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Item Context-based Space Filling Curves(Blackwell Publishers Ltd and the Eurographics Association, 2000) Dafner, Revital; Cohen-Or, Daniel; Matias, YossiA context-based scanning technique for images is presented. An image is scanned along a context-based space filling curve that is computed so as to exploit inherent coherence in the image. The resulting one-dimensional representation of the image has improved autocorrelation compared with universal scans such as the Peano-Hilbert space filling curve. An efficient algorithm for computing context-based space filling curves is presented. We also discuss the potential of improved autocorrelation of context-based space filling curves for image and video lossless compression.Item Skeleton-Intrinsic Symmetrization of Shapes(The Eurographics Association and John Wiley & Sons Ltd., 2015) Zheng, Qian; Hao, Zhuming; Huang, Hui; Xu, Kai; Zhang, Hao; Cohen-Or, Daniel; Chen, Baoquan; Olga Sorkine-Hornung and Michael WimmerEnhancing the self-symmetry of a shape is of fundamental aesthetic virtue. In this paper, we are interested in recovering the aesthetics of intrinsic reflection symmetries, where an asymmetric shape is symmetrized while keeping its general pose and perceived dynamics. The key challenge to intrinsic symmetrization is that the input shape has only approximate reflection symmetries, possibly far from perfect. The main premise of our work is that curve skeletons provide a concise and effective shape abstraction for analyzing approximate intrinsic symmetries as well as symmetrization. By measuring intrinsic distances over a curve skeleton for symmetry analysis, symmetrizing the skeleton, and then propagating the symmetrization from skeleton to shape, our approach to shape symmetrization is skeleton-intrinsic. Specifically, given an input shape and an extracted curve skeleton, we introduce the notion of a backbone as the path in the skeleton graph about which a self-matching of the input shape is optimal. We define an objective function for the reflective self-matching and develop an algorithm based on genetic programming to solve the global search problem for the backbone. The extracted backbone then guides the symmetrization of the skeleton, which in turn, guides the symmetrization of the whole shape. We show numerous intrinsic symmetrization results of hand drawn sketches and artist-modeled or reconstructed 3D shapes, as well as several applications of skeleton-intrinsic symmetrization of shapes.Item Smart Variations: Functional Substructures for Part Compatibility(The Eurographics Association and Blackwell Publishing Ltd., 2013) Zheng, Youyi; Cohen-Or, Daniel; Mitra, Niloy J.; I. Navazo, P. PoulinAs collections of 3D models continue to grow, reusing model parts allows generation of novel model variations. Naïvely swapping parts across models, however, leads to implausible results, especially when mixing parts across different model families. Hence, the user has to manually ensure that the final model remains functionally valid. We claim that certain symmetric functional arrangements (SFARR-s), which are special arrangements among symmetrically related substructures, bear close relation to object functions. Hence, we propose a purely geometric approach based on such substructures to match, replace, and position triplets of parts to create non-trivial, yet functionally plausible, model variations. We demonstrate that starting even from a small set of models such a simple geometric approach can produce a diverse set of non-trivial and plausible model variations.Item Locally Adapted Projections to Reduce Panorama Distortions(The Eurographics Association and Blackwell Publishing Ltd, 2009) Kopf, Johannes; Lischinski, Dani; Deussen, Oliver; Cohen-Or, Daniel; Cohen, MichaelDisplaying panoramic and wide angle views on a flat 2D display surface is necessarily prone to distortions. Perspective projections are limited to fairly narrow view angles. Cylindrical and spherical projections can show full 360 panoramas, but at the cost of curving straight lines, interfering with the perception of salient shapes in the scene.In this paper, we introduce locally-adapted projections. Such projections are defined by a continuous projection surface consisting of both near-planar and curved parts. A simple and intuitive user interface allows the specification of regions of interest to be mapped to the near-planar parts, thereby reducing bending artifacts. We demonstrate the effectiveness of our approach on a variety of panoramic and wide angle images, including both indoor and outdoor scenes.Item Repetition Maximization based Texture Rectification(The Eurographics Association and John Wiley and Sons Ltd., 2012) Aiger, Dror; Cohen-Or, Daniel; Mitra, Niloy J.; P. Cignoni and T. ErtlMany photographs are taken in perspective. Techniques for rectifying resulting perspective distortions typically rely on the existence of parallel lines in the scene. In scenarios where such parallel lines are hard to automatically extract or manually annotate, the unwarping process remains a challenge. In this paper, we introduce an automatic algorithm to rectifying images containing textures of repeated elements lying on an unknown plane. We unwrap the input by maximizing for image self-similarity over the space of homography transformations. We map a set of detected regional descriptors to surfaces in a transformation space, compute the intersection points among triplets of such surfaces, and then use consensus among the projected intersection points to extract the correcting transform. Our algorithm is global, robust, and does not require explicit or accurate detection of similar elements. We evaluate our method on a variety of challenging textures and images. The rectified outputs are directly useful for various tasks including texture synthesis, image completion, etc.Item Geosemantic Snapping for Sketch-Based Modeling(The Eurographics Association and Blackwell Publishing Ltd., 2013) Shtof, Alex; Agathos, Alexander; Gingold, Yotam; Shamir, Ariel; Cohen-Or, Daniel; I. Navazo, P. PoulinModeling 3D objects from sketches is a process that requires several challenging problems including segmentation, recognition and reconstruction. Some of these tasks are harder for humans and some are harder for the machine. At the core of the problem lies the need for semantic understanding of the shape's geometry from the sketch. In this paper we propose a method to model 3D objects from sketches by utilizing humans specifically for semantic tasks that are very simple for humans and extremely difficult for the machine, while utilizing the machine for tasks that are harder for humans. The user assists recognition and segmentation by choosing and placing specific geometric primitives on the relevant parts of the sketch. The machine first snaps the primitive to the sketch by fitting its projection to the sketch lines, and then improves the model globally by inferring geosemantic constraints that link the different parts. The fitting occurs in real-time, allowing the user to be only as precise as needed to have a good starting configuration for this non-convex optimization problem. We evaluate the accessibility of our approach with a user study.Item Flower Reconstruction from a Single Photo(The Eurographics Association and John Wiley and Sons Ltd., 2014) Yan, Feilong; Gong, Minglun; Cohen-Or, Daniel; Deussen, Oliver; Chen, Baoquan; B. Levy and J. KautzWe present a semi-automatic method for reconstructing flower models from a single photograph. Such reconstruction is challenging since the 3D structure of a flower can appear ambiguous in projection. However, the flower head typically consists of petals embedded in 3D space that share similar shapes and form certain level of regular structure. Our technique employs these assumptions by first fitting a cone and subsequently a surface of revolution to the flower structure and then computing individual petal shapes from their projection in the photo. Flowers with multiple layers of petals are handled through processing different layers separately. Occlusions are dealt with both within and between petal layers. We show that our method allows users to quickly generate a variety of realistic 3D flowers from photographs and to animate an image using the underlying models reconstructed from our method.Item A Part-aware Surface Metric for Shape Analysis(The Eurographics Association and Blackwell Publishing Ltd, 2009) Liu, Rong; Zhang, Hao; Shamir, Ariel; Cohen-Or, DanielThe notion of parts in a shape plays an important role in many geometry problems, including segmentation, correspondence, recognition, editing, and animation. As the fundamental geometric representation of 3D objects in computer graphics is surface-based, solutions of many such problems utilize a surface metric, a distance function defined over pairs of points on the surface, to assist shape analysis and understanding. The main contribution of our work is to bring together these two fundamental concepts: shape parts and surface metric. Specifically, we develop a surface metric that is part-aware. To encode part information at a point on a shape, we model its volumetric context - called the volumetric shape image (VSI) - inside the shape s enclosed volume, to capture relevant visibility information. We then define the part-aware metric by combining an appropriate VSI distance with geodesic distance and normal variation. We show how the volumetric view on part separation addresses certain limitations of the surface view, which relies on concavity measures over a surface as implied by the well-known minima rule. We demonstrate how the new metric can be effectively utilized in various applications including mesh segmentation, shape registration, part-aware sampling and shape retrieval.Item Patch2Vec: Globally Consistent Image Patch Representation(The Eurographics Association and John Wiley & Sons Ltd., 2016) Fried, Ohad; Avidan, Shai; Cohen-Or, Daniel; Jernej Barbic and Wen-Chieh Lin and Olga Sorkine-HornungMany image editing applications rely on the analysis of image patches. In this paper, we present a method to analyze patches by embedding them to a vector space, in which the Euclidean distance reflects patch similarity. Inspired by Word2Vec, we term our approach Patch2Vec. However, there is a significant difference between words and patches. Words have a fairly small and well defined dictionary. Image patches, on the other hand, have no such dictionary and the number of different patch types is not well defined. The problem is aggravated by the fact that each patch might contain several objects and textures. Moreover, Patch2Vec should be universal because it must be able to map never-seen-before texture to the vector space. The mapping is learned by analyzing the distribution of all natural patches. We use Convolutional Neural Networks (CNN) to learn Patch2Vec. In particular, we train a CNN on labeled images with a triplet-loss objective function. The trained network encodes a given patch to a 128D vector. Patch2Vec is evaluated visually, qualitatively, and quantitatively. We then use several variants of an interactive single-click image segmentation algorithm to demonstrate the power of our method.Item Sketch-to-Design: Context-Based Part Assembly(The Eurographics Association and Blackwell Publishing Ltd., 2013) Xie, Xiaohua; Xu, Kai; Mitra, Niloy J.; Cohen-Or, Daniel; Gong, Wenyong; Su, Qi; Chen, Baoquan; Holly Rushmeier and Oliver DeussenDesigning 3D objects from scratch is difficult, especially when the user intent is fuzzy and lacks a clear target form. We facilitate design by providing reference and inspiration from existing model contexts. We rethink model design as navigating through different possible combinations of part assemblies based on a large collection of pre‐segmented 3D models. We propose an interactive sketch‐to‐design system, where the user sketches prominent features of parts to combine. The sketched strokes are analysed individually, and more importantly, in context with the other parts to generate relevant shape suggestions via adesign galleryinterface. As a modelling session progresses and more parts get selected, contextual cues become increasingly dominant, and the model quickly converges to a final form. As a key enabler, we use pre‐learned part‐based contextual information to allow the user to quickly explore different combinations of parts. Our experiments demonstrate the effectiveness of our approach for efficiently designing new variations from existing shape collections.Designing 3D objects from scratch is difficult, especially when the user intent is fuzzy and lacks a clear target form. We facilitate design by providing reference and inspiration from existing model contexts. We rethink model design as navigating through different possible combinations of part assemblies based on a large collection of pre‐segmented 3D models. We propose an interactive sketch‐to‐design system, where the user sketches prominent features of parts to combine. The sketched strokes are analyzed individually, and more importantly, in context with the other parts to generate relevant shape suggestions via a design gallery interface. As a modeling session progresses and more parts get selected, contextual cues become increasingly dominant, and the model quickly converges to a final form. As a key enabler, we use pre‐learned part‐based contextual information to allow the user to quickly explore different combinations of parts.
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