Cosmetic makeup is used worldwide as a means to enhance beauty and express moods. An art form in its own right, cosmetic styles continuously change and evolve to reflect cultural and societal trends. While countless magazines and books are dedicated to demonstrating cosmetic art, the actual application of makeup still remains a physical endeavor. In this paper, we describe a procedure to apply cosmetic makeup to the image of a person's face with the click of a mouse. Our approach works from before- and-after example images created by professional makeup artists. Using our "cosmetic-transfer" procedure, we can realistically transfer the cosmetic style captured in the example-pair to another person's face. This greatly reduces the time and effort needed to demonstrate a cosmetic style on a new person's face. In addition, our approach can be used to mix-and- match, and even fine-tune, example styles, all virtually, without the need for any physical makeup.

Inspired by multi-scale tensor voting, a computational framework for perceptual grouping and segmentation, we propose an edge-directed technique for color image superresolution given a single low-resolution color image. Our multi-scale technique combines the advantages of edgedirected, reconstruction-based and learning-based methods, and is unique in two ways. First, we consider simultaneously all the three color channels in our multi-scale tensor voting framework to produce a multi-scale edge representation to guide the process of high-resolution color image reconstruction, which is subject to the back projection constraint. Fine details are inferred without noticeable blurry or ringing artifacts. Second, the inference of highresolution curves is achieved by multi-scale tensor voting, using the dense voting field as an edge-preserving smoothness prior which is derived geometrically without any timeconsuming learning procedure. Qualitative and quantitative results indicate that our method produces convincing results in complex test cases typically used by state-of-theart image super-resolution techniques.

Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.

We address the problem of simultaneous two-view epipolar geometry estimation and motion segmentation from nonstatic scenes. Given a set of noisy image pairs containing matches of n objects, we propose an unconventional, efficient, and robust method, 4D tensor voting, for estimating the unknown n epipolar geometries, and segmenting the static and motion matching pairs into n independent motions. By considering the 4D isotropic and orthogonal joint image space, only two tensor voting passes are needed, and a very high noise to signal ratio (up to five) can be tolerated. Epipolar geometries corresponding to multiple, rigid motions are extracted in succession. Only two uncalibrated frames are needed, and no simplifying assumption (such as affine camera model or homographic model between images) other than the pin-hole camera model is made. Our novel approach consists of propagating a local geometric smoothness constraint in the 4D joint image space, followed by global consistency enforcement for extracting the fundamental matrices corresponding to independent motions. We have performed extensive experiments to compare our method with some representative algorithms to show that better performance on nonstatic scenes are achieved. Results on challenging data sets are presented.

Most computer vision applications require the reliable detection of boundaries. In the presence of outliers, missing data, orientation discontinuities, and occlusion, this problem is particularly challenging. We propose to address it by complementing the tensor voting framework, which was limited to second order properties, with first order representation and voting. First order voting fields and a mechanism to vote for 3D surface and volume boundaries and curve endpoints in 3D are defined. Boundary inference is also useful for a second difficult problem in grouping, namely, automatic scale selection. We propose an algorithm that automatically infers the smallest scale that can preserve the finest details. Our algorithm then proceeds with progressively larger scales to ensure continuity where it has not been achieved. Therefore, the proposed approach does not oversmooth features or delay the handling of boundaries and discontinuities until model misfit occurs. The interaction of smooth features, boundaries, and outliers is accommodated by the unified representation, making possible the perceptual organization of data in curves, surfaces, volumes, and their boundaries simultaneously. We present results on a variety of data sets to show the efficacy of the improved formalism.

We propose a novel 2D representation for 3D visibility sorting, the Binary-Space-Partitioned Image (BSPI), to accelerate real-time image-based rendering. BSPI is an efficient 2D realization of a 3D BSP tree, which is commonly used in computer graphics for time-critical visibility sorting. Since the overall structure of a BSP tree is encoded in a BSPI, traversing a BSPI is comparable to traversing the corresponding BSP tree. BSPI performs visibility sorting efficiently and accurately in the 2D image space by warping the reference image triangle-by-triangle instead of pixel-by-pixel. Multiple BSPIs can be combined to solve "disocclusion," when an occluded portion of the scene becomes visible at a novel viewpoint. Our method is highly automatic, including a tensor voting preprocessing step that generates candidate image partition lines for BSPIs, filters the noisy input data by rejecting outliers, and interpolates missing information. Our system has been applied to a variety of real data, including stereo, motion, and range images.

A "graphics for vision" approach is proposed to address the problem of reconstruction from a large and imperfect data set: reconstruction on demand by tensor voting, or ROD-TV. ROD-TV simultaneously delivers good efficiency and robustness, by adapting to a continuum of primitive connectivity, view dependence, and levels of detail (LOD). Locally inferred surface elements are robust to noise and better capture local shapes. By inferring per-vertex normals at sub-voxel precision on the fly, we can achieve interpolative shading. Since these missing details can be recovered at the current level of detail, our result is not upper bounded by the scanning resolution. By relaxing the mesh connectivity requirement, we extend ROD-TV and propose a simple but effective multiscale feature extraction algorithm. ROD-TV consists of a hierarchical data structure that encodes different levels of detail. The local reconstruction algorithm is tensor voting. It is applied on demand to the visible subset of data at a desired level of detail, by traversing the data hierarchy and collecting tensorial support in a neighborhood. We compare our approach and present encouraging results.

Many computer vision systems depend on reliable detection of 3D boundaries and regions in order to proceed. In the presence of outliers, missing data and orientation discontinuities due to occlusion, it is difficult to detect boundaries and interpolate data without over-smoothing important feature curves. The authora address these problems by incorporating first order tensor information into the tensor voting formalism, which is second-order based. To propagate an adaptive smoothness constraint at a preferred orientation non-iteratively, we vote for a first order tensor (or vector) to capture polarity and orientation information. To integrate first and second order tensors, we propose an algorithm for inferring the proper scale based on the continuity constraint, and preserving the finest details. Given a noisy 3D point set, the new and improved formalism can better localize boundary curves and orientation discontinuities. Unlike many approaches that over-smooth features, or delay the handling of boundaries and discontinuities until model misfit occurs, the interaction of smooth features, boundaries, discontinuities, outliers are encoded at the representation level. We present results from a variety of datasets to show the efficacy of the improved formalism.

In the presence of false matches and moving objects, image registration is challenging, as outlier rejection, matching and registration become interdependent. We present an efficient and robust method, 4D tensor voting to estimate epipolar geometries for non-static scenes, and identify matching points due to salient and independent motions. Unlike other optimization techniques, data communication in 4D tensor voting does not involve any iterative search. Thus, initialization, local optimum, convergence, and dimensionality of parameter space are not problematic. Like the 8D counterpart, the only assumption we make is the pinhole camera model. Two advancements are made in this work. First, we reduce the dimensionality, and the 4D joint image space is an isotropic and orthogonal one, validating the general assumptions of tensor voting. This improvement is evidenced by the facts that only two passes are needed, and that 4D tensor voting can tolerate an even larger noise/signal ratio (up to a ratio of five). Second, instead of discarding motion pixels as outliers, we successively extract the epipolar geometries contributed by the static background and by the matching points due to salient motions. Only two frames are needed, and no simplifying assumption (such as affine camera model or homographic model between images) is made. Our 4D algorithm consists of two stages: local continuity constraint propagation to remove outliers, and global consistency checking to localize a 4D topological point cone. Results on challenging datasets are presented.