Figure 1:We are able to accurately vectorize raster images ("Input") by automatically tracing a sparse set of multi-scale diffusion curves to a broad class of images, including vector art (i.e., diffusion curve images), fluid simulations with turbulent flows, and natural images. AbstractDiffusion curve primitives are a compact and powerful representation for vector images. While several vector image authoring tools leverage these representations, automatically and accurately vectorizing arbitrary raster images using diffusion curves remains a difficult problem. We automatically generate sparse diffusion curve vectorizations of raster images by fitting curves in the Laplacian domain. Our approach is fast, combines Laplacian and bilaplacian diffusion curve representations, and generates a hierarchical representation that accurately reconstructs both vector art and natural images. The key idea of our method is to trace curves in the Laplacian domain, which captures both sharp and smooth image features, across scales, more robustly than previous image-and gradientdomain fitting strategies. The sparse set of curves generated by our method accurately reconstructs images and often closely matches tediously hand-authored curve data. Also, our hierarchical curves are readily usable in all existing editing frameworks. We validate our method on a broad class of images, including natural images, synthesized images with turbulent multi-scale details, and traditional vector-art, as well as illustrating simple multi-scale abstraction and color editing results.

Figure 1: Our method provides a compact and explicit representation of diffusion curve images for texture mapping onto a surface. The sharp features and detailed color variations of textures are well preserved in the rendering results. AbstractWe introduce a vector representation called diffusion curve textures for mapping diffusion curve images (DCI) onto arbitrary surfaces. In contrast to the original implicit representation of DCIs [Orzan et al. 2008], where determining a single texture value requires iterative computation of the entire DCI via the Poisson equation, diffusion curve textures provide an explicit representation from which the texture value at any point can be solved directly, while preserving the compactness and resolution independence of diffusion curves. This is achieved through a formulation of the DCI diffusion process in terms of Green's functions. This formulation furthermore allows the texture value of any rectangular region (e.g. pixel area) to be solved in closed form, which facilitates anti-aliasing. We develop a GPU algorithm that renders anti-aliased diffusion curve textures in real time, and demonstrate the effectiveness of this method through high quality renderings with detailed control curves and color variations.

Many applications in rendering rely on integrating functions over spherical polygons. We present a new numerical solution for computing the integral of spherical harmonics (SH) expansions clipped to polygonal domains. Our solution, based on zonal decompositions of spherical integrands and discrete contour integration, introduces an important numerical operating for SH expansions in rendering applications. Our method is simple, efficient, and scales linearly in the bandlimited integrand’s harmonic expansion. We apply our technique to problems in rendering, including surface and volume shading, hierarchical product importance sampling, and fast basis projection for interactive rendering. Moreover, we show how to handle general, nonpolynomial integrands in a Monte Carlo setting using control variates. Our technique computes the integral of bandlimited spherical functions with performance competitive to (or faster than) more general numerical integration methods for a broad class of problems, both in offline and interactive rendering contexts. Our implementation is simple, relying only on self-contained SH evaluation and discrete contour integration routines, and we release a full source CPU-only and shader-based implementations (<750 lines of commented code).

a) 1 spp in 5D. (b) 64 spp in 5D, (c) Refocused (a). (d) Refocused (b). (e) 1 spp in 2D. (f) Reference. drop to 1 spp in 2D.Figure 1: Comparison of temporal light field reconstruction [Lehtinen et al. 2011] with different schemes for low discrepancy sampling. The samples in (a) have blue-noise properties in 5D light field space, and the properties are greatly diminished in 2D image space. The samples in (b) and (e) maintain blue-noise properties in 2D image space, which greatly enhances the rendering quality. The quality of refocus rendering in (c) and (d) is consistent to the blue-noise properties in 2D image space. Please refer to Section 4.4 for a detailed description. AbstractLine segment sampling has recently been adopted in many rendering algorithms for better handling of a wide range of effects such as motion blur, defocus blur and scattering media. A question naturally raised is how to generate line segment samples with good properties that can effectively reduce variance and aliasing artifacts observed in the rendering results. This paper studies this problem and presents a frequency analysis of line segment sampling. The analysis shows that the frequency content of a line segment sample is equivalent to the weighted frequency content of a point sample. The weight introduces anisotropy that smoothly changes among point samples, line segment samples and line samples according to the lengths of the samples. Line segment sampling thus makes it possible to achieve a balance between noise (point sampling) and aliasing (line sampling) under the same sampling rate. Based on the analysis, we propose a line segment sampling scheme to preserve blue-noise properties of samples which can significantly reduce noise and aliasing artifacts in reconstruction results. We demonstrate that our sampling scheme improves the quality of depth-offield rendering, motion blur rendering, and temporal light field reconstruction.

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