This paper presents a novel approach to edge-aware image manipulation. Our method processes a Gaussian pyramid from coarse to fine, and at each level, applies a nonlinear filter bank to the neighborhood of each pixel. Outputs of these spatially-varying filters are merged using global optimization. The optimization problem is solved using an explicit mixed-domain (real space and DCT transform space) solution, which is efficient, accurate, and easy-to-implement. We demonstrate applications of our method to a set of problems, including detail and contrast manipulation, HDR compression, nonphotorealistic rendering, and haze removal.

We present a new method for interpolating both boundary values and gradients over a 2D polygonal domain. Despite various previous efforts, it remains challenging to define a closed-form interpolant that produces natural-looking functions while allowing flexible control of boundary constraints. Our method builds on an existing transfinite interpolant over a continuous domain, which in turn extends the classical mean value interpolant. We re-derive the interpolant from the mean value property of biharmonic functions, and prove that the interpolant indeed matches the gradient constraints when the boundary is piece-wise linear. We then give closed-form formula (as generalized barycentric coordinates) for boundary constraints represented as polynomials up to degree 3 (for values) and 1 (for normal derivatives) over each polygon edge. We demonstrate the flexibility and efficiency of our coordinates in two novel applications, smooth image deformation using curved cage networks and adaptive simplification of gradient meshes.

Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.

This paper gives an automatic method for online video stream abstraction, producing a temporally coherent output video stream, in a style with large regions of constant color and highlighted bold edges. Our system includes two novel components. Firstly, to provide coherent and simplified output, we segment frames, and use optical flow to propagate segmentation information from frame to frame; an error control strategy is used to help ensure that the propagated information is reliable. Secondly, to achieve coherent and attractive coloring of the output, we use a color scheme replacement algorithm specifically designed for an online video stream. We demonstrate real-time performance for CIF videos, allowing our approach to be used for live communication and other related applications.

Pop-up books are a fascinating form of paper art with intriguing geometric properties. In this paper, we present a systematic study of a simple but common class of pop-ups consisting of patches falling into four parallel groups, which we call v-style pop-ups. We give sufficient conditions for a v-style paper structure to be pop-uppable. That is, it can be closed flat while maintaining the rigidity of the patches, the closing and opening do not need extra force besides holding two patches and are free of intersections, and the closed paper is contained within the page border. These conditions allow us to identify novel mechanisms for making pop-ups. Based on the theory and mechanisms, we developed an interactive tool for designing v-style pop-ups and an automated construction algorithm from a given geometry, both of which guaranteeing the pop-uppability of the results.

Paper architectures are 3D paper buildings created by folding and cutting. The creation process of paper architecture is often labor-intensive and highly skill-demanding, even with the aid of existing computer-aided design tools. We propose an automatic algorithm for generating paper architectures given a user-specified 3D model. The algorithm is grounded on geometric formulation of planar layout for paper architectures that can be popped-up in a rigid and stable manner, and sufficient conditions for a 3D surface to be popped-up from such a planar layout. Based on these conditions, our algorithm computes a class of paper architectures containing two sets of parallel patches that approximate the input geometry while guaranteed to be physically realizable. The method is demonstrated on a number of architectural examples, and physically engineered results are presented.