Estimating Color and Texture Parameters for Vector Graphics

Abstract

Figure 1: Top row from left to right: original image, coloring result by [OBW * 08], new coloring result, automatic noise fitting result. Bottom row: input curves, the 665 color points by [OBW * 08], the 283 color points by the new algorithm, final result after manual editing. AbstractDiffusion curves are a powerful vector graphic representation that stores an image as a set of 2D Bezier curves with colors defined on either side. These colors are diffused over the image plane, resulting in smooth color regions as well as sharp boundaries. In this paper, we introduce a new automatic diffusion curve coloring algorithm. We start by defining a geometric heuristic for the maximum density of color control points along the image curves. Following this, we present a new algorithm to set the colors of these points so that the resulting diffused image is as close as possible to a source image in a least squares sense. We compare our coloring solution to the existing one which fails for textured regions, small features, and inaccurately placed curves. The second contribution of the paper is to extend the diffusion curve representation to include texture details based on Gabor noise. Like the curves themselves, the defined texture is resolution independent, and represented compactly. We define methods to automatically make an initial guess for the noise texure, and we provide intuitive manual controls to edit the parameters of the Gabor noise. Finally, we show that the diffusion curve representation itself extends to storing any number of attributes in an image, and we demonstrate this functionality with image stippling an hatching applications.

Hierarchical diffusion curves for accurate automatic image vectorization

“…Given a set of existing Bezier curves, Jeschke et al [2011] also use a global optimization to solve the diffusion curve coloring problem, including positioning color points and fitting color values, which can well reconstruct image features of given curves. We use another different fitting algorithm.…”

“…15 (a)), we first extract Laplacian diffusion curves and color profiles to reconstruct the original image (Fig. 15 (c)) before modifying the normal derivate weights in order to generate the edited Hierarchical Diffusion Curves for Accurate Automatic Image Vectorization [Jeschke et al 2011]: (e) is reconstructed using our method with the curves from Jeschke et al's [2011] …”

“…Although this vectorization scheme works well for "vector-art-like" raster images, it is not capable of capturing all forms of color variation present in natural images. Jeschke et al [2011] extended diffusion curves with more general color and texture functions, as well as leveraging an alternative formulation of the problem as a solution to 2D Laplace equations with Dirichlet boundary conditions. Finch et al [2011] employed higher-order profile functions based on thin-plate splines with userspecifiable discontinuities.…”

“…(2) Jeschke et al [2011]); thirdly, if we only use Laplacian curves, all the 8C's above further reduce to 4C; lastly, due to connected Bezier curves having shared endpoints, we use shared endpoints to interpolate two connected Bezier curves and furthermore reduce the matrix dimension. Through these strategies, we reduce the number of unknowns and highly accelerate the computation.…”

Gradient Art: Creation and Vectorization

“…This is the reason why several extensions have been proposed to improve artistic control using directional diffusion and blockers [3,4], or to produce a smoother color propagation [10]. Jeschke et al [13] also use diffusion curves to control the parameters of procedural textures, while Hnaidi et al [11] create height fields by diffusing height from curves that represent ridges and cliffs. Finally, Takayama et al [24] extend diffusion curves to diffusion surfaces to create volumetric models with 3D color gradients.…”