Laurent Balmelli

Space-optimized texture maps

Texture mapping is a common operation to increase the realism of three‐dimensional meshes at low cost. We propose a new texture optimization algorithm based on the reduction of the physical space allotted to the texture image. Our algorithm optimizes the use of texture space by computing a warping function for the image and new texture coordinates. Neither the mesh geometry nor its connectivity are modified by the optimization. Our method uniformly distributes frequency content of the image in the spatial domain. In other words, the image is stretched in high frequency areas, whereas low frequency regions are shrunk. We also take into account distortions introduced by the mapping onto the model geometry in this process. The resulting image can be resampled at lower rate while preserving its original details. The unwarping is performed by the texture mapping function. Hence, the space‐optimized texture is stored as‐is in texture memory and is fully supported by current graphics hardware. We present several examples showing that our method significantly decreases texture memory usage without noticeable loss in visual quality.

Model-driven systems development

This publication contains reprint articles for which IEEE does not hold copyright. Full text is not available on IEEE Xplore for these articles.

Quadtrees for embedded surface visualization: constraints and efficient data structures

The quadtree data structure is widely used in digital image processing and computer graphics for modeling spatial segmentation of images and surfaces. A quadtree is a tree in which each node has four descendants. Since most algorithms based on quadtrees require complex navigation between nodes, efficient traversal methods as well as efficient storage techniques are of great interest. In this paper we first propose an efficient indexing scheme for a linear (pointerless) quadtree data structure. Such a quadtree is stored using a unidimensional array of nodes. Our indexing scheme has the property that the navigation between any pair of nodes can be computed in constant time. Moreover the navigation across multiple quadtrees can be achieved at the same cost. We illustrate our results on applications in computer graphics. We first show how the problem of computing a so-called restricted quadtree can be solved at optimal cost, e.g. with a computational complexity having the order of magnitude of the problem size. Then, we explain how this problem can be solved in the case of surfaces modeled using multiple quadtrees. Finally, we show how a tessellated sphere can be implemented and navigated using our data structure.

Interactive DSP education using Java

We argue that Java is a natural language to develop interactive teaching material that can be shared and distributed widely. Unlike any other programming language or platform we know, Java development is justified because of its almost universal acceptance. We develop a block diagram (BD) based approach that allows one to develop interactive and downloadable signal processing laboratories. As an example, we show how specific experiments for a DSP class, as well as for an advanced course on wavelets have been developed. The article first explains why the Java language has been chosen, and then describes what has been realized today. Finally, we show how the BD representation can be efficiently used for the development of a wavelet theory course. It is shown that only a few simple blocks are sufficient for creating many didactic programs. This can be seen as an a posteriori justification of the BD model.

Volume warping for adaptive isosurface extraction

Polygonal approximations of isosurfaces extracted from uniformly sampled volumes are increasing in size due to the availability of higher resolution imaging techniques. The large number of I primitives represented hinders the interactive exploration of the dataset. Though many solutions have been proposed to this problem, many require the creation of isosurfaces at multiple resolutions or the use of additional data structures, often hierarchical, to represent the volume. We propose a technique for adaptive isosurface extraction that is easy to implement and allows the user to decide the degree of adaptivity as well as the choice of isosurface extraction algorithm. Our method optimizes the extraction of the isosurface by warping the volume. In a warped volume, areas of importance (e.g. containing significant details) are inflated while unimportant ones are contracted. Once the volume is warped, any extraction algorithm can be applied. The extracted mesh is subsequently unwarped such that the warped areas are rescaled to their initial proportions. The resulting isosurface is represented by a mesh that is more densely sampled in regions decided as important.

Wavelet domain features for texture description, classification and replicability analysis

In this paper we present a new wavelet domain technique for texture analysis and test of pattern replicability. The main property of the proposed features is that they measure texture quality along the most important perceptual dimensions. In other words, we quantify and classify textures according to their directionality, symmetry regularity and type of regularity. After the feature extraction, texture classification is performed by traversing a tree. The algorithm is tested on a database with 340 images demonstrating an excellent classification accuracy.

Efficient algorithms for embedded rendering of terrain models

Digital terrains are generally large files and need to be simplified to be rendered efficiently. We propose to build an adaptive embedded triangulation based on a binary tree structure to generate multiple levels of details. We present a O(nlogn) decimation algorithm and a O(nlogn) refinement algorithm, where n is the number of elevation points. We compare them in a rate-distortion (RD) framework. The algorithms are based on an improved version of the optimal tree pruning algorithm G-BFOS allowing one to deal with constrained tree structures and non-monotonic tree functionals.

Computational analysis of mesh simplification using global error

Meshes with (recursive) subdivision connectivity, such as subdivision surfaces, are increasingly popular in computer graphics. They present several advantages over their Delaunay-type based counterparts, e.g., Triangulated Irregular Networks (TINs), such as efficient processing, compact storage and numerical robustness. A mesh having subdivision connectivity can be described using a tree structure and recent work exploits this inherent hierarchy in applications such as progressive terrain visualization, surface compression and transmission. We propose a hierarchical, fine to coarse (i.e., using vertex decimation) algorithm to reduce the number of vertices in meshes whose connectivity is based on quadrilateral quadrisection (e.g., subdivision surfaces obtained from Catmull-Clark or 4-8 subdivision rules). Our method is derived from optimal tree pruning algorithms used in modeling of adaptive quantizers for compression. The main advantage of our method is that it allows control of the global error of the approximation, whereas previous methods are based on local error heuristics only. We present a set of operations allowing the use of global error and use them to build an O(n log n) simplification algorithm transforming an input mesh of n vertices into a multiresolution hierarchy. Note that a single approximation having k < n vertices is obtained in linear running time. We show that, without using these operations, mesh simplification using global error has O(n2) computational complexity in the RAM model. Our approach uses a generalized vertex decimation method which allows for choosing the optimal vertex in the rate-distortion sense. Additionally, our algorithm can also be applied to other types of subdivision connectivity such as triangular quadrisection, e.g., obtained from Loop subdivision.

Image-based object editing

We examine the problem of editing complex 3D objects. We convert the problem of editing a 3D object of arbitrary size and surface properties to a problem of editing a 2D image. We allow the user to specify edits in both geometry and surface properties from any view and at any resolution they find convenient, regardless of the interactive rendering capability of their computer. We use specially-constrained shape from shading algorithms to convert a shaded image specified by the user into a 3D geometry.

Mesh optimization using global error with application to geometry simplification

This paper presents a linear running time optimization algorithm for meshes with subdivision connectivity, e.g., subdivision surfaces. The algorithm optimizes a model using a metric defined by the user. Two functionals are used to build the metric: a rate functional and a distortion (i.e. error) functional. The distortion functional defines the error function to minimize, whereas the rate functional defines the minimization constraint. The algorithm computes approximations within this metric using jointly global error and an optimal vertex selection technique inspired from optimal tree pruning algorithms used in compression. We present an update mechanism, that we name merging domain intersections (MDIs), allowing the control of global error through the optimization process at low cost. Our method has application in progressive model decomposition, compression, rendering, and finite element methods. We apply our method to geometry simplification and present an algorithm to compute a decomposition of a model into a multiresolution hierarchy in O(n log n) time using global error, where n is the number of vertices in the full-resolution model. We show that a direct approach, i.e. not using MDIs, recomputing global error has at least cost O(n2). We analyze the optimality of the algorithm and give several for its properties. We present results for semi-regular meshes obtained from approximation of subdivision surfaces whose connectivity is obtain from (triangulated) quadrilateral quadrisection (e.g. 4-8 or Catmull-Clark subdivision).