We propose an automatic approach to tree detection from aerial imagery. First a pixel-level classifier is trained to assign a {tree, non-tree} label to each pixel in an aerial image. The pixel-level classification is then refined by a partitioning algorithm to a clean image segmentation of tree and non-tree regions. Based on the refined segmentation results, we adopt template matching followed by greedy selection to locate individual tree crowns.

Decorating arbitrary meshes with Celtic knots requires polygonal meshes with regular connectivity and close to regular face geometry. Because these properties are often irregular, especially in scanned or reconstructed models, the Celtic knots produced may be erratic and undesirable. In this paper we remesh models based on planar tilings defined by the user. Such pattern-oriented surfaces allow us to decorate models with attractive Celtic knots in a consistent fashion and may be applicable to a large number of algorithms that are sensitive to mesh structure.

We consider the problem of creating a map between two arbitrary triangle meshes. Whereas previous approaches compose parametrizations over a simpler intermediate domain, we directly create and optimize a continuous map between the meshes. Map distortion is measured with a new symmetric metric, and is minimized during interleaved coarse-to-fine refinement of both meshes. By explicitly favoring low inter-surface distortion, we obtain maps that naturally align corresponding shape elements. Typically, the user need only specify a handful of feature correspondences for initial registration, and even these constraints can be removed during optimization. Our method robustly satisfies hard constraints if desired. Inter-surface mapping is shown using geometric and attribute morphs. Our general framework can also be applied to parametrize surfaces onto simplicial domains, such as coarse meshes (for semi-regular remeshing), and octahedron and toroidal domains (for geometry image remeshing). In these settings, we obtain better parametrizations than with previous specialized techniques, thanks to our fine-grain optimization.

Volume rendering is a flexible technique for visualizing dense 3D volumetric datasets. A central element of volume rendering is the conversion between data values and observable quantities such as color and opacity. This process is usually realized through the use of transfer functions that are precomputed and stored in lookup tables. For multidimensional transfer functions applied to multivariate data, these lookup tables become prohibitively large. We propose the direct evaluation of a particular type of transfer functions based on a sum of Gaussians. Because of their simple form (in terms of number of parameters), these functions and their analytic integrals along line segments can be evaluated efficiently on current graphics hardware, obviating the need for precomputed lookup tables. We have adopted these transfer functions because they are well suited for classification based on a unique combination of multiple data values that localize features in the transfer function domain. We apply this technique to the visualization of several multivariate datasets (CT, cryosection) that are difficult to classify and render accurately at interactive rates using traditional approaches.

The traditional approach for parametrizing a surface involves cutting it into charts and mapping these piecewise onto a planar domain. We introduce a robust technique for directly parametrizing a genus-zero surface onto a spherical domain. A key ingredient for making such a parametrization practical is the minimization of a stretch-based measure, to reduce scale-distortion and thereby prevent undersampling. Our second contribution is a scheme for sampling the spherical domain using uniformly subdivided polyhedral domains, namely the tetrahedron, octahedron, and cube. We show that these particular semi-regular samplings can be conveniently represented as completely regular 2D grids, i.e. geometry images. Moreover, these images have simple boundary extension rules that aid many processing operations. Applications include geometry remeshing, level-of-detail, morphing, compression, and smooth surface subdivision.

We introduce a method for real-time rendering of fur on surfaces of arbitrary topology. As a pre-process, we simulate virtual hair with a particle system, and sample it into a volume texture. Next, we parameterize the texture over a surface of arbitrary topology using "lapped textures" --- an approach for applying a sample texture to a surface by repeatedly pasting patches of the texture until the surface is covered. The use of lapped textures permits specifying a global direction field for the fur over the surface. At runtime, the patches of volume textures are rendered as a series of concentric shells of semi-transparent medium. To improve the visual quality of the fur near silhouettes, we place "fins" normal to the surface and render these using conventional 2D texture maps sampled from the volume texture in the direction of hair growth. The method generates convincing imagery of fur at interactive rates for models of moderate complexity. Furthermore, the scheme allows real-time modification of viewing and lighting conditions, as well as local control over hair color, length, and direction.

Drawing surfaces using hatching strokes simultaneously conveys material, tone, and form. We present a real-time system for non-photorealistic rendering of hatching strokes over arbitrary surfaces. During an automatic preprocess, we construct a sequence of mipmapped hatch images corresponding to different tones, collectively called a tonal art map. Strokes within the hatch images are scaled to attain appropriate stroke size and density at all resolutions, and are organized to maintain coherence across scales and tones. At runtime, hardware multitexturing blends the hatch images over the rendered faces to locally vary tone while maintaining both spatial and temporal coherence. To render strokes over arbitrary surfaces, we build a lapped texture parametrization where the overlapping patches align to a curvature-based direction field. We demonstrate hatching strokes over complex surfaces in a variety of styles.

A basic element of Digital Geometry Processing algorithms is the establishment of a smooth parameterization for a given model. In this paper we propose an algorithm which establishes parameterizations for a set of models. The parameterizations are called consistent because they share the same base domain and respect features. They give immediate correspondences between models and allow remeshes with the same connectivity. Such remeshes form the basis for a large class of algorithms, including principal component analysis, wavelet transforms, detail and texture transfer between models, and n-way shape blending. We demonstrate the versatility of our algorithm with a number of examples. 1

We present for creating texture over an surface mesh using an example 2D texture. The approach is to identify interesting regions (texture patches) in the 2D example, and to repeatedly paste them onto the surface until it is completely covered. We call such a collection of overlapping patches a lapped texture. It is rendered using compositing operations, either into a traditional global texture map during a preprocess, or directly with the surface at runtime. The runtime compositing approach avoids resampling artifacts and drastically reduces texture memory requirements.

Watermarking provides a mechanism for copyright protection of digital media by embedding infor-mation identifying the owner in the data. The bulk of the research on digital watermarks has focused on media such as images, video, audio, and text. Robust watermarks must be able to survive a va-riety of “attacks”, including resizing, cropping, and filtering. For resilience to such attacks, recent watermarking schemes employ a “spread-spectrum ” approach — they transform the document to the frequency domain (e.g. using DCT) and perturb the coefficients of the perceptually most significant basis functions. In this paper we extend this spread-spectrum approach for the robust watermarking of arbitrary triangle meshes. Generalization of the spread spectrum techniques to surfaces presents two major challenges. First, arbitrary surfaces lack a natural parametrization for frequency-based decomposition. Our solution is to construct a set of scalar basis function over the mesh vertices using a multiresolution analysis of the mesh. The watermark is embedded in the mesh by perturbing vertices along the direction of the surface normal, weighted by the basis functions. The second challenge is that attacks such as simplification may modify the connectivity of the mesh. We use an optimization technique to resam-ple an attacked mesh using the original mesh connectivity. Results demonstrate that our watermarks are resistant to common mesh processing operations such as translation, rotation, scaling, cropping, smoothing, simplification, and resampling, as well as malicious attacks such as the insertion of noise, modification of low-order bits, or even insertion of other watermarks.