Figure 1: Our texture generation process takes an example texture patch (left) and a random noise (middle) as input, and modifies this random noise to make it look like the given example texture. The synthesized texture (right) can be of arbitrary size, and is perceived as very similar to the given example. Using our algorithm, textures can be generated within seconds, and the synthesized results are always tileable. Texture synthesis is important for many applications in computer graphics, vision, and image processing. However, it remains difficult to design an algorithm that is both efficient and capable of generating high quality results. In this paper, we present an efficient algorithm for realistic texture synthesis. The algorithm is easy to use and requires only a sample texture as input. It generates textures with perceived quality equal to or better than those produced by previous techniques, but runs two orders of magnitude faster. This permits us to apply texture synthesis to problems where it has traditionally been considered impractical. In particular, we have applied it to constrained synthesis for image editing and temporal texture generation. Our algorithm is derived from Markov Random Field texture models and generates textures through a deterministic searching process. We accelerate this synthesis process using tree-structured vector quantization.

We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We present tools to increase or decrease the density of the points, thus, allowing an adjustment of the spacing among the points to control the fidelity of the representation. To display the point set surface, we introduce a novel point rendering technique. The idea is to evaluate the local maps according to the image resolution. This results in high quality shading effects and smooth silhouettes at interactive frame rates.

We describe an image based rendering approach that generalizes many image based rendering algorithms currently in use including light field rendering and view-dependent texture mapping. In particular it allows for lumigraph style rendering from a set of input cameras that are not restricted to a plane or to any specific manifold. In the case of regular and planar input camera positions, our algorithm reduces to a typical lumigraph approach. In the case of fewer cameras and good approximate geometry, our algorithm behaves like view-dependent texture mapping. Our algorithm achieves this flexibility because it is designed to meet a set of desirable goals that we describe. We demonstrate this flexibility with a variety of examples. Keyword Image-Based Rendering 1

The power crust is a construction which takes a sample of points from the surface of a three-dimensional object and produces a surface mesh and an approximate medial axis. The approach is to first approximate the medial axis transform (MAT) of the object. We then use an inverse transform to produce the surface representation from the MAT.

Realism in computer-generated images requires accurate input models for lighting, textures and BRDFs. One of the best ways of obtaining high-quality data is through measurements of scene attributes from real photographs by inverse rendering. However, inverse rendering methods have been largely limited to settings with highly controlled lighting. One of the reasons for this is the lack of a coherent mathematical framework for inverse rendering under general illumination conditions. Our main contribution is the introduction of a signal-processing framework which describes the reflected light field as a convolution of the lighting and BRDF, and expresses it mathematically as a product of spherical harmonic coefficients of the BRDF and the lighting. Inverse rendering can then be viewed as deconvolution. We apply this theory to a variety of problems in inverse rendering, explaining a number of previous empirical results. We will show why certain problems are ill-posed or numerically ill-conditioned, and why other problems are more amenable to solution. The theory developed here also leads to new practical representations and algorithms. For instance, we present a method to factor the lighting and BRDF from a small number of views, i.e. to estimate both simultaneously when neither is known.

We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). The computation of points on the surface is local, which results in an out-of-core technique that can handle any point set.

We present a shape representation, the multi-level partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighting functions (the partitions of unity) that blend together these local shape functions, and 3) an octree subdivision method that adapts to variations in the complexity of the local shape.

Algorithms exist for synthesizing a wide variety of textures over rectangular domains. However, it remains difficult to synthesize general textures over arbitrary manifold surfaces. In this paper, we present a solution to this problem for surfaces defined by dense polygon meshes. Our solution extends Wei and Levoy's texture synthesis method [25] by generalizing their definition of search neighborhoods. For each mesh vertex, we establish a local parameterization surrounding the vertex, use this parameterization to create a small rectangular neighborhood with the vertex at its center, and search a sample texture for similar neighborhoods. Our algorithm requires as input only a sample texture and a target model. Notably, it does not require specification of a global tangent vector field; it computes one as it goes - either randomly or via a relaxation process. Despite this, the synthesized texture contains no discontinuities, exhibits low distortion, and is perceived to be similar to the sample texture. We demonstrate that our solution is robust and is applicable to a wide range of textures. Keywords: Texture Synthesis, Texture Mapping, Curves & Surfaces 1

In this paper we introduce, analyze and quantitatively compare a number of surface simplification methods for point-sampled geometry. We have implemented incremental and hierarchical clustering, iterative simplification, and particle simulation algorithms to create approximations of point-based models with lower sampling density. All these methods work directly on the point cloud, requiring no intermediate tesselation. We show how local variation estimation and quadric error metrics can be employed to diminish the approximation error and concentrate more samples in regions of high curvature. To compare the quality of the simplified surfaces, we have designed a new method for computing numerical and visual error estimates for point-sampled surfaces. Our algorithms are fast, easy to implement, and create high-quality surface approximations, clearly demonstrating the effectiveness of point-based surface simplification.

Abstract—In this paper, we present a framework for high quality splatting based on elliptical Gaussian kernels. To avoid aliasing artifacts, we introduce the concept of a resampling filter, combining a reconstruction kernel with a low-pass filter. Because of the similarity to Heckbert’s EWA (elliptical weighted average) filter for texture mapping, we call our technique EWA splatting. Our framework allows us to derive EWA splat primitives for volume data and for point-sampled surface data. It provides high image quality without aliasing artifacts or excessive blurring for volume data and, additionally, features anisotropic texture filtering for point-sampled surfaces. It also handles nonspherical volume kernels efficiently; hence, it is suitable for regular, rectilinear, and irregular volume datasets. Moreover, our framework introduces a novel approach to compute the footprint function, facilitating efficient perspective projection of arbitrary elliptical kernels at very little additional cost. Finally, we show that EWA volume reconstruction kernels can be reduced to surface reconstruction kernels. This makes our splat primitive universal in rendering surface and volume data. Index Terms—Rendering systems, volume rendering, texture mapping, splatting, antialiasing. 1