up factors with visually indistinguishable results. We developed a technique that generates space-optimized texture atlases for the particular encoding of uncontinuous signals projected onto geometry. The scene is partitioned using a texture atlas tree that contains for each node a texture atlas. The leaf nodes of the tree contain scene geometry. The level of detail is controlled by traversing the tree and selecting the appropriate texture atlas for a given viewer position and orientation. In a preprocessing step, textures associated to each texture atlas node of the tree are packed. Textures are resized according to a given user-de ned texel size and the size of the geometry that are projected onto. We also use perceptual measures to assign texture space in accordance to image detail. We also explore different techniques for supporting texture wrapping of uncontinuous signals, which involved the development of e cient techniques for compressing texture coordinates via the GPU. Our approach supports texture ltering and DXTC compression without noticeable artifacts. We have implemented a prototype version of our space-optimized texture atlases technique and used it to render the 3D city model of Barcelona achieving interactive rendering frame rates. The whole model was composed by more than three million triangles and contained more than twenty thousand different textures representing the building facades with an average original resolution of 512 pixels per texture. Our scheme achieves up 100:1 compression ratios and speed-up factors of 20 with visually indistinguishable results

Skeletal representations of orthogonal shapes

Skeletal representations are important shape descriptors which encode topological and geometrical properties of shapes and reduce their dimension. Skeletons are used in several fields of science and attract the attention of many researchers. In the biocad field, the analysis of structural properties such as porosity of biomaterials requires the previous computation of a skeleton. As the size of three-dimensional images become larger, efficient and robust algorithms that extract simple skeletal structures are required. The most popular and prominent skeletal representation is the medial axis, defined as the shape points which have at least two closest points on the shape boundary. Unfortunately, the medial axis is highly sensitive to noise and perturbations of the shape boundary. That is, a small change of the shape boundary may involve a considerable change of its medial axis. Moreover, the exact computation of the medial axis is only possible for a few classes of shapes. For example, the medial axis of polyhedra is composed of non planar surfaces, and its accurate and robust computation is difficult. These problems led to the emergence of approximate medial axis representations. There exists two main approximation methods: the shape is approximated with another shape class or the Euclidean metric is approximated with another metric. The main contribution of this thesis is the combination of a specific shape and metric simplification. The input shape is approximated with an orthogonal shape, which are polygons or polyhedra enclosed by axis-aligned edges or faces, respectively. In the same vein, the Euclidean metric is replaced by the L infinity or Chebyshev metric. Despite the simpler structure of orthogonal shapes, there are few works on skeletal representations applied to orthogonal shapes. Much of the efforts have been devoted to binary images and volumes, which are a subset of orthogonal shapes. Two new skeletal representations based on this paradigm are introduced: the cube skeleton and the scale cube skeleton. The cube skeleton is shown to be composed of straight line segments or planar faces and to be homotopical equivalent to the input shape. The scale cube skeleton is based upon the cube skeleton, and introduces a family of skeletons that are more stable to shape noise and perturbations. In addition, the necessary algorithms to compute the cube skeleton of polygons and polyhedra and the scale cube skeleton of polygons are presented. Several experimental results confirm the efficiency, robustness and practical use of all the presented methods

A practical and robust method to compute the boundary of three-dimensional axis-aligned boxes

The union of axis-aligned boxes results in a constrained structure that is advantageous for solving certain geometrical problems. A widely used scheme for solid modelling systems is the boundary representation (Brep). We present a method to obtain the B-rep of a union of axis-aligned boxes. Our method computes all boundary vertices, and additional information for each vertex that allows us to apply already existing methods to extract the B-rep. It is based on dividing the three-dimensional problem into two-dimensional boundary computations and combining their results. The method can deal with all geometrical degeneracies that may arise. Experimental results prove that our approach outperforms existing general methods, both in efficiency and robustness.)Peer ReviewedPostprint (author’s final draft

Skeleton computation of an image using a geometric approach

In this work we develop two algorithms to compute the skeleton of a binary 2D images. Both algorithms follow a geometric approach and work directly with the boundary of the image wich is an orthogonal polygon (OP). One of these algorithms processes the edges of the polygon while the other uses its vertices. Compared to a thinning method, the presented algorithms show a good performance.Postprint (published version

Space-optimized texture atlases

Texture atlas parameterization provides an effective way to map a variety of colour and data attributes from 2D texture domains onto polygonal surface meshes. Most of the existing literature focus on how to build seamless texture atlases for continuous photometric detail, but little e ort has been devoted to devise e cient techniques for encoding self-repeating, uncontinuous signals such as building facades. We present a perception-based scheme for generating space-optimized texture atlases speci cally designed for intentionally non-bijective parameterizations. Our scheme combines within-chart tiling support with intelligent packing and perceptual measures for assigning texture space in accordance to the amount of information contents of the image and on its saliency. We demonstrate our optimization scheme in the context of real-time navigation through a gigatexel urban model of an European city. Our scheme achieves signi cant compression ratios and speed-up factors with visually indistinguishable results. We developed a technique that generates space-optimized texture atlases for the particular encoding of uncontinuous signals projected onto geometry. The scene is partitioned using a texture atlas tree that contains for each node a texture atlas. The leaf nodes of the tree contain scene geometry. The level of detail is controlled by traversing the tree and selecting the appropriate texture atlas for a given viewer position and orientation. In a preprocessing step, textures associated to each texture atlas node of the tree are packed. Textures are resized according to a given user-de ned texel size and the size of the geometry that are projected onto. We also use perceptual measures to assign texture space in accordance to image detail. We also explore different techniques for supporting texture wrapping of uncontinuous signals, which involved the development of e cient techniques for compressing texture coordinates via the GPU. Our approach supports texture ltering and DXTC compression without noticeable artifacts. We have implemented a prototype version of our space-optimized texture atlases technique and used it to render the 3D city model of Barcelona achieving interactive rendering frame rates. The whole model was composed by more than three million triangles and contained more than twenty thousand different textures representing the building facades with an average original resolution of 512 pixels per texture. Our scheme achieves up 100:1 compression ratios and speed-up factors of 20 with visually indistinguishable results

The three-dimensional cube and scale cube skeleton

The recently introduced cube and scale cube skeleton of Martínez et al. (Graph Models 75:189–207, 2013) are a new type of skeletal representations for polygons or polyhedra enclosed by axis-aligned edges or faces. In this paper, we present efficient algorithms to compute the three-dimensional cube and scale cube skeleton. In addition, we analyze the combinatorial complexity of the three-dimensional cube skeleton. We also introduce the three-dimensional interior cube skeleton, which is homotopically equivalent to the input shape. Finally, we experimentally evaluate the efficiency and robustness of all the presented algorithms and compare the obtained skeletons with other relevant skeletal representations.Postprint (published version

The three-dimensional cube and scale cube skeleton

The recently introduced cube and scale cube skeleton of Martínez et al. (Graph Models 75:189–207, 2013) are a new type of skeletal representations for polygons or polyhedra enclosed by axis-aligned edges or faces. In this paper, we present efficient algorithms to compute the three-dimensional cube and scale cube skeleton. In addition, we analyze the combinatorial complexity of the three-dimensional cube skeleton. We also introduce the three-dimensional interior cube skeleton, which is homotopically equivalent to the input shape. Finally, we experimentally evaluate the efficiency and robustness of all the presented algorithms and compare the obtained skeletons with other relevant skeletal representations

Static and dynamic brittle fracture

SIGLEAvailable from British Library Document Supply Centre- DSC:DX178345 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

A practical and robust method to compute the boundary of three-dimensional axis-aligned boxes

The union of axis-aligned boxes results in a constrained structure that is advantageous for solving certain geometrical problems. A widely used scheme for solid modelling systems is the boundary representation (Brep). We present a method to obtain the B-rep of a union of axis-aligned boxes. Our method computes all boundary vertices, and additional information for each vertex that allows us to apply already existing methods to extract the B-rep. It is based on dividing the three-dimensional problem into two-dimensional boundary computations and combining their results. The method can deal with all geometrical degeneracies that may arise. Experimental results prove that our approach outperforms existing general methods, both in efficiency and robustness.)Peer Reviewe

Efficient algorithms for boundary extraction of 2D and 3D orthogonal pseudomanifolds

In this paper we present algorithms to extract the boundary representation of orthogonal polygons and polyhedra, either manifold or pseudomanifold. The algorithms we develop reconstruct not only the polygons of the boundaries but also the hole-face inclusion relationship. Our algorithms have a simple input in order that they can be used to convert many different kinds of models to B-Rep. For the 2D case, the input is the set of vertices, and for the 3D case, some small additional information must be supplied for every vertex. All proposed algorithms run in $mathcal{O}(nlog n)$ time and use $mathcal{O}(n)$ space, where $n$ is the number of vertices of the input. Besides, we explain how to use our proposal to extract the boundary from the well-known voxel and octree models and from other models found in the related literature: the neighbourhood, the EVM, and the weighted vertex list models