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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 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 Hallucinating Stereoscopy from a Single Image(The Eurographics Association and John Wiley & Sons Ltd., 2015) Zeng, Qiong; Chen, Wenzheng; Wang, Huan; Tu, Changhe; Cohen-Or, Daniel; Lischinski, Dani; Chen, Baoquan; Olga Sorkine-Hornung and Michael WimmerWe introduce a novel method for enabling stereoscopic viewing of a scene from a single pre-segmented image. Rather than attempting full 3D reconstruction or accurate depth map recovery, we hallucinate a rough approximation of the scene's 3D model using a number of simple depth and occlusion cues and shape priors. We begin by depth-sorting the segments, each of which is assumed to represent a separate object in the scene, resulting in a collection of depth layers. The shapes and textures of the partially occluded segments are then completed using symmetry and convexity priors. Next, each completed segment is converted to a union of generalized cylinders yielding a rough 3D model for each object. Finally, the object depths are refined using an iterative ground fitting process. The hallucinated 3D model of the scene may then be used to generate a stereoscopic image pair, or to produce images from novel viewpoints within a small neighborhood of the original view. Despite the simplicity of our approach, we show that it compares favorably with state-of-the-art depth ordering methods. A user study was conducted showing that our method produces more convincing stereoscopic images than existing semi-interactive and automatic single image depth recovery methods.Item Recurring Part Arrangements in Shape Collections(The Eurographics Association and John Wiley and Sons Ltd., 2014) Zheng, Youyi; Cohen-Or, Daniel; Averkiou, Melinos; Mitra, Niloy J.; B. Levy and J. KautzExtracting semantically related parts across models remains challenging, especially without supervision. The common approach is to co-analyze a model collection, while assuming the existence of descriptive geometric features that can directly identify related parts. In the presence of large shape variations, common geometric features, however, are no longer sufficiently descriptive. In this paper, we explore an indirect top-down approach, where instead of part geometry, part arrangements extracted from each model are compared. The key observation is that while a direct comparison of part geometry can be ambiguous, part arrangements, being higher level structures, remain consistent, and hence can be used to discover latent commonalities among semantically related shapes. We show that our indirect analysis leads to the detection of recurring arrangements of parts, which are otherwise difficult to discover in a direct unsupervised setting. We evaluate our algorithm on ground truth datasets and report advantages over geometric similarity-based bottom-up co-segmentation algorithms.Item Prior Knowledge for Part Correspondence(The Eurographics Association and Blackwell Publishing Ltd., 2011) Kaick, Oliver van; Tagliasacchi, Andrea; Sidi, Oana; Zhang, Hao; Cohen-Or, Daniel; Wolf, Lior; Hamarneh, Ghassan; M. Chen and O. DeussenClassical approaches to shape correspondence base their computation purely on the properties, in particular geometric similarity, of the shapes in question. Their performance still falls far short of that of humans in challenging cases where corresponding shape parts may differ significantly in geometry or even topology. We stipulate that in these cases, shape correspondence by humans involves recognition of the shape parts where prior knowledge on the parts would play a more dominant role than geometric similarity. We introduce an approach to part correspondence which incorporates prior knowledge imparted by a training set of pre-segmented, labeled models and combines the knowledge with content-driven analysis based on geometric similarity between the matched shapes. First, the prior knowledge is learned from the training set in the form of per-label classifiers. Next, given two query shapes to be matched, we apply the classifiers to assign a probabilistic label to each shape face. Finally, by means of a joint labeling scheme, the probabilistic labels are used synergistically with pairwise assignments derived from geometric similarity to provide the resulting part correspondence. We show that the incorporation of knowledge is especially effective in dealing with shapes exhibiting large intra-class variations. We also show that combining knowledge and content analyses outperforms approaches guided by either attribute alone.Item Smooth Image Sequences for Data-driven Morphing(The Eurographics Association and John Wiley & Sons Ltd., 2016) Averbuch-Elor, Hadar; Cohen-Or, Daniel; Kopf, Johannes; Joaquim Jorge and Ming LinSmoothness is a quality that feels aesthetic and pleasing to the human eye. We present an algorithm for finding ''as-smoothas- possible'' sequences in image collections. In contrast to previous work, our method does not assume that the images show a common 3D scene, but instead may depict different object instances with varying deformations, and significant variation in lighting, texture, and color appearance. Our algorithm does not rely on a notion of camera pose, view direction, or 3D representation of an underlying scene, but instead directly optimizes the smoothness of the apparent motion of local point matches among the collection images. We increase the smoothness of our sequences by performing a global similarity transform alignment, as well as localized geometric wobble reduction and appearance stabilization. Our technique gives rise to a new kind of image morphing algorithm, in which the in-between motion is derived in a data-driven manner from a smooth sequence of real images without any user intervention. This new type of morph can go far beyond the ability of traditional techniques. We also demonstrate that our smooth sequences allow exploring large image collections in a stable manner.Item Structure-Aware Shape Processing(The Eurographics Association, 2013) Mitra, Niloy J.; Wand, Michael; Zhang, Hao; Cohen-Or, Daniel; Bokeloh, Martin; M. Sbert and L. Szirmay-KalosShape structure is about the arrangement and relations between shape parts. Structure-aware shape processing goes beyond local geometry and low level processing, and analyzes and processes shapes at a high level. It focuses more on the global inter and intra semantic relations among the parts of shape rather than on their local geometry. With recent developments in easy shape acquisition, access to vast repositories of 3D models, and simple-to-use desktop fabrication possibilities, the study of structure in shapes has become a central research topic in shape analysis, editing, and modeling. A whole new line of structure-aware shape processing algorithms has emerged that base their operation on an attempt to understand such structure in shapes. The algorithms broadly consist of two key phases: an analysis phase, which extracts structural information from input data; and a (smart) processing phase, which utilizes the extracted information for exploration, editing, and synthesis of novel shapes. In this survey paper, we organize, summarize, and present the key concepts and methodological approaches towards efficient structure-aware shape processing. We discuss common models of structure, their implementation in terms of mathematical formalism and algorithms, and explain the key principles in the context of a number of state-ofthe- art approaches. Further, we attempt to list the key open problems and challenges, both at the technical and at the conceptual level, to make it easier for new researchers to better explore and contribute to this topic. Our goal is to both give the practitioner an overview of available structure-aware shape processing techniques, as well as identify future research questions in this important, emerging, and fascinating research area.