Freeform vector graphics with controlled thin-plate splines

Freeform vector graphics with controlled thin-plate splines
Mark Finch, John Snyder, Hugues Hoppe.
ACM Trans. Graphics (SIGGRAPH Asia), 30(6), 2011.
Rich set of curve and point controls for intuitive and expressive color interpolation.
Abstract: Recent work defines vector graphics using diffusion between colored curves. We explore higher-order fairing to enable more natural interpolation and greater expressive control. Specifically, we build on thin-plate splines which provide smoothness everywhere except at user-specified tears and creases (discontinuities in value and derivative respectively). Our system lets a user sketch discontinuity curves without fixing their colors, and sprinkle color constraints at sparse interior points to obtain smooth interpolation subject to the outlines. We refine the representation with novel contour and slope curves, which anisotropically constrain interpolation derivatives. Compound curves further increase editing power by expanding a single curve into multiple offsets of various basic types (value, tear, crease, slope, and contour). The vector constraints are discretized over an image grid, and satisfied using a hierarchical solver. We demonstrate interactive authoring on a desktop CPU.
Hindsights: We should have mentioned the work of [Xia et al. 2009. Patch-Based Image Vectorization with Automatic Curvilinear Feature Alignment] which also introduces higher-order color reconstruction for vector graphics. It optimizes parametric Bezier patches with Thin-Plate Spline color functions to approximate a given image.
ACM Copyright Notice
Copyright by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Publications Dept, ACM Inc., fax +1 (212) 869-0481, or The definitive version of this paper can be found at ACM's Digital Library