Vectorizing hand-drawn sketches is a challenging task, which is of paramount importance for creating CAD vectorized versions for the fashion and creative workflows. This paper proposes a complete framework that automatically transforms noisy and complex hand-drawn sketches with different stroke types in a precise, reliable and highly-simplified vectorized model. The proposed framework includes a novel line extraction algorithm based on a multi-resolution application of Pearson's cross correlation and a new unbiased thinning algorithm that can get rid of scribbles and variable-width strokes to obtain clean 1-pixel lines. Other contributions include variants of pruning, merging and edge linking procedures to post-process the obtained paths. Finally, a modification of the original Schneider's vectorization algorithm is designed to obtain fewer control points in the resulting Bezier splines. All the proposed steps of the framework have been extensively tested and compared with state-of-the-art algorithms, showing (both qualitatively and quantitatively) its outperformance.
@cite_2 provided a more complete study of the whole vectorization process. They provide a neat derivation-based algorithm to estimate accurate centerlines for sketches. They also provide a good insight of the problem of correct junction selection. Unfortunately, they work under the assumption of somewhat clean'' lines, that does not hold in many real case scenarios, such as those we are aiming at.
@cite_2
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Vectorization provides a link between raster scans of pencil-and-paper drawings and modern digital processing algorithms that require accurate vector representations. Even when input drawings are comprised of clean, crisp lines, inherent ambiguities near junctions make vectorization deceptively difficult. As a consequence, current vectorization approaches often fail to faithfully capture the junctions of drawn strokes. We propose a vectorization algorithm specialized for clean line drawings that analyzes the drawing's topology in order to overcome junction ambiguities. A gradient-based pixel clustering technique facilitates topology computation. This topological information is exploited during centerline extraction by a new “reverse drawing” procedure that reconstructs all possible drawing states prior to the creation of a junction and then selects the most likely stroke configuration. For cases where the automatic result does not match the artist's interpretation, our drawing analysis enables an efficient user interface to easily adjust the junction location. We demonstrate results on professional examples and evaluate the vectorization quality with quantitative comparison to hand-traced centerlines as well as the results of leading commercial algorithms. We propose a robust and accurate method to extract the centerlines and scale of tubular structures in 2D images and 3D volumes. Existing techniques rely either on filters designed to respond to ideal cylindrical structures, which lose accuracy when the linear structures become very irregular, or on classification, which is inaccurate because locations on centerlines and locations immediately next to them are extremely difficult to distinguish. We solve this problem by reformulating centerline detection in terms of a regression problem. We first train regressors to return the distances to the closest centerline in scale-space, and we apply them to the input images or volumes. The centerlines and the corresponding scale then correspond to the regressors local maxima, which can be easily identified. We show that our method outperforms state-of-the-art techniques for various 2D and 3D datasets. The determination of camera position and orientation from known correspondences of 3D reference points and their images is known as pose estimation in computer vision and space resection in photogrammetry. It is well-known that from three corresponding points there are at most four algebraic solutions. Less appears to be known about the cases of four and five corresponding points. We propose a family of linear methods that yield a unique solution to 4- and 5-point pose determination for generic reference points. We first review the 3-point algebraic method. Then we present our two-step, 4-point and one-step, 5-point linear algorithms. The 5-point method can also be extended to handle more than five points. Finally, we demonstrate our methods on both simulated and real images. We show that they do not degenerate for coplanar configurations and even outperform the special linear algorithm for coplanar configurations in practice. The paper describes an algorithm for generating an approximation of the medial axis transform (MAT) for planar objects with free form boundaries. The algorithm generates the MAT by a tracing technique that marches along the object boundary rather than the bisectors of the boundary entities. The level of approximation is controlled by the choice of the step size in the tracing procedure. Criteria based on distance and local curvature of boundary entities are used to identify the junction or branch points and the search for these branch points is more efficient than while tracing the bisectors. The algorithm works for multiply connected objects as well. Results of implementation are provided. In the isogeometric analysis framework, a computational domain is exactly described using the same representation as the one employed in the CAD process. For a CAD object, various computational domains can be constructed with the same shape but with different parameterizations; however one basic requirement is that the resulting parameterization should have no self-intersections. Moreover we will show, with an example of a 3D thermal conduction problem, that different parameterizations of a computational domain have different impacts on the simulation results and efficiency in isogeometric analysis. In this paper, a linear and easy-to-check sufficient condition for the injectivity of a trivariate B-spline parameterization is proposed. For problems with exact solutions, we will describe a shape optimization method to obtain an optimal parameterization of a computational domain. The proposed injective condition is used to check the injectivity of the initial trivariate B-spline parameterization constructed by discrete Coons volume method, which is a generalization of the discrete Coons patch method. Several examples and comparisons are presented to show the effectiveness of the proposed method. During the refinement step, the optimal parameterization can achieve the same accuracy as the initial parameterization but with less degrees of freedom. We present a new technique for extracting line-type features on point-sampled geometry. Given an unstructured point cloud as input, our method first applies principal component analysis on local neighborhoods to classify points according to the likelihood that they belong to a feature. Using hysteresis thresholding, we then compute a minimum spanning graph as an initial approximation of the feature lines. To smooth out the features while maintaining a close connection to the underlying surface, we use an adaptation of active contour models. Central to our method is a multi-scale classification operator that allows feature analysis at multiple scales, using the size of the local neighborhoods as a discrete scale parameter. This significantly improves the reliability of the detection phase and makes our method more robust in the presence of noise. To illustrate the usefulness of our method, we have implemented a non-photorealistic point renderer to visualize point-sampled surfaces as line drawings of their extracted feature curves. In this paper we present a prototype system for image based localization in urban environments. Given a database of views of city street scenes tagged by GPS locations, the system computes the GPS location of a novel query view. We first use a wide-baseline matching technique based on SIFT features to select the closest views in the database. Often due to a large change of viewpoint and presence of repetitive structures, a large percentage of matches (> 50 ) are not correct correspondences. The subsequent motion estimation between the query view and the reference view, is then handled by a novel and efficient robust estimation technique capable of dealing with large percentage of outliers. This stage is also accompanied by a model selection step among the fundamental matrix and the homography. Once the motion between the closest reference views is estimated, the location of the query view is then obtained by triangulation of translation directions. Approximate solutions for cases when triangulation cannot be obtained reliably are also described. The presented system is tested on the dataset used in ICCV 2005 Computer Vision Contest and is shown to have higher accuracy than previous reported results. Junctions are strong cues for understanding the geometry of a scene. In this paper, we consider the problem of detecting junctions and using them for recovering the spatial layout of an indoor scene. Junction detection has always been challenging due to missing and spurious lines. We work in a constrained Manhattan world setting where the junctions are formed by only line segments along the three principal orthogonal directions. Junctions can be classified into several categories based on the number and orientations of the incident line segments. We provide a simple and efficient voting scheme to detect and classify these junctions in real images. Indoor scenes are typically modeled as cuboids and we formulate the problem of the cuboid layout estimation as an inference problem in a conditional random field. Our formulation allows the incorporation of junction features and the training is done using structured prediction techniques. We outperform other single view geometry estimation methods on standard datasets. We propose a novel approach for optical flow estimation , targeted at large displacements with significant oc-clusions. It consists of two steps: i) dense matching by edge-preserving interpolation from a sparse set of matches; ii) variational energy minimization initialized with the dense matches. The sparse-to-dense interpolation relies on an appropriate choice of the distance, namely an edge-aware geodesic distance. This distance is tailored to handle occlusions and motion boundaries -- two common and difficult issues for optical flow computation. We also propose an approximation scheme for the geodesic distance to allow fast computation without loss of performance. Subsequent to the dense interpolation step, standard one-level variational energy minimization is carried out on the dense matches to obtain the final flow estimation. The proposed approach, called Edge-Preserving Interpolation of Correspondences (EpicFlow) is fast and robust to large displacements. It significantly outperforms the state of the art on MPI-Sintel and performs on par on Kitti and Middlebury. This paper presents a solution to panoramic image stitching of two images with coinciding optical centers, but unknown focal length and radial distortion. The algorithm operates with a minimal set of corresponding points (three) which means that it is well suited for use in any RANSAC style algorithm for simultaneous estimation of geometry and outlier rejection. Compared to a previous method for this problem, we are able to guarantee that the right solution is found in all cases. The solution is obtained by solving a small system of polynomial equations. The proposed algorithm has been integrated in a complete multi image stitching system and we evaluate its performance on real images with lens distortion. We demonstrate both quantitative and qualitative improvements compared to state of the art methods. Motivated by drawing route sketches, we consider the d-regular path schematization problem. For this problem we are given an embedded path P (e.g., a route in a road network) and a positive integer d. The goal is to find a d-schematized embedding of P in which the orthogonal order of all vertices in the input is preserved and in which every edge has a direction that is an integer multiple of (90 d)^o. We show that deciding whether a path can be d-schematized is NP-complete for any positive integer d. Despite the NP-hardness of the problem we still want to be able to generate route sketches and thus need to solve the d-regular path schematization problem. We explore two different algorithmic approaches, both of which consider two additional quality constraints: We require that every edge is drawn with a user-specified minimum length and we want to maximize the number of edges that are drawn with their preferred direction. The first algorithmic approach restricts the input paths to be axis-monotone. We show that there exists a polynomial-time algorithm that solves the d-regular path schematization problem for this restricted class of embedded paths. We extend this approach by a heuristic such that it can handle arbitrary simple paths. However, for the second step we cannot guarantee that the orthogonal order of the input embedding is maintained. The second approach is a formulation of the d-regular path schematization problem as a mixed integer linear program. Finally, we give an experimental evaluation which shows that both approaches generate reasonable route sketches for real-world data. We propose a novel approach for optical flow estimation, targeted at large displacements with significant occlusions. It consists of two steps: i) dense matching by edge-preserving interpolation from a sparse set of matches; ii) variational energy minimization initialized with the dense matches. The sparse-to-dense interpolation relies on an appropriate choice of the distance, namely an edge-aware geodesic distance. This distance is tailored to handle occlusions and motion boundaries - two common and difficult issues for optical flow computation. We also propose an approximation scheme for the geodesic distance to allow fast computation without loss of performance. Subsequent to the dense interpolation step, standard one-level variational energy minimization is carried out on the dense matches to obtain the final flow estimation. The proposed approach, called Edge-Preserving Interpolation of Correspondences (EpicFlow) is fast and robust to large displacements. It significantly outperforms the state of the art on MPI-Sintel and performs on par on Kitti and Middlebury. We study two versions of the 2-center problem for moving points in the plane. Given a set P of n points, the Euclidean 2-center problem asks for two congruent disks of minimum size that together cover P; the rectilinear 2-center problem correspondingly asks for two congruent axis-aligned squares of minimum size that together cover P. Our methods work in the black-box KDS model, where we receive the locations of the points at regular time steps and we know an upper bound d_ max on the maximum displacement of any point within one time step. We show how to maintain the rectilinear 2-center in amortized sub-linear time per time step, under certain assumptions on the distribution of the point set P. For the Euclidean 2-center we give a similar result: we can maintain in amortized sub-linear time (again under certain assumptions on the distribution) a (1+e)-approximation of the optimal 2-center. In many cases---namely when the distance between the centers of the disks is relatively large or relatively small---the solution we maintain is actually optimal. We also present results for the case where the maximum speed of the centers is bounded. We describe a simple scheme to maintain a 2-approximation of the rectilinear 2-center, and we provide a scheme which gives a better approximation factor depending on several parameters of the point set and the maximum allowed displacement of the centers. The latter result can be used to obtain a 2.29-approximation for the Euclidean 2-center; this is an improvement over the previously best known bound of 8 π approx 2.55. These algorithms run in amortized sub-linear time per time step, as before under certain assumptions on the distribution. A comprehensive scheme is described to construct rational trivariate solid T-splines from boundary triangulations with arbitrary topology. To extract the topology of the input geometry, we first compute a smooth harmonic scalar field defined over the mesh, and saddle points are extracted to determine the topology. By dealing with the saddle points, a polycube whose topology is equivalent to the input geometry is built, and it serves as the parametric domain for the trivariate T-spline. A polycube mapping is then used to build a one-to-one correspondence between the input triangulation and the polycube boundary. After that, we choose the deformed octree subdivision of the polycube as the initial T-mesh, and make it valid through pillowing, quality improvement and applying templates to handle extraordinary nodes and partial extraordinary nodes. The T-spline that is obtained is C^2-continuous everywhere over the boundary surface except for the local region surrounding polycube corner nodes. The efficiency and robustness of the presented technique are demonstrated with several applications in isogeometric analysis. We consider the following instance of projective clustering, known as the 2-line-center problem: Given a set S of n points in R2, cover S by two congruent strips of minimum width. Algorithms that find the optimal solution for this problem have near-quadratic running time. In this paper we present an algorithm that, for any e > 0, computes in time O(n(logn + e-2 log(1 e)) + e-7 2 log(1 e)) a cover of S by two strips of width at most (1 + e)w*. Abstract A simple method of analyzing symmetries of a line drawing is presented. The procedure consists of three stages: (1) computing the axes of ‘microsymmetry’ for pairs of microsegments based on the mean square error criterion, (2) mapping the axes into two-dimensional parameter space, and (3) detecting the peaks in the parameter space to obtain the global axes of symmetry. Abstract This paper mathematically analyzes and proposes new solutions for the problem of estimating the camera 3D location and orientation ( pose determination ) from a matched set of 3D model and 2D image landmark features. Least-squares techniques for line tokens, which minimize both rotation and translation simultaneously, are developed and shown to be far superior to the earlier techniques which solved for rotation first and then translation. However, least-squares techniques fail catastrophically when outliers (or gross errors) are present in the match data. Outliers arise frequently due to incorrect correspondences or gross errors in the 3D model. Robust techniques for pose determination are developed to handle data contaminated by fewer than 50.0 outliers. Finally, the sensitivity of pose determination to incorrect estimates of camera parameters is analyzed. It is shown that for small field of view systems, offsets in the image center do not significantly affect the location of the camera in a world coordinate system. Errors in the focal length significantly affect only the component of translation along the optical axis in the pose computation. In this paper we derive and test a probability-based weighting that can balance residuals of different types in spline fitting. In contrast to previous formulations, the proposed spline error weighting scheme also incorporates a prediction of the approximation error of the spline fit. We demonstrate the effectiveness of the prediction in a synthetic experiment, and apply it to visual-inertial fusion on rolling shutter cameras. This results in a method that can estimate 3D structure with metric scale on generic first-person videos. We also propose a quality measure for spline fitting, that can be used to automatically select the knot spacing. Experiments verify that the obtained trajectory quality corresponds well with the requested quality. Finally, by linearly scaling the weights, we show that the proposed spline error weighting minimizes the estimation errors on real sequences, in terms of scale and end-point errors. Analysis-by-synthesis has been a successful approach for many tasks in computer vision, such as 6D pose estimation of an object in an RGB-D image which is the topic of this work. The idea is to compare the observation with the output of a forward process, such as a rendered image of the object of interest in a particular pose. Due to occlusion or complicated sensor noise, it can be difficult to perform this comparison in a meaningful way. We propose an approach that "learns to compare", while taking these difficulties into account. This is done by describing the posterior density of a particular object pose with a convolutional neural network (CNN) that compares an observed and rendered image. The network is trained with the maximum likelihood paradigm. We observe empirically that the CNN does not specialize to the geometry or appearance of specific objects, and it can be used with objects of vastly different shapes and appearances, and in different backgrounds. Compared to state-of-the-art, we demonstrate a significant improvement on two different datasets which include a total of eleven objects, cluttered background, and heavy occlusion. A method is presented for automated segmentation of vessels in two-dimensional color images of the retina. This method can be used in computer analyses of retinal images, e.g., in automated screening for diabetic retinopathy. The system is based on extraction of image ridges, which coincide approximately with vessel centerlines. The ridges are used to compose primitives in the form of line elements. With the line elements an image is partitioned into patches by assigning each image pixel to the closest line element. Every line element constitutes a local coordinate frame for its corresponding patch. For every pixel, feature vectors are computed that make use of properties of the patches and the line elements. The feature vectors are classified using a kNN-classifier and sequential forward feature selection. The algorithm was tested on a database consisting of 40 manually labeled images. The method achieves an area under the receiver operating characteristic curve of 0.952. The method is compared with two recently published rule-based methods of and . The results show that our method is significantly better than the two rule-based methods (p<0.01). The accuracy of our method is 0.944 versus 0.947 for a second observer.