M. Gopi

Surface Reconstruction based on Lower Dimensional Localized Delaunay Triangulation

We present a fast, memory efficient algorithm that generates a manifold triangular mesh S passing through a set of unorganized points P R 3. Nothing is assumed about the geometry, topology or presence of boundaries in the data set except that P is sampled from a real manifold surface. The speed of our algorithm is derived from a projection‐based approach we use to determine the incident faces on a point. We define our sampling criteria to sample the surface and guarantee a topologically correct mesh after surface reconstruction for such a sampled surface. We also present a new algorithm to find the normal at a vertex, when the surface is sampled according our given criteria. We also present results of our surface reconstruction using our algorithm on unorganized point clouds of various models.

A fast and efficient projection-based approach for surface reconstruction

We present a fast and memory efficient algorithm that generates a manifold triangular mesh S with or without boundary passing through a set of unorganized points P/spl sub//spl Rscr//sup 3/ with no other additional information. Nothing is assumed about the geometry or topology of the sampled manifold model, except for its reasonable smoothness. The speed of our algorithm is derived from a projection-based approach we use to determine the incident faces on a point. Our algorithm has successfully reconstructed the surfaces of unorganized point clouds of sizes varying from 10,000 to 100,000 in about 3-30 seconds on a 250 MHz, R10000 SGI Onyx2. Our technique can be specialized for different kinds of input and applications. For example, our algorithm can be specialized to handle data from height fields like terrain and range scan, even in the presence of noise. We have successfully generated meshes for range scan data of size 900,000 points in less than 40 seconds.

A Generic Scheme for Progressive Point Cloud Coding

In this paper, we propose a generic point cloud encoder that provides a unified framework for compressing different attributes of point samples corresponding to 3D objects with an arbitrary topology. In the proposed scheme, the coding process is led by an iterative octree cell subdivision of the object space. At each level of subdivision, the positions of point samples are approximated by the geometry centers of all tree-front cells, whereas normals and colors are approximated by their statistical average within each of the tree-front cells. With this framework, we employ attribute-dependent encoding techniques to exploit the different characteristics of various attributes. All of these have led to a significant improvement in the rate-distortion (R-D) performance and a computational advantage over the state of the art. Furthermore, given sufficient levels of octree expansion, normal space partitioning, and resolution of color quantization, the proposed point cloud encoder can be potentially used for lossless coding of 3D point clouds.

Rapid and Accurate Contact Determination between Spline Models using ShellTrees

In this paper, we present an efficient algorithm for contact determination between spline models. We make use of a new hierarchy, called ShellTree, that comprises of spherical shells and oriented bounding boxes. Each spherical shell corresponds to a portion of the volume between two concentric spheres. Given large spline models, our algorithm decomposes each surface into Bézier patches as part of pre‐processing. At runtime it dynamically computes a tight fitting axis‐aligned bounding box across each Bézier patch and efficiently checks all such boxes for overlap. Using off‐line and on‐line techniques for tree construction, our algorithm computes ShellTrees for Bézier patches and performs fast overlap tests between them to detect collisions. The overall approach can trade off runtime performance for reduced memory requirements. We have implemented the algorithm and tested it on large models, each composed of hundred of patches. Its performance varies with the configurations of the objects. For many complex models composed of hundreds of patches, it can accurately compute the contacts in a few milliseconds.

Immersive teleconferencing: a new algorithm to generate seamless panoramic video imagery

This paper presents a new algorithm for immersive teleconferencing, which addresses the problem of registering and blending multiple images together to create a single seamless panorama. In the immersive teleconference paradigm, one frame of the teleconference is a panorama that is constructed from a compound-image sensing device. These frames are rendered at the remote site on a projection surface that surrounds the user, creating an immersive feeling of presence and participation in the teleconference. Our algorithm efficiently creates panoramic frames for a teleconference session that are both geometrically registered and intensity blended. We demonstrate a prototype that is able to capture images from a compound-image sensor, register them into a seamless panoramic frame, and render those panoramic frames on a projection surface at 30 frames per second.

Octree-based progressive geometry coding of point clouds

We propose a generic point cloud encoder that compresses geometry data including positions and normals of point samples corresponding to 3D objects with arbitrary topology. In this work, the coding process is led by an iterative octree cell subdivision of the object space. At each level of subdivision, positions of point samples are approximated by the geometry centers of all tree-front cells while normals are approximated by their statistical average within each of the tree-front cells. With this framework, we employ attribute-dependent encoding techniques to exploit different characteristics of various attributes. As a result, significant improvement in the rate-distortion (R-D) performance has been obtained with respect to the prior art. Furthermore, the proposed point cloud encoder can be potentially used for lossless geometry coding of 3D point clouds, given sufficient levels of octree expansion and normal space partitioning.

Color Seamlessness in Multi-Projector Displays Using Constrained Gamut Morphing

Multi-projector displays show significant spatial variation in 3D color gamut due to variation in the chromaticity gamuts across the projectors, vignetting effect of each projector and also overlap across adjacent projectors. In this paper we present a new constrained gamut morphing algorithm that removes all these variations and results in true color seamlessness across tiled multi-projector displays. Our color morphing algorithm adjusts the intensities of light from each pixel of each projector precisely to achieve a smooth morphing from one projectors gamut to the others through the overlap region. This morphing is achieved by imposing precise constraints on the perceptual difference between the gamuts of two adjacent pixels. In addition, our gamut morphing assures a C1 continuity yielding visually pleasing appearance across the entire display. We demonstrate our method successfully on a planar and a curved display using both low and high-end projectors. Our approach is completely scalable, efficient and automatic. We also demonstrate the real-time performance of our image correction algorithm on GPUs for interactive applications. To the best of our knowledge, this is the first work that presents a scalable method with a strong foundation in perception and realizes, for the first time, a truly seamless display where the number of projectors cannot be deciphered.

Single-Strip Triangulation of Manifolds with Arbitrary Topology

Triangle strips have been widely used for efficient rendering. It is NP‐complete to test whether a given triangulated model can be represented as a single triangle strip, so many heuristics have been proposed to partition models into few long strips. In this paper, we present a new algorithm for creating a single triangle loop or strip from a triangulated model. Our method applies a dual graph matching algorithm to partition the mesh into cycles, and then merges pairs of cycles by splitting adjacent triangles when necessary. New vertices are introduced at midpoints of edges and the new triangles thus formed are coplanar with their parent triangles, hence the visual fidelity of the geometry is not changed. We prove that the increase in the number of triangles due to this splitting is 50% in the worst case, however for all models we tested the increase was less than 2%. We also prove tight bounds on the number of triangles needed for a single‐strip representation of a model with holes on its boundary. Our strips can be used not only for efficient rendering, but also for other applications including the generation of space filling curves on a manifold of any arbitrary topology.

Hardware accelerated real time charcoal rendering

In this paper, we present simple rendering techniques implemented using traditional graphics hardware to achieve the effects of charcoal drawing. The effects include characteristics of charcoal drawings like broad grainy strokes and smooth tonal variations that are achieved by smudging the charcoal by hand. Further, we also generate the closure effect that is used by artists at times to avoid hard silhouette edges. All these effects are achieved using contrast enhancement operators on textures and/or colors of the 3D model.Our contribution lies in unifying the methods to achieve these effects under the common framework of contrast enhancement operators. Further, since the effects have been implemented using traditional graphics hardware, a single rendering pass is sufficient to create different effects. Hence, we can render highly complex models with large number of triangles at interactive rates. Thus, our method is especially suited for applications like scientific visualization and preliminary sketches/animations.

Feature Oriented Progressive Lossless Mesh Coding

A feature‐oriented generic progressive lossless mesh coder (FOLProM) is proposed to encode triangular meshes with arbitrarily complex geometry and topology. In this work, a sequence of levels of detail (LODs) are generated through iterative vertex set split and bounding volume subdivision. The incremental geometry and connectivity updates associated with each vertex set split and/or bounding volume subdivision are entropy coded. Due to the visual importance of sharp geometric features, the whole geometry coding process is optimized for a better presentation of geometric features, especially at low coding bitrates. Feature‐oriented optimization in FOLProM is performed in hierarchy control and adaptive quantization. Efficient coordinate representation and prediction schemes are employed to reduce the entropy of data significantly. Furthermore, a simple yet efficient connectivity coding scheme is proposed. It is shown that FOLProM offers a significant rate‐distortion (R‐D) gain over the prior art, which is especially obvious at low bitrates.