ACM Transactions on Graphics

Published by Association for Computing Machinery

Online ISSN: 1557-7368


Print ISSN: 0730-0301


Discovering Structural Regularity in 3D Geometry
  • Article
  • Full-text available

August 2008


411 Reads


Niloy J Mitra


Johannes Wallner




We introduce a computational framework for discovering regular or repeated geometric structures in 3D shapes. We describe and classify possible regular structures and present an effective algorithm for detecting such repeated geometric patterns in point- or mesh-based models. Our method assumes no prior knowledge of the geometry or spatial location of the individual elements that define the pattern. Structure discovery is made possible by a careful analysis of pairwise similarity transformations that reveals prominent lattice structures in a suitable model of transformation space. We introduce an optimization method for detecting such uniform grids specifically designed to deal with outliers and missing elements. This yields a robust algorithm that successfully discovers complex regular structures amidst clutter, noise, and missing geometry. The accuracy of the extracted generating transformations is further improved using a novel simultaneous registration method in the spatial domain. We demonstrate the effectiveness of our algorithm on a variety of examples and show applications to compression, model repair, and geometry synthesis.

Fig. 1. (a) Rendering a cityscape with a pinhole aperture results in no perceptible blur. The scene looks large and far away. (b) Simulating a 60mwide aperture produces blur consistent with a shallow depth of field, making the scene appear to be a miniature model.
Fig. 5. Comparison of blur patterns produced by three rendering techniques: consistent blur (a), simulated tilt-and-shift lens (b), and linear blur gradient (c). The settings in (b) and (c) were chosen to equate the maximum blur-circle diameters with those in (a). The percent differences in blur-circle diameters between the images are plotted in (d), (e), and (f). Panels (d) and (e) show that the simulated tilt-and-shift lens and linear blur gradient do not closely approximate consistent blur rendering. The large differences are due to the buildings, which protrude from the ground plane. Panel (f) shows that the linear blur gradient provides essentially the same blur pattern as a simulated tilt-and-shift lens. Most of the differences in (f) are less than 7%; the only exceptions are in the band near the center, where the blur diameters are less than one pixel and not detectable in the final images.
Fig. 6. Focal distance as a function of relative distance and retinal-image blur. Relative distance is defined as the ratio of the distance to an object and the distance to the focal plane. The three colored curves represent different amounts of image blur expressed as the diameter of the blur circle, c, in degrees. We use angular units because in these units, the image device's focal length drops out [Kingslake 1992]. The variance in the distribution was determined by assuming that pupil diameter is Gaussian distributed with a mean of 4.6mm and standard deviation of 1mm [Spring and Stiles 1948]. For a given amount of blur, it is impossible to recover the original focal distance without knowing the relative distance. Note that as the relative distance approaches 1, the object moves closer to the focal plane. There is a singularity at a relative distance of 1 because the object is by definition completely in focus at this distance.
Using Blur to Affect Perceived Distance and Size

March 2010


897 Reads

We present a probabilistic model of how viewers may use defocus blur in conjunction with other pictorial cues to estimate the absolute distances to objects in a scene. Our model explains how the pattern of blur in an image together with relative depth cues indicates the apparent scale of the image's contents. From the model, we develop a semiautomated algorithm that applies blur to a sharply rendered image and thereby changes the apparent distance and scale of the scene's contents. To examine the correspondence between the model/algorithm and actual viewer experience, we conducted an experiment with human viewers and compared their estimates of absolute distance to the model's predictions. We did this for images with geometrically correct blur due to defocus and for images with commonly used approximations to the correct blur. The agreement between the experimental data and model predictions was excellent. The model predicts that some approximations should work well and that others should not. Human viewers responded to the various types of blur in much the way the model predicts. The model and algorithm allow one to manipulate blur precisely and to achieve the desired perceived scale efficiently.

Meshless Animation of Fracturing Solids

July 2005


239 Reads

We present a new meshless animation framework for elastic and plastic materials that fracture. Central to our method is a highly dynamic surface and volume sampling method that supports arbitrary crack initiation, propagation, and termination, while avoiding many of the stability problems of traditional mesh-based techniques. We explicitly model advancing crack fronts and associated fracture surfaces embedded in the simulation volume. When cutting through the material, crack fronts directly affect the coupling between simulation nodes, requiring a dynamic adaptation of the nodal shape functions. We show how local visibility tests and dynamic caching lead to an efficient implementation of these effects based on point collocation. Complex fracture patterns of interacting and branching cracks are handled using a small set of topological operations for splitting, merging, and terminating crack fronts. This allows continuous propagation of cracks with highly detailed fracture surfaces, independent of the spatial resolution of the simulation nodes, and provides effective mechanisms for controlling fracture paths. We demonstrate our method for a wide range of materials, from stiff elastic to highly plastic objects that exhibit brittle and/or ductile fracture.

Figure 1: Benefits of Reliable CCD Queries: We highlight the benefits of our exact CCD algorithm on cloth simulation. Our algorithm can be used to generate a plausible simulation (a). If parameters are not properly tuned, floating-point-based CCD algorithms (b) can result in penetrations and artifacts. 
Figure 6: Benchmarks: We use five different benchmarks arising from cloth and FEM simulations. 
Fast and Exact Continuous Collision Detection with Bernstein Sign Classification

November 2014


329 Reads

We present fast algorithms to perform accurate CCD queries between triangulated models. Our formulation uses properties of the Bernstein basis and Bézier curves and reduces the problem to evaluating signs of polynomials. We present a geometrically exact CCD algorithm based on the exact geometric computation paradigm to perform reliable Boolean collision queries. Our algorithm is more than an order of magnitude faster than prior exact algorithms. We evaluate its performance for cloth and FEM simulations on CPUs and GPUs, and highlight the benefits.

Optimizing Cubature for Efficient Integration of Subspace Deformations

December 2009


116 Reads

We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multi-dimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an r-dimensional deformation subspace with O(r) cubature points, our method is able to evaluate subspace forces at O(r(2)) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St.Venant-Kirchhoff, Mooney-Rivlin, Arruda-Boyce), and multimodal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration. CR CATEGORIES: I.6.8 [Simulation and Modeling]: Types of Simulation-Animation, I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Physically based modeling G.1.4 [Mathematics of Computing]: Numerical Analysis-Quadrature and Numerical Differentiation.

Figure 1: (A) Image formation with converging cameras. P o is coordinates of point P, f is camera focal length, t is separation between the cameras, C is distance to which the camera optical axes are converged, V c is angle between cameras’ optical axes, W c is width of camera sensors, x cl and x cr are x-coordinates of P’s projection onto left and right camera sensors. (B) The cameras’ optical axes can be made to converge by laterally offsetting the sensors relative to the lens axes. h is offset between sensor center and intersection of lens axis with the sensor. (C) Reconstruction of P from sensor images. Rays are projected from eye centers through corresponding points on picture. The ray intersection is estimated location of P. E l and E r are 3d coordinates of left and right eyes; P l and P r are locations of image points in the picture of P for left and right eyes; I is inter-ocular distance; d is distance between centers of pictures. The green and red horizontal lines represent the images presented to the left and right eyes, respectively. another, the optical axes can be parallel ( h = 0, V c = 0) or describe this: one with its origin on the display surface and one converging ( h ≠ 0, V c ≠ 0) (Figure 1A and 1B). P ’s coordinates with its origin at the viewer. For the first set, X and Y are the in the left and right cameras are ( x cl , y cl ) and ( x cr , y cr ), where x horizontal and vertical axes centered on the display surface and Z and y are horizontal and vertical coordinates in the sensors: is orthogonal to them. In these coordinates, the eyes’ positions are E l and E r . The positions of the points in picture are: x cl = f tan ⎡ ⎣ ⎢ tan − 1 ⎛ ⎝ ⎜ t 2 P + o P ( z o ) ( x ) ⎠ ⎞ ⎟ − V 2 c ⎦ ⎤ ⎥ − h P l = ( X sl , Y sl ,0) P r = ( X sr , Y sr ,0) 
Figure 1: Estimated 3d scenes for different acquisition and viewing situations. Each panel is a plan view of the viewer, stereo cameras, display surface, actual 3d stimulus, and estimated 3d stimulus. Red lines represent cameras’ optical axes. E) Proper viewing situation. Parameters are listed in Section 3. The actual and estimated stimuli are the same. B) Viewer is too distant from picture. H) Viewer is too close. D) Viewer is too far to the left relative to the picture. F) Viewer is too far to the right. A) Cameras are too close together for viewer’s inter-ocular distance. I) Cameras are too far apart. C) Distance between centers of the left and right stereo pictures is too great. G) Distance between the centers of pictures is too small. 
Figure 2: 
Figure 3: Anaglyph stereograms captured with the acquisition settings listed in Section 3.1. Top: cameras with parallel optical axes. Bottom: cameras’ optical axes were converged at 0.55m (center of cube). To view the stereograms, use red-green glasses with green filter over left eye. Try different viewing situations. 1) Move closer to and farther away from the page. 2) Move left and right while holding the head parallel to the page. 3) Position yourself directly in front of the page and rotate the head about a vertical axis (yaw) and then about a forward axis (roll). In each case, notice the changes in the cube’s apparent shape. Points in the cube were randomly perturbed to lessen contributions of perspective cues to 3d percept. 
Figure 4: Disparity as a function of azimuth and elevation. Fick coordinates (azimuth and elevation measured as longitudes and latitudes, respectively) were used. Vectors represent the direction and magnitude of disparities on the retinas produced by a stereoscopic image of a cube 0.3m on a side and placed 0.55m in front of the stereo cameras. Unless otherwise noted, the conditions listed in Section 3 were used to generate the figures. Arrow tails represent points on right eye’s retina, and arrowheads represent corresponding points in left eye’s retina. Panels A, B, and C contain points from the proximal face of the cube, where the eyes are fixating. D, E, and F represent the cube’s distal face. In A and D, the observer is viewing the display at a 45deg angle. In B and E, the viewer’s head has been rolled 20deg. In C and F, the cameras converge at 0.55m. from stereoscopic displays, particularly when the acquisition and of a shared space. In Proceedings of ACM SIGGRAPH 97 , viewing parameters are improper as necessarily occurs with ACM Press/Addison-Wesley, New York. Computer Graphics multiple viewers. The standard model makes reasonable Proceedings, Annual Conference Series, ACM, 327-332. predictions in many situations, but fails to make predictions in some important ones that are known to produce misperceptions. B ACKUS , B.T., B ANKS , M. S., VAN E E , R., AND C ROWELL , J. A. Those situations involve rotation of the viewer’s head relative to 1999. Horizontal and vertical disparity, eye position, and the display and the use of converging cameras in acquisition with stereoscopic slant perception, Vision Research , 39, 6, 1143- single displays for viewing. The skew rays that occur in those 1170. situations give rise to vertical disparities in the retinal images that were not present before the viewer rotation or before converging B ANKS , M. S., H OOGE , I. T., AND B ACKUS , B. T. 2001. Perceiving cameras were used. We described findings in the vision-science slant about a horizontal axis from stereopsis, Journal of Vision , literature that point to how the visual system determines 3d 1, 2, 55-79. structure in these situations. In particular, the system uses vertical disparity as an additional signal for determining the structure. C HAN , H. P., G OODSITT , M. M., H ELVIE , M. A., H ADJIISKI , L. M., Preliminary observations are consistent with the predictions L YDICK , J. T., R OUBIDOUX , M. A., B AILEY , J. E., N EES , A., derived from this model. B LANE , C. E., AND S AHINER , B. 2005. ROC study of the effect 
Misperceptions in Stereoscopic Displays: A Vision Science Perspective

August 2008


922 Reads

3d shape and scene layout are often misperceived when viewing stereoscopic displays. For example, viewing from the wrong distance alters an object's perceived size and shape. It is crucial to understand the causes of such misperceptions so one can determine the best approaches for minimizing them. The standard model of misperception is geometric. The retinal images are calculated by projecting from the stereo images to the viewer's eyes. Rays are back-projected from corresponding retinal-image points into space and the ray intersections are determined. The intersections yield the coordinates of the predicted percept. We develop the mathematics of this model. In many cases its predictions are close to what viewers perceive. There are three important cases, however, in which the model fails: 1) when the viewer's head is rotated about a vertical axis relative to the stereo display (yaw rotation); 2) when the head is rotated about a forward axis (roll rotation); 3) when there is a mismatch between the camera convergence and the way in which the stereo images are displayed. In these cases, most rays from corresponding retinal-image points do not intersect, so the standard model cannot provide an estimate for the 3d percept. Nonetheless, viewers in these situations have coherent 3d percepts, so the visual system must use another method to estimate 3d structure. We show that the non-intersecting rays generate vertical disparities in the retinal images that do not arise otherwise. Findings in vision science show that such disparities are crucial signals in the visual system's interpretation of stereo images. We show that a model that incorporates vertical disparities predicts the percepts associated with improper viewing of stereoscopic displays. Improving the model of misperceptions will aid the design and presentation of 3d displays.

Figure 4: Example stimuli. Left: The corner in the center looks undistorted. Right: the corner looks like an obtuse angle. The corners participants are asked to look at are indicated by the crosshairs (or by a blinking red dot in the experiment).  
Figure 6: The hinge device (left) and our experimental setup (right).  
Figure 12: (a) The deviation of averaged perceived angles (Experiment 1) from 90° has a similar pattern as (b), the interpolated medians of ratings from Experiment 2 (both linearly interpolated). (c) Perceived angles predicted by Eq. 19 mapped to ratings using Eq. 20, and (d) the same for an extended domain.
Perception of Perspective Distortions in Image-Based Rendering

July 2013


225 Reads

Image-based rendering (IBR) creates realistic images by enriching simple geometries with photographs, e.g., mapping the photograph of a building façade onto a plane. However, as soon as the viewer moves away from the correct viewpoint, the image in the retina becomes distorted, sometimes leading to gross misperceptions of the original geometry. Two hypotheses from vision science state how viewers perceive such image distortions, one claiming that they can compensate for them (and therefore perceive scene geometry reasonably correctly), and one claiming that they cannot compensate (and therefore can perceive rather significant distortions). We modified the latter hypothesis so that it extends to street-level IBR. We then conducted a rigorous experiment that measured the magnitude of perceptual distortions that occur with IBR for façade viewing. We also conducted a rating experiment that assessed the acceptability of the distortions. The results of the two experiments were consistent with one another. They showed that viewers' percepts are indeed distorted, but not as severely as predicted by the modified vision science hypothesis. From our experimental results, we develop a predictive model of distortion for street-level IBR, which we use to provide guidelines for acceptability of virtual views and for capture camera density. We perform a confirmatory study to validate our predictions, and illustrate their use with an application that guides users in IBR navigation to stay in regions where virtual views yield acceptable perceptual distortions.

Trainable videorealistic speech animation
We describe how to create with machine learning techniques a generative, videorealistic, and speech animation module. A human subject is first recorded using a videocamera as he/she utters a pre-determined speech corpus. After processing the corpus automatically, a visual speech module is learned from the data that is capable of synthesizing the human subject's mouth uttering entirely novel utterances that were not recorded in the original video. The synthesized utterance is re-composited onto a background sequence, which contains natural head and eye movement. The final output is videorealistic in the sense that it looks like a video camera recording of the subject. At run time, the input to the system can be either real audio sequences or synthetic audio produced by a text-to-speech system, as long as they have been phonetically aligned.

Figure 1. Intuitive explanation. (a) the two endpoints of the curve detect the new points in A and B; (b) the grown curve  
Reconstructing B-spline Curves from Point Clouds--A Tangential Flow Approach Using Least Squares Minimization
We present a novel algorithm based on least-squares minimization to approximate point cloud data in 2D plane with a smooth B-spline curve. The point cloud data may represent an open curve with self intersection and sharp corner. Unlike other existing methods, such as the moving least-squares method and the principle curve method, our algorithm does not need a thinning process. The idea of our algorithm is intuitive and simple - we make a B-spline curve grow along the tangential directions at its two end-points following local geometry of point clouds. Our algorithm generates appropriate control points of the fitting B-spline curve in the least squares sense. Although presented for the 2D case, our method can be extended in a straightforward manner to fitting data points by a B-spline curve in higher dimensions

Gap Processing for Adaptive Maximal Poisson-Disk Sampling

November 2013


100 Reads

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing.

Automatic Photo Adjustment Using Deep Neural Networks

May 2016


3,957 Reads

Photo retouching enables photographers to invoke dramatic visual impressions by artistically enhancing their photos through stylistic color and tone adjustments. However, it is also a time-consuming and challenging task that requires advanced skills beyond the abilities of casual photographers. Using an automated algorithm is an appealing alternative to manual work but such an algorithm faces many hurdles. Many photographic styles rely on subtle adjustments that depend on the image content and even its semantics. Further, these adjustments are often spatially varying. Because of these characteristics, existing automatic algorithms are still limited and cover only a subset of these challenges. Recently, deep machine learning has shown unique abilities to address hard problems that resisted machine algorithms for long. This motivated us to explore the use of deep learning in the context of photo editing. In this paper, we explain how to formulate the automatic photo adjustment problem in a way suitable for this approach. We also introduce an image descriptor that accounts for the local semantics of an image. Our experiments demonstrate that our deep learning formulation applied using these descriptors successfully capture sophisticated photographic styles. In particular and unlike previous techniques, it can model local adjustments that depend on the image semantics. We show on several examples that this yields results that are qualitatively and quantitatively better than previous work.

Figure 5-II: Mapping a line to a point and vice versa.
Simulation of simplicity. A technique to cope with degenerate cases in geometric algorithms

October 1994


304 Reads

This paper describes a general-purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software. Comment: 38 pages

Three-Dimensional Alpha Shapes

October 1994


1,965 Reads

Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal notion of the family of $\alpha$-shapes of a finite point set in $\Real^3$. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter $\alpha \in \Real$ controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size $n$ in time $O(n^2)$, worst case. A robust implementation of the algorithm is discussed and several applications in the area of scientific computing are mentioned. Comment: 32 pages

Toric Degenerations of Bezier Patches

June 2010


162 Reads

The control polygon of a Bezier curve is well-defined and has geometric significance---there is a sequence of weights under which the limiting position of the curve is the control polygon. For a Bezier surface patch, there are many possible polyhedral control structures, and none are canonical. We propose a not necessarily polyhedral control structure for surface patches, regular control surfaces, which are certain C^0 spline surfaces. While not unique, regular control surfaces are exactly the possible limiting positions of a Bezier patch when the weights are allowed to vary.

Spoke Darts for Efficient High Dimensional Blue Noise Sampling

August 2014


400 Reads

Blue noise refers to sample distributions that are random and well-spaced, with a variety of applications in graphics, geometry, and optimization. However, prior blue noise sampling algorithms typically suffer from the curse-of-dimensionality, especially when striving to cover a domain maximally. This hampers their applicability for high dimensional domains. We present a blue noise sampling method that can achieve high quality and performance across different dimensions. Our key idea is spoke-dart sampling, sampling locally from hyper-annuli centered at prior point samples, using lines, planes, or, more generally, hyperplanes. Spoke-dart sampling is more efficient at high dimensions than the state-of-the-art alternatives: global sampling and advancing front point sampling. Spoke-dart sampling achieves good quality as measured by differential domain spectrum and spatial coverage. In particular, it probabilistically guarantees that each coverage gap is small, whereas global sampling can only guarantee that the sum of gaps is not large. We demonstrate advantages of our method through empirical analysis and applications across dimensions 8 to 23 in Delaunay graphs, global optimization, and motion planning.

Parallel Chen-Han (PCH) Algorithm for Discrete Geodesics

May 2013


443 Reads

In many graphics applications, the computation of exact geodesic distance is very important. However, the high computational cost of the existing geodesic algorithms means that they are not practical for large-scale models or time-critical applications. To tackle this challenge, we propose the parallel Chen-Han (or PCH) algorithm, which extends the classic Chen-Han (CH) discrete geodesic algorithm to the parallel setting. The original CH algorithm and its variant both lack a parallel solution because the windows (a key data structure that carries the shortest distance in the wavefront propagation) are maintained in a strict order or a tightly coupled manner, which means that only one window is processed at a time. We propose dividing the CH's sequential algorithm into four phases, window selection, window propagation, data organization, and events processing so that there is no data dependence or conflicts in each phase and the operations within each phase can be carried out in parallel. The proposed PCH algorithm is able to propagate a large number of windows simultaneously and independently. We also adopt a simple yet effective strategy to control the total number of windows. We implement the PCH algorithm on modern GPUs (such as Nvidia GTX 580) and analyze the performance in detail. The performance improvement (compared to the sequential algorithms) is highly consistent with GPU double-precision performance (GFLOPS). Extensive experiments on real-world models demonstrate an order of magnitude improvement in execution time compared to the state-of-the-art.

Table 1 : Performance of our point vs. line darts.
k-d Darts: Sampling by k-Dimensional Flat Searches

February 2013


224 Reads

We formalize sampling a function using k-d darts. A k-d Dart is a set of independent, mutually orthogonal, k-dimensional hyperplanes called k-d flats. A dart has d choose k flats, aligned with the coordinate axes for efficiency. We show k-d darts are useful for exploring a function's properties, such as estimating its integral, or finding an exemplar above a threshold. We describe a recipe for converting some algorithms from point sampling to k-d dart sampling, if the function can be evaluated along a k-d flat. We demonstrate that k-d darts are more efficient than point-wise samples in high dimensions, depending on the characteristics of the domain: for example, the subregion of interest has small volume and evaluating the function along a flat is not too expensive. We present three concrete applications using line darts (1-d darts): relaxed maximal Poisson-disk sampling, high-quality rasterization of depth-of-field blur, and estimation of the probability of failure from a response surface for uncertainty quantification. Line darts achieve the same output fidelity as point sampling in less time. For Poisson-disk sampling, we use less memory, enabling the generation of larger point distributions in higher dimensions. Higher-dimensional darts provide greater accuracy for a particular volume estimation problem.

Figure 3: Left: for a facade layout we show a terminal region, R i , with parameters (x i , y i , w i , h i ). Right: a selection of terminal regions that are used in the layout is shown on the top. Two nonterminal regions are shown on the bottom. The location of these regions in the layout is highlighted in red on the left. 
Figure 4: A visual representation of the effect of the split rule, F1 (left), and the repeat rule, F2 (right), described in the text. The rectangles of F1 and F2 are not drawn to scale. 
Inverse Procedural Modeling of Facade Layouts

August 2014


1,068 Reads

In this paper, we address the following research problem: How can we generate a meaningful split grammar that explains a given facade layout? To evaluate if a grammar is meaningful, we propose a cost function based on the description length and minimize this cost using an approximate dynamic programming framework. Our evaluation indicates that our framework extracts meaningful split grammars that are competitive with those of expert users, while some users and all competing automatic solutions are less successful.

Protected Interactive 3D Graphics Via Remote Rendering

June 2004


340 Reads

Valuable 3D graphical models, such as high-resolution digital scans of cultural heritage objects, may require protection to prevent piracy or misuse, while still allowing for interactive display and manipulation by a widespread audience. We have investigated techniques for protecting 3D graphics content, and we have developed a remote rendering system suitable for sharing archives of 3D models while protecting the 3D geometry from unauthorized extraction. The system consists of a 3D viewer client that includes lowresolution versions of the 3D models, and a rendering server that renders and returns images of high-resolution models according to client requests. The server implements a number of defenses to guard against 3D reconstruction attacks, such as monitoring and limiting request streams, and slightly perturbing and distorting the rendered images. We consider several possible types of reconstruction attacks on such a rendering server, and we examine how these attacks can be defended against without excessively compromising the interactive experience for non-malicious users.

Real-Time 3D Model Acquisition

May 2002


265 Reads

The digitization of the 3D shape of real objects is a rapidly expanding field, with applications in entertainment, design, and archaeology. We propose a new 3D model acquisition system that permits the user to rotate an object by hand and see a continuously-updated model as the object is scanned. This tight feedback loop allows the user to find and fill holes in the model in real time, and determine when the object has been completely covered. Our system is based on a 60 Hz. structured-light rangefinder, a real-time variant of ICP (iterative closest points) for alignment, and point-based merging and rendering algorithms. We demonstrate the ability of our prototype to scan objects faster and with greater ease than conventional model acquisition pipelines.

Figure 6: The Zerobit Encoding Scheme
Figure 11: A Sample Slice in the Cropped Region (Abdomen)  
Figure 17: Sample Slices from the four 3D Textures
Figure 18: Four Renderings of Polygonal Models with 3D Textures  
Figure 20: Aliasing Artifacts of Compression-Based 3D Texture Mapping (2X)  
3D RGB Image Compression for Interactive Applications

March 2000


364 Reads

This paper presents a new 3D RGB image compression scheme designed for interactive real-time applications. In designing our compression method, we have compromised between two important goals: high compression ratio and fast random access ability, and have tried to minimize the overhead caused during runtime reconstruction. Our compression technique is suitable for applications wherein data are accessed in a somewhat unpredictable fashion, and real-time performance of decompression is necessary. The experimental results on three different kinds of 3D images from medical imaging, image-based rendering, and solid texture mapping suggest that the compression method can be used effectively in developing real-time applications that must handle large volume data, made of color samples taken in three- or higher-dimensional space. Keywords: 3D volume data, Data compression, Haar wavelets, Random access, Interactive real-time applications, Medical imaging, Image-based rendering, 3D text...

Figure 3: Equifaced tetrahedron in rectangular parallelpiped.  
Figure 4: Two quite different Tutte embeddings of the same mesh. Colored points mark corresponding vertices.  
Fundamentals of Spherical Parameterization for 3D Meshes

April 2003


615 Reads

Parametrization of 3D mesh data is important for many graphics applications, in particular for texture mapping, remeshing and morphing. Closed manifold genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parametrizing a triangle mesh onto the sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity do not overlap. Satisfying the non-overlapping requirement is the most difficult and critical component of this process. We present a generalization of the method of barycentric coordinates for planar parametrization which solves the spherical parametrization problem, prove its correctness by establishing a connection to spectral graph theory and describe efficient numerical methods for computing these parametrizations.

Figure 2: Reflection paths obey Fermat's variational principle, stating that the length of the optical path connecting p and q is a local extremum. For any p and q there may be many such paths.
Fig. 5. One-bounce reflection images generated by the perturbation method for a polygon (left) and a solid object (right). The visibility in the right image is correctly handled by z-buffering. The results are nearly identical to the ray traced image, yet the perturbed images can be computed very rapidly (approximately 0.1 seconds per update) as the lizard-shaped polygon or the cube is moved interactively.  
Abstract Theory and Application of Specular Path Perturbation

December 2000


205 Reads

In this paper we apply perturbation methods to the problem of computing specular reflections in curved surfaces. The key idea is to generate families of closely related optical paths by expanding a given path into a high-dimensional Taylor series. Our path perturbation method is based on closed-form expressions for linear and higher-order approximations of ray paths, which are derived using Fermat's Variation Principle and the Implicit Function Theorem. The perturbation formula presented here holds for general multiple-bounce reflection paths and provides a mathematical foundation for exploiting path coherence in ray tracing acceleration techniques and incremental rendering. To illustrate its use, we describe an algorithm for fast approximation of specular reflections on curved surfaces; the resulting images are of high accuracy and nearly indistinguishable from ray traced images. Keywords: perturbation theory, implicit surfaces, optics, ray tracing, specular reflection 1 1 Introduct...

Radiance Interpolants for Accelerated Bounded-Error Ray Tracing

November 2000


123 Reads

Ray tracers, which sample radiance, are usually regarded as offline rendering algorithms that are too slow for interactive use. In this article we present a system that exploits object-space, ray-space, image-space, and temporal coherence to accelerate ray tracing. Our system uses per-surface interpolants to approximate radiance while conservatively bounding error. The techniques introduced in this article should enhance both interactive and batch ray tracers. Our approach explicitly decouples the two primary operations of a ray tracer - shading and visibility determination - and accelerates each of them independently. Shading is accelerated by quadrilinearly interpolating lazily acquired radiance samples. Interpolation error does not exceed a user-specified bound, allowing the user to control performance/quality tradeoffs. Error is bounded by adaptive sampling at discontinuities and radiance nonlinearities. Visibility determination at pixels is accelerated by reprojecting interpolants as the user's viewpoint changes. A fast scan-line algorithm then achieves high performance without sacrificing image quality. For a smoothly varying viewpoint, the combination of lazy interpolants and reprojection substantially accelerates the ray tracer. Additionally, an efficient cache management algorithm keeps the memory footprint of the system small with negligible overhead.

Building Efficient, Accurate Character Skins from Examples

June 2003


72 Reads

Good character animation requires convincing skin deformations including subtleties and details like muscle bulges. Such effects are typically created in commercial animation packages which provide very general and powerful tools. While these systems are convenient and flexible for artists, the generality often leads to characters that are slow to compute or that require a substantial amount of memory and thus cannot be used in interactive systems. Instead, interactive systems restrict artists to a specific character deformation model which is fast and memory efficient but is notoriously difficult to author and can suffer from many deformation artifacts. This paper presents an automated framework that allows character artists to use the full complement of tools in high-end systems to create characters for interactive systems. Our method starts with an arbitrarily rigged character in an animation system. A set of examples is exported, consisting of skeleton configurations paired with the deformed geometry as static meshes. Using these examples, we fit the parameters of a deformation model that best approximates the original data yet remains fast to compute and compact in memory. Keywords: Interactive, Skin, Approximation I

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