Hierarchical diffusion curves for accurate automatic image vectorization

Abstract

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.

Depth-aware image vectorization and editing

“…Solid color and gradient fills later became standard and permitted the compact representation of a wide range of expressive, scalable images. More recently, research has sought to increase the expressive range of colors and textures in vector graphics via methods that can be classified as patch-based [13,31], mesh-based [12,29], and curve-based [32].…”

“…Several other papers use a bi-Laplacian formulation of diffusion curves in order to provide more control over color diffusion from boundary curves [2,4,8]. Xie et al [32] proposed an automatic vectorization method based on extracting hierarchical diffusion curves in both the Laplacian and bi-Laplacian domains. Although their work achieves a high-quality reconstruction both for vector art and for natural images, their diffusion curves and colors are mostly static and cannot be edited later, apart from tasks such as detail removal and stylization.…”

“…Current diffusion curve image representations consist of relatively sparse sets of disconnected curves, each of which must be edited individually rather than at the level of the objects in the image. Although Xie et al [32] employed a hierarchy of multiresolution diffusion curves to make their results more editable, their method was limited to rendering at multiple levels of visual abstraction and could not support shape and color editing. Our method combines color and depth information and is therefore capable of defining diffusion curves that align accurately with both important image features and object contours.…”

Generalized Diffusion Curves: An Improved Vector Representation for Smooth‐Shaded Images

“…This behaviour is conceptually similar to Hermite curve interpolation as sketched at the top of Figure 2, and it is clearly not desirable in 2D image editing and animation applications. Recently, Xie et al [XSTN14] showed how to automatically convert a raster image to a set of Bezier curves together with a Bilaplace image model. Another issue is that Bilaplace functions are known to be much more computationally expensive and subject to numerical instability because the system is less well-conditioned, as opposed to Laplace functions.…”

“…But this makes fitting a given color image to a set of Bezier curves challenging because selecting the right constraints is not trivial. Recently, Xie et al [XSTN14] showed how to automatically convert a raster image to a set of Bezier curves together with a Bilaplace image model. However, their representation is based on the boundary element method so that colors and Bezier curve geometry remain mostly static, i.e., both cannot be edited later.…”