There are many highly respectable motives which may lead men to prosecute research, but three which are much more important than the rest: intellectual curiosity, professional pride, and finally, ambition, desire for reputation, and the position, even the power or the money, which it brings ... if (anyone) were to tell me that the driving force in his work had been the desire to benefit humanity, then I should not believe him (nor should I think the better of him if I did). - G. H. Hardy (A Mathematician's Apology)

## Selected publications by year (by category)

2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 and before

H-index: 41 | Google citation | DBLP

### 2017

 7. Ruizhen Hu, Wenchao Li, Oliver van Kaick, Ariel Shamir, Hao Zhang, and Hui Huang, "Learning to Predict Part Mobility from a Single Static Snapshot", ACM Transactions on Graphics (Special Issue of SIGGRAPH Asia), Vol. 36, No. 6, Article 227, 2017. [PDF | Project Page | bibtex] We introduce a method for learning a model for the mobility of parts in 3D objects. Our method allows not only to understand the dynamic function- alities of one or more parts in a 3D object, but also to apply the mobility functions to static 3D models. Specifically, the learned part mobility model can predict mobilities for parts of a 3D object given in the form of a single static snapshot reflecting the spatial configuration of the object parts in 3D space, and transfer the mobility from relevant units in the training data ... 6. Zhaoliang Lun, Changqing Zou (joint first author), Haibin Huang, Evangelos Kalogerakis, Ping Tan, Marie-Paule Cani, and Hao Zhang, "Learning to Group Discrete Graphical Patterns", ACM Transactions on Graphics (Special Issue of SIGGRAPH Asia), Vol. 36, No. 6, Article 225, 2017. [PDF | Project page | bibtex] We introduce a deep learning approach for grouping discrete patterns common in graphical designs. Our approach is based on a convolutional neural network architecture that learns a grouping measure defined over a pair of pattern elements. Motivated by perceptual grouping principles, the key feature of our network is the encoding of element shape, context, symmetries, and structural arrangements. These element properties are all jointly considered and appropriately weighted in our grouping measure ... 5. Zili Yi, Hao Zhang, Ping Tan, and Minglun Gong, "DualGAN: Unsupervised Dual Learning for Image-to-Image Translation", Proc. of ICCV, also available at arXiv:1704.02510, 2017. [PDF | bibtex] Conditional Generative Adversarial Networks (GANs) for cross-domain image-to-image translation have made much progress recently. Depending on the task complexity, thousands to millions of labeled image pairs are needed to train a conditional GAN. However, human labeling is expensive, even impractical, and large quantities of data may not always be available. Inspired by dual learning from natural language translation, we develop a novel dual-GAN mechanism, which enables image translators to be trained from two sets of unlabeled images from two domains. In our architecture, the primal GAN learns to translate images from domain U to those in domain V, while the dual GAN learns to invert the task. The closed loop made by the primal and dual tasks allows images from either domain to be translated and then reconstructed. Hence a loss function that accounts for the reconstruction error of images can be used to train the translators. 4. Warunika Ranaweera, Parmit Chilana, Daniel Cohen-Or, and Hao Zhang, "ExquiMo: An Exquisite Corpse Tool for Co-creative 3D Shape Modeling", International Conference on Computer-Aided Design and Computer Graphics (CAD/Graphics), Zhangjiajie, China, August 25-27, 2017. One of three Best Paper Awards at the conference. [PDF | bibtex] We introduce a shape modeling tool, ExquiMo, which is guided by the idea of improving the creativity of 3D shape designs through collaboration. Inspired by the game of Exquisite Corpse, our tool allocates distinct parts of a shape to multiple players who model the assigned parts in a sequence. Our approach is motivated by the understanding that effective surprise leads to creative outcomes. Hence, to maintain the surprise factor of the output, we conceal the previously modeled parts from the most recent player. Part designs from individual players are fused together to produce an often unexpected, hence creative, end result ... 3. Chenyang Zhu, Renjiao Yi, Wallace Lira, Ibraheem Alhashim, Kai Xu, and Hao Zhang, "Deformation-Driven Shape Correspondence via Shape Recognition", ACM Transactions on Graphics (Special Issue of SIGGRAPH), Vol. 36, No. 4, Article 51, 2017. [PDF (31MB) | PDF reduced (1.7MB) | bibtex] Many approaches to shape comparison and recognition start by establishing a shape correspondence. We turn the table'' and show that quality shape correspondences can be obtained by performing many shape recognition tasks. What is more, the method we develop computes a fine-grained, topology-varying part correspondence between two 3D shapes where the core evaluation mechanism only recognizes shapes globally. This is made possible by casting the part correspondence problem in a deformation-driven framework and relying on a data-driven deformation energy'' which rates visual similarity between deformed shapes and models from a shape repository. Our basic premise is that if a correspondence between two chairs (or airplanes, bicycles, etc.) is correct, then a reasonable deformation between the two chairs anchored on the correspondence ought to produce plausible, chair-like'' in-between shapes. 2. Jun Li, Kai Xu, Siddhartha Chaudhuri, Ersin Yumer, Hao Zhang, Leonidas Guibas, "GRASS: Generative Recursive Autoencoders for Shape Structures", ACM Transactions on Graphics (Special Issue of SIGGRAPH), Vol. 36, No. 4, Article 52, 2017. [PDF | arXiv | Project page | bibtex] We introduce a novel neural network architecture for encoding and synthesis of 3D shapes, particularly their structures. Our key insight is that 3D shapes are effectively characterized by their hierarchical organization of parts, which reflects fundamental intra-shape relationships such as adjacency and symmetry. We develop a recursive neural net (RvNN) based autoencoder to map a flat, unlabeled, arbitrary part layout to a compact code. The code effectively captures the hierarchical structures of varying complexity despite being fixed-dimensional: an associated decoder maps a code back to a full hierarchy. The learned bidirectional mapping is further tuned using an adversarial setup to yield a generative model of plausible structures, from which novel structures can be sampled. Finally, our structure synthesis framework is augmented by a second trained module that produces fine-grained part geometry, conditioned on global and local structural context, leading to a full generative pipeline for 3D shapes. 1. Ruizhen Hu, Wenchao Li, Oliver van Kaick, Hui Huang, Melinos Averkiou, Daniel Cohen-Or, and Hao Zhang, "Co-Locating Style-Defining Elements on 3D Shapes", ACM Transactions on Graphics (to be presented at SIGGRAPH), Vol. 36, No. 3, pp. 33:1-33:15, 2017. [PDF (58 MB) | bibtex] We introduce a method for co-locating style-defining elements over a set of 3D shapes. Our goal is to translate high-level style descriptions, such as "Ming" or "European" for furniture models, into explicit and localized regions over the geometric models that characterize each style. For each style, the set of style-defining elements is defined as the union of all the elements that are able to discriminate the style. Another property of the style-defining elements is that they are frequently-occurring, reflecting shape characteristics that appear across multiple shapes of the same style ...

### 2016

 8. Rui Ma, Honghua Li, Changqing Zou, Zicheng Liao, Xin Tong, and Hao Zhang, "Action-Driven 3D Indoor Scene Evolution", ACM Trans. on Graphics (Special Issue of SIGGRAPH Asia), Vol. 35, No. 6, Article 173, 2016. [PDF (high-res: 37 MB) | Projet page | bibtex] We introduce a framework for action-driven evolution of 3D indoor scenes, where the goal is to simulate how scenes are altered by human actions, and specifically, by object placements necessitated by the actions. To this end, we develop an action model with each type of action combining information about one or more human poses, one or more object categories, and spatial configurations of object-object and object-human relations for the action. Importantly, all these pieces of information are learned from annotated photos. 7. Lei Li, Zhe Huang, Changqing Zou, Chiew-Lan Tai, Rynson W.H. Lau, Hao Zhang, Ping Tan, and Hongbo Fu, "Model-driven Sketch Reconstruction with Structure-oriented Retrieval", SIGGRAPH Asia Technical Brief, 2016. [PDF | bibtex] We propose an interactive system that aims at lifting a 2D sketch into a 3D sketch with the help of existing models in shape collections. The key idea is to exploit part structure for shape retrieval and sketch reconstruction. We adopt sketch-based shape retrieval and develop a novel matching algorithm which considers structure in addition to traditional shape features. 6. Zeinab Sadeghipour, Zicheng Liao, Ping Tan, and Hao Zhang, "Learning 3D Scene Synthesis from Annotated RGB-D Images", Computer Graphics Forum (Special Issue of SGP), Vol. 35, No. 5, pp. 197-206, 2016. [PDF | bibtex] We present a data-driven method for synthesizing 3D indoor scenes by inserting objects progressively into an initial, possibly, empty scene. Instead of relying on few hundreds of hand-crafted 3D scenes, we take advantage of existing large-scale annotated RGB-D datasets, in particular, the SUN RGB-D database consisting of 10,000+ depth images of real scenes, to form the prior knowledge for our synthesis task. Our object insertion scheme follows a co-occurrence model and an arrangement model, both learned from the SUN dataset. 5. Ruizhen Hu, Oliver van Kaick, Bojian Wu, Hui Huang, Ariel Shamir, and Hao Zhang, "Learning How Objects Function via Co-Analysis of Interactions", ACM Trans. on Graphics (Special Issue of SIGGRAPH), Vol. 35, No. 4, Article 47, 2016. [PDF (high-res: 50MB) | [PDF (low-res: 2.5MB) | Projet page | bibtex] We introduce a co-analysis method which learns a functionality model for an object category, e.g., strollers or backpacks. Like previous works on functionality, we analyze object-to-object interactions and intra-object properties and relations. Differently from previous works, our model goes beyond providing a functionalityoriented descriptor for a single object; it prototypes the functionality of a category of 3D objects by co-analyzing typical interactions involving objects from the category. 4. Changqing Zou, Junjie Cao, Warunika Ranaweera, Ibraheem Alhashim, Ping Tan, Alla Sheffer, and Hao Zhang, "Legible Compact Calligrams", ACM Trans. on Graphics (Special Issue of SIGGRAPH), Vol. 35, No. 4, Article 122, 2016. [PDF | bibtex] A calligram is an arrangement of words or letters that creates a visual image, and a compact calligram fits one word into a 2D shape. We introduce a fully automatic method for the generation of legible compact calligrams which provides a balance between conveying the input shape, legibility, and aesthetics. 3. Haisen Zhao, Fanglin Gu, Qi-Xing Huang, Jorge Garcia, Yong Chen, Changhe Tu, Bedrich Benes, Hao Zhang, Daniel Cohen-Or, and Baoquan Chen, "Connected Fermat Spirals for Layered Fabrication", ACM Trans. on Graphics (Special Issue of SIGGRAPH), Vol. 35, No. 4, Article 100, 2016. [PDF | Project page | bibtex] We develop a new kind of "space-filling" curves, connected Fermat spirals, and show their compelling properties as a tool path fill pattern for layered fabrication. Unlike classical space-filling curves such as the Peano or Hilbert curves, which constantly wind and bind to preserve locality, connected Fermat spirals are formed mostly by long, low-curvature paths. This geometric property, along with continuity, influences the quality and efficiency of layered fabrication. 2. Lili Wan, Changqing Zou, and Hao Zhang, "Full and Partial Shape Similarity through Sparse Descriptor Reconstruction", The Visual Computer, to appear, 2016. [PDF | bibtex] We introduce a novel approach to measure similarity between two 3D shapes based on sparse reconstruction of shape descriptors. The main feature of our approach is its applicability to handle incomplete shapes. We characterize the shapes by learning a sparse dictionary from their local descriptors. The similarity between two shapes A and B is defined by the error incurred when reconstructing B's descriptor set using the basis signals from A’s dictionary. 1. Daniel Cohen-Or and Hao Zhang, "From inspired modeling to creative modeling", Visual Computer (invited paper), Vol. 32, No. 1, 2016. [PDF | bibtex] An intriguing and reoccurring question in many branches of computer science is whether machines can be creative, like humans. In this exploratory paper, we examine the problem from a computer graphics, and more specifically, geometric modeling, perspective. We focus our discussions on the weaker but still intriguing question: "Can machines assist or inspire humans in a creative endeavor for the generation of geometric forms?"

### 2015

 11. Ibraheem Alhashim, Kai Xu, Yixin Zhuang, Junjie Cao, Patricio Simari, and Hao Zhang, "Deformation-Driven Topology-Varying 3D Shape Correspondence", ACM Trans. on Graphics (Special Issue of SIGGRAPH Asia), Vol. 34, No. 6, Article 236, 2015. [PDF (20 MB) | PDF reduced (12 MB) | Project page | bibtex] We present a deformation-driven approach to topology-varying 3D shape correspondence. In this paradigm, the best correspondence between two shapes is the one that results in a minimal-energy, possibly topology-varying, deformation that transforms one shape to conform to the other while respecting the correspondence. Our deformation model allows both geometric and topological operations such as part split, duplication, and merging ... 10. Xuelin Chen, Hao Zhang, Jinjie Lin, Ruizhen Hu, Lin Lu, Qixing Huang, Bedrich Benes, Daniel Cohen-Or, and Baoquan Chen, "Dapper: Decompose-and-Pack for 3D Printing", ACM Trans. on Graphics (Special Issue of SIGGRAPH Asia), Vol. 34, No. 6, Article 213, 2015. [PDF (37 MB) | PDF reduced (0.75 MB) | Project page | bibtex] We pose the decompose-and-pack or DAP problem, which tightly combines shape decomposition and packing. While in general, DAP seeks to decompose an input shape into a small number of parts which can be efficiently packed, our focus is geared towards 3D printing. The goal is to optimally decompose-and-pack a 3D object into a printing volume to minimize support material, build time, and assembly cost. We present Dapper, a global optimization algo- rithm for the DAP problem which can be applied to both powder- and FDM-based 3D printing. 9. Yang Zhou, Kangxue Yin, Hui Huang, Hao Zhang, Minglun Gong, and Daniel Cohen-Or, "Generalized Cylinder Decomposition", ACM Trans. on Graphics (Special Issue of SIGGRAPH Asia), Vol. 34, No. 6, Article 171, 2015. [PDF (85 MB) | PDF reduced (3.5 MB) | Project page | bibtex] Decomposing a complex shape into geometrically simple primitives is a fundamental problem in geometry processing. We are interested in a shape decomposition problem where the simple primitives sought are generalized cylinders. We introduce a quantitative measure of cylindricity for a shape part and develop a cylindricity-driven optimization algorithm, with a global objective function, for generalized cylinder decomposition. 8. Ruizhen Hu, Chenyang Zhu, Oliver van Kaick, Ligang Liu, Ariel Shamir, and Hao Zhang, "Interaction Context (ICON): Towards a Geometric Functionality Descriptor", ACM Trans. on Graphics (Special Issue of SIGGRAPH), Vol. 34, No. 4, Article 83, 2015. [PDF (28 MB) | PDF reduced (16 MB) | Project page | bibtex] We introduce a contextual descriptor which aims to provide a geometric description of the functionality of a 3D object in the context of a given scene. Differently from previous works, we do not regard functionality as an abstract label or represent it implicitly through an agent. Our descriptor, called interaction context or ICON for short, explicitly represents the geometry of object-to-object interactions. Our approach to object functionality analysis is based on the key premise that functionality should mainly be derived from interactions between objects and not objects in isolation. 7. Honghua Li, Ruizhen Hu (co-first author), Ibraheem Alhashim, and Hao Zhang, "Foldabilizing Furniture", ACM Trans. on Graphics (Special Issue of SIGGRAPH), Vol. 34, No. 4, Article 90, 2015. [PDF (35 MB) | PDF reduced (6 MB) | bibtex] We introduce the foldabilization problem for space-saving furniture design. Namely, given a 3D object representing a piece of furniture, the goal is to apply a minimum amount of modification to the object so that it can be folded to save space —-- the object is thus foldabilized. We focus on one instance of the problem where folding is with respect to a prescribed folding direction and allowed object modifications include hinge insertion and part shrinking. We develop an automatic algorithm for foldabilization by formulating and solving a nested optimization problem ... 6. Lili Wan, Jingyu Jiang, and Hao Zhang, "Incomplete 3D Shape Retrieval via Sparse Dictionary Learning", Pacific Graphics (short paper), 2015. [PDF | bibtex] In this paper, we are interested in the problem of 3D shape retrieval where the query shape is incomplete with moderate to significant portions of the original shape missing. The key idea of our method is to grasp the basis local descriptors for each shape in the retrieved database by sparse dictionary learning and apply them in sparsely coding the local descriptors of an incomplete query 5. Honghua Li and Hao Zhang, "Shape Compaction", in Perspectives in Shape Analysis, Dagstuhl Seminar, editors: M. Breu, A. Bruckstein, P. Maragos, and S. Wuhrer, to appear, 2015. [PDF | bibtex] We cover techniques designed for compaction of shape representations or shape configurations. The goal of compaction is to reduce storage space, a fundamental problem in many application domains. Compaction of shape representations focuses on reducing the memory space allocated for storing the shape geometry data digitally, whilst shape compaction techniques in the physical domain reduce the physical space occupied by shape configurations ... 4. Daniel Cohen-Or, Chen Greif, Tao Ju, Niloy J. Mitra, Ariel Shamir, Olga Sorkine-Hornung, and Hao Zhang, A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing, CRC Press, 2015. A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing shows how to use a collection of mathematical techniques to solve important problems in applied mathematics and computer science areas. The book discusses fundamental tools in analytical geometry ... 3. Qian Zheng, Zhuming Hao, Hui Huang, Kai Xu, Hao Zhang, Daniel Cohen-Or, and Baoquan Chen, "Skeleton-Intrinsic Symmetrization of Shapes", Computer Graphics Forum (Special Issue of Eurographics), Vol. 34, No. 2, pp. 275-286, 2015. [PDF | bibtex] Enhancing the self-symmetry of a shape is of fundamental aesthetic virtue. In this paper, we are interested in recov- ering 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 ... 2. Hadar Averbuch-Elor, Yunhai Wang, Yiming Qian, Minglun Gong, Johannes Kopf, Hao Zhang, and Daniel Cohen-Or, "Distilled Collections from Textual Image Queries", Computer Graphics Forum (Special Issue of Eurographics), Vol. 34, No. 2, pp. 131-142, 2015. [PDF | bibtex] We present a distillation algorithm which operates on a large, unstructured, and noisy collection of internet images returned from an online object query. We introduce the notion of a distilled set, which is a clean, coherent, and structured subset of inlier images. In addition, the object of interest is properly segmented out throughout the distilled set. Our approach is unsupervised, built on a novel clustering scheme, and solves the distillation and object segmentation problems simultaneously. In essence, instead of distilling the collection of images, we distill a collection of loosely cutout foreground “shapes”, which may or may not contain the queried object. Our key observation, which motivated our clustering scheme, is that outlier shapes are expected to be random in nature, whereas, inlier shapes, which do tightly enclose the object of interest, tend to be well supported by similar shapes captured in similar views ... 1. Zhenbao Liu, Caili Xie, Shuhui Bu, Xiao Wang, and Hao Zhang, "Indirect Shape Analysis for 3D Shape Retrieval", Computer & Graphics (Special Issue of SMI 2014), Vol. 46, pp. 110-116, 2015. [PDF | bibtex] We introduce indirect shape analysis, or ISA, where a given shape is analyzed not based on geometric or topological features computed directly from the shape itself, but by studying how external agents interact with the shape. The potential benefits of ISA are two-fold. First, agent-object interactions often reveal an object’s function, which plays a key role in shape understanding. Second, compared to direct shape analysis, ISA, which utilizes pre-selected agents, is less affected by imperfections of, or inconsistencies between, the geometry or topology of the analyzed shapes. We employ digital human models as the external agents and develop a prototype ISA scheme for 3D shape classification and retrieval ...

### 2014

 6. Ruizhen Hu, Honghua Li, Hao Zhang, and Daniel Cohen-Or "Approximate Pyramidal Shape Decomposition", ACM Trans. on Graphics (Special Issue of SIGGRAPH Asia), Vol. 33, No. 6, Article 213, 2014. [Project page | PDF (highres 41MB) | PDF (lowres 9MB) | bibtex] A shape is pyramidal if it has a flat base with the remaining boundary forming a height function over the base. Pyramidal shapes are optimal for molding, casting, and layered 3D printing. We introduce an algorithm for approximate pyramidal shape decomposition. The general exact pyramidal decomposition problem is NP-hard. We turn this problem into an NP-complete Exact Cover Problem which admits a practical solution ... Our solution is equally applicable to 2D or 3D shapes, to shapes with polygonal or smooth boundaries, with or without holes ... 5. Kangxue Yin, Hui Huang, Hao Zhang, Minglun Gong, Daniel Cohen-Or, and Baoquan Chen, "Morfit: Interactive Surface Reconstruction from Incomplete Point Clouds with Curve-Driven Topology and Geometry Control", ACM Trans. on Graphics (Special Issue of SIGGRAPH Asia), Vol. 33, No. 6, Article 202, 2014. [Project page | PDF (42MB) | PDF (lowres 2MB) | Code | bibtex] We present an interactive technique for surface reconstruction from incomplete and sparse scans of 3D objects possessing sharp features ... We factor 3D editing by the user into two "orthogonal" interactions acting on skeletal and profile curves of the underlying shape, controlling its topology and geometric features, respectively. For surface completion, we introduce a novel skeleton-driven morph-to-fit, or morfit, scheme which reconstructs the shape as an ensemble of generalized cylinders. Morfit is a hybrid operator which optimally interpolates between adjacent curve profiles (the "morph") and snaps the surface to input points (the "fit") ... 4. Ibraheem Alhashim, Honghua Li, Kai Xu, Junjie Cao, Rui Ma, and Hao Zhang, "Topology-Varying 3D Shape Creation via Structural Blending", ACM Trans. on Graphics (Special Issue of SIGGRAPH), Vol. 33, No. 4, Article 158, 2014. [Project page | Code | bibtex] We introduce an algorithm for generating novel 3D models via topology-varying shape blending. Given a source and a target shape, our method blends them topologically and geometrically, producing continuous series of in-betweens as new shape creations. The blending operations are defined on a spatio-structural graph composed of medial curves and sheets. Such a shape abstraction is structure-oriented, part-aware, and facilitates topology manipulations. Fundamental topological operations including split and merge are realized by allowing one-to-many correspondences between the source and the target ... 3. Kai Xu, Rui Ma, Hao Zhang, Chenyang Zhu, Ariel Shamir, Daniel Cohen-Or, and Hui Huang, "Organizing Heterogeneous Scene Collections through Contextual Focal Points", ACM Trans. on Graphics (Special Issue of SIGGRAPH), Vol. 33, No. 4, Article 35, 2014. [Project page | bibtex] We introduce focal points for characterizing, comparing, and organizing collections of complex and heterogeneous data and apply the concepts and algorithms developed to collections of 3D indoor scenes. We represent each scene by a graph of its constituent objects and define focal points as representative substructures in a scene collection. To organize a heterogenous scene collection, we cluster the scenes based on a set of extracted focal points: scenes in a cluster are closely connected when viewed from the perspective of the representative focal points of that cluster ... The problem of focal point extraction is intermixed with the problem of clustering groups of scenes based on their representative focal points. We present a co-analysis algorithm ... 2. Xiaowu Chen, Dongqing Zou, Jianwei Li, Xiaochun Cao, Qinping Zhao, and Hao Zhang, "Sparse Dictionary Learning for Edit Propagation of High-resolution Images", Proc. of IEEE CVPR, pp. 2854-2861, 2014. [PDF | bibtex] We introduce the use of sparse representation for edit propagation of high-resolution images or video. Previous approaches for edit propagation typically employ a global optimization over the whole set of image pixels, incurring a prohibitively high memory and time consumption for high-resolution images. Rather than propagating an edit pixel by pixel, we follow the principle of sparse representation to obtain a compact set of representative samples (or features) and perform edit propagation on the samples instead ... 1. Hui Wang, Patricio Simari, Zhixun Su, and Hao Zhang, "Spectral Global Intrinsic Symmetry Invariant Functions", Proc. of Graphics Interface, pp. 209-215, 2014. [Project page | PDF | bibtex] We introduce spectral Global Intrinsic Symmetry Invariant Functions (GISIFs), a class of GISIFs obtained via eigendecomposition of the Laplace-Beltrami operator on compact Riemannian manifolds. We discretize the spectral GISIFs for 2D manifolds approximated either by triangle meshes or point clouds. In contrast to GISIFs obtained from geodesic distances, our spectral GISIFs are robust to local topological changes. Additionally, for symmetry analysis our spectral GISIFs can be viewed as generalizations of the classical Heat (HKSs) and Wave Kernel Signatures (WKSs), and, as such, represent a more expressive and versatile class of functions ...

### 2012

 10. Kai Xu, Hao Zhang, Wei Jiang, Ramsay Dyer, Zhiquan Cheng, Ligang Liu, and Baoquan Chen, "Multi-Scale Partial Intrinsic Symmetry Detection," ACM Trans. on Graphics (Special Issue of SIGGRAPH Asia), Vol. 31, No. 6, Article 181, 2012. [PDF | Project page (with data) | bibtex] We present an algorithm for multi-scale partial intrinsic symmetry detection over 2D and 3D shapes, where the scale of a symmetric region is defined by intrinsic distances between symmetric points over the region. To identify prominent symmetric regions which overlap and vary in form and scale, we decouple scale extraction and symmetry extraction by performing two levels of clustering. First, significant symmetry scales are identified by clustering sample point pairs from an input shape ... 9. Honghua Li, Ibraheem Alhashim, Hao Zhang, Ariel Shamir, and Daniel Cohen-Or, "Stackabilization," ACM Trans. on Graphics (Special Issue of SIGGRAPH Asia), Vol. 31, No. 6, Article 158, 2012. [PDF | Project page | Code | bibtex] We introduce the geometric problem of stackabilization: how to geometrically modify a 3D object so that it is more amenable to stacking. Given a 3D object and a stacking direction, we define a measure of stackability, which is derived from the gap between the lower and upper envelopes of the object in a stacking configuration along the stacking direction. The main challenge in stackabilization lies in the desire to modify the object's geometry only subtly so that the intended functionality and aesthetic appearance of the original object are not significantly affected ... 8. Hui Huang, Minglun Gong, Daniel Cohen-Or, Yaobin Ouyang, Fuwen Tao, and Hao Zhang, "Field-Guided Registration for Feature-Conforming Shape Composition," ACM Trans. on Graphics (Special Issue of SIGGRAPH Asia), Vol. 31, No. 6, Article 179, 2012. [PDF | bibtex] We present an automatic shape composition method to fuse two shape parts which may not overlap and possibly contain sharp features, a scenario often encountered when modeling man-made objects. At the core of our method is a novel field-guided approach to automatically align two input parts in a feature-conforming manner. The key to our field-guided shape registration is a natural continuation of one part into the ambient field as a means to introduce an overlap with the distant part, which then allows a surface-to-field registration ... 7. Yunhai Wang, Shmulik Asafi, Oliver van Kaick, Hao Zhang, Daniel Cohen-Or, and Baoquan Chen, "Active Co-Analysis of a Set of Shapes," ACM Trans. on Graphics (Special Issue of SIGGRAPH Asia), Vol. 31, No. 6, Article 165, 2012. [PDF | Project page | The Shape COSEG Dataset | bibtex] We consider the use of a semi-supervised learning method where the user actively assists in the co-analysis by iteratively providing input that progressively constrains the system. We introduce a novel constrained clustering method based on a spring system which embeds elements to better respect their inter-distances in feature space together with the user given set of constraints. We also present an active learning method that suggests to the user where his input is likely to be the most effective in refining the results. 6. Nima Aghdaii, Hamid Younesy, and Hao Zhang, "5-6-7 Meshes: Remeshing and Analysis" Computer & Graphics, extended version of GI'12 paper, Vol. 36, No. 8, pp. 1072-1083, 2012. [PDF | bibtex] We introduce a new type of meshes called 5-6-7 meshes, analyze their properties, and present a 5-6-7 remeshing algorithm. A 5-6-7 mesh is a closed triangle mesh where each vertex has valence 5, 6, or 7. We prove that it is always possible to convert an arbitrary mesh into a 5-6-7 mesh. We present a remeshing algorithm which converts a closed triangle mesh with arbitrary genus into a 5-6-7 mesh which a) closely approximates the original mesh geometrically, e.g., in terms of feature preservation, and b) has a comparable vertex count as the original mesh. 5. Andrea Tagliassachi, Ibraheem Alhashim, Matt Olson, and Hao Zhang, "Mean Curvature Skeletons," Computer Graphics Forum (Special Issue of SGP), Volume 31, Number 5, pp. 1735-1744, 2012. [PDF | bibtex] We formulate the skeletonization problem via mean curvature flow (MCF). While the classical application of MCF is surface fairing, we take advantage of its area-minimizing characteristic to drive the curvature flow towards the extreme so as to collapse the input mesh geometry and obtain a skeletal structure. By analyzing the differential characteristics of the flow, we reveal that MCF locally increases shape anisotropy. This justifies the use of curvature motion for skeleton computation, and leads to the generation of what we call "mean curvature skeletons" ... 4. Kai Xu, Hao Zhang, Daniel Cohen-Or, and Baoquan Chen "Fit and Diverse: Set Evolution for Inspiring 3D Shape Galleries," ACM Trans. on Graphics (Special Issue of SIGGRAPH), Vol. 31, No. 4, pp. 57:1-57:10, 2012. [PDF (15 MB) | bibtex] We introduce set evolution as a means for creative 3D shape modeling, where an initial population of 3D models is evolved to produce generations of novel shapes. Part of the evolving set is presented to a user as a shape gallery to offer modeling suggestions. User preferences define the fitness for the evolution so that over time, the shape population will mainly consist of individuals with good fitness. However, to inspire the user's creativity, we must also keep the evolving set diverse. Hence the evolution is fit and diverse'' ... 3. Nima Aghdaii, Hamid Younesy, and Hao Zhang, "5-6-7 Meshes," Proc. of Graphics Interface, pp. 27-34, 2012. [PDF | bibtex] A 5-6-7 mesh is a closed triangle mesh where each vertex has valence 5, 6, or 7. An intriguing question is whether it is always possible to convert an arbitrary mesh into a 5-6-7 mesh. In this paper, we answer the question in the positive. We present a 5-6-7 remeshing algorithm which converts any closed triangle mesh with arbitrary genus into a 5-6-7 mesh which a) closely approximates the original mesh geometrically, e.g., in terms of feature preservation, and b) has a comparable vertex count as the original mesh. 2. Hui Wang, Zhixun Su, Jinjie Cao, Ye Wang, and Hao Zhang, "Empirical Mode Decomposition on Surfaces," Graphical Models (Special Issue of GMP), Vol. 74, No. 4, pp. 173-183, 2012. [PDF | bibtex] Empirical Mode Decomposition (EMD) is a powerful tool for the analysis of non-stationary and nonlinear signals, and has drawn a great deal of attention in various areas. In this paper, we generalize the classical EMD from Euclidean space to surfaces represented as triangular meshes. Inspired by the EMD, we also make a first step in using the extremal envelope method for feature-preserving smoothing. 1. Ibraheem Alhashim, Hao Zhang, and Ligang Liu, "Detail-Replicating Shape Stretching," the Visual Computer, Vol. 28, No. 12, pp. 1153-1166, 2012. [PDF | Video | Code | bibtex] We propose a simple and efficient method that helps create model variations by applying non-uniform stretching on 3D models with organic geometric details. The method replicates the geometric details and synthesizes extensions by adopting texture synthesis techniques on surface details.

### 2011

 9. Oana Sidi, Oliver van Kaick, Yanir Kleiman, Hao Zhang, and Daniel Cohen-Or, "Unsupervised Co-Segmentation of a Set of Shapes via Descriptor-Space Spectral Clustering," ACM Trans. on Graphics (Proceeding of SIGGRAPH Asia 2011), Volume 30, Number 6, Article 126, 2011. [PDF (11 MB) | Project page | bibtex] We introduce an algorithm for unsupervised co-segmentation of a set of shapes so as to reveal the semantic shape parts and establish their correspondence across the set. Our algorithm exploits a key enabling feature of the input set, namely, dissimilar parts may be linked'' through third-parties present in the set ... 8. Jinjie Lin, Daniel Cohen-Or, Hao Zhang, Cheng Liang, Andrei Sharf, Oliver Deussen, and Baoquan Chen, "Structure-Preserving Retargeting of Irregular 3D Architecture," ACM Trans. on Graphics (Proceeding of SIGGRAPH Asia 2011), Volume 30, Number 6, Article 183, 2011. [PDF | Highres PDF (29MB) | Project page | bibtex] We present an algorithm for interactive structure-preserving retargeting of irregular 3D architecture models, offering the modeler an easy-to-use tool to quickly generate a variety of 3D models that resemble an input piece in its structural style ... 7. Andrea Tagliassachi, Matt Olson, Hao Zhang, Ghassan Hamarneh, and Daniel Cohen-Or, "VASE: Volume-Aware Surface Evolution for Surface Reconstruction from Incomplete Point Clouds," Computer Graphics Forum (Special Issue of SGP), Volume 30, Number 5, pp. 1563-1571, 2011. [PDF | bibtex] Objects with many concavities are difficult to acquire using laser scanners. The resulting point scan typically suffers from large amounts of missing data. We introduce weak volumetric priors which assume that the volume of a shape varies smoothly and that each point cloud sample is visible from outside the shape. Specifically, the union of view-rays given by the scanner implicitly carves the exterior volume, while volumetric smoothness regularizes the internal volume. 6. Kai Xu, Hanlin Zheng, Hao Zhang, Daniel Cohen-Or, Ligang Liu, and Yueshan Xiong, "Photo-Inspired Model-Driven 3D Object Modeling," ACM Trans. on Graphics (Proceedings of SIGGRAPH 2011), Volume 30, Number 4, pp. 80:1-80:10, 2011. [PDF | bibtex] We introduce an algorithm for 3D object modeling where the user draws creative inspiration from an object captured in a single photograph. Our method leverages the rich source of photographs for creative 3D modeling. However, with only a photo as a guide, creating a 3D model from scratch is a daunting task. We support the modeling process by utilizing an available set of 3D candidate models. Specifically, the user creates a digital 3D model as a geometric variation from a 3D candidate. 5. Matt Olson, Ramsay Dyer, Hao Zhang, and Alla Sheffer, "Point Set Silhouettes via Local Reconstruction," Computer & Graphics (Special Issue of SMI 2011), Volume 35, Number 3, pp. 500-509, 2011. [PDF (4MB) | bibtex] We present an algorithm to compute the silhouette set of a point cloud. Previous methods extract point set silhouettes by thresholding point normals, which can lead to simultaneous over- and under-detection of silhouettes. We argue that additional information such as surface curvature is necessary to resolve these issues. To this end, we develop a local reconstruction scheme using Gabriel and intrinsic Delaunay criteria and defi?ne point set silhouettes based on the notion of a silhouette generating set ... 4. Yanzhen Wang, Kai Xu, Jun Li, Hao Zhang, Ariel Shamir, Ligang Liu, Zhiquan Cheng, and Yueshan Xiong, "Symmetry Hierarchy of Man-Made Objects," Computer Graphics Forum (Special Issue of Eurographics 2011), Volume 30, Number 2, pp. 287-296, 2011. [PDF (14MB) | PDF reduced (500K) | Project page | bibtex] We introduce symmetry hierarchy of man-made objects, a high-level structural representation of a 3D model providing a symmetry-induced, hierarchical organization of the model's constituent parts. We show that symmetry hierarchy naturally implies a hierarchical segmentation that is more meaningful than those produced by local geometric considerations. We also develop an application of symmetry hierarchies for structural shape editing. 3. Oliver van Kaick, Andrea Tagliasacchi, Oana Sidi, Hao Zhang, Daniel Cohen-Or, Lior Wolf, and Ghassan Hamarneh, "Prior Knowledge for Part Correspondence," Computer Graphics Forum (Special Issue of Eurographics 2011), Volume 30, Number 2, pp. 553-562, 2011. [PDF (10 MB) | PDF reduced | bibtex] We stipulate that under challenging scenarios, 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 and combines the knowledge with content-driven analysis based on geometric similarity between the matched shapes ... 2. Oliver van Kaick, Hao Zhang, Ghassan Hamarneh, Daniel Cohen-Or, "A Survey on Shape Correspondence," Computer Graphics Forum (extended version of Eurographics STAR), Volume 30, Number 6, pp. 1681-1707, 2011. [PDF | bibtex] We review methods that are designed to compute correspondences between geometric shapes represented by triangle meshes, contours, or point sets. This survey is motivated in part by some recent developments in space-time registration, where one seeks to correspond non-rigid and time-varying surfaces, and semantic shape analysis, which underlines a recent trend to incorporate shape understanding into the analysis pipeline ... 1. Joe Kahlert, Matt Olson, and Hao Zhang, "Width-Bounded Geodesic Strips for Surface Tiling," The Visual Computer, Vol. 27, No. 1, pp. 45-56, 2011. [PDF | bibtex] We present an algorithm for computing families of geodesic curves over an open mesh patch to partition the patch into strip-like segments. Specifically, the segments can be well approximated using strips obtained by trimming long, rectangular pieces of material possessing a prescribed width. We call this width-bounded geodesic strip tiling of a curved surface, a problem with practical applications such as the surfacing of curved roofs.

### 2009

 10. Kai Xu, Hao Zhang, Andrea Tagliasacchi, Ligang Liu, Guo Li, Min Meng, and Yueshan Xiong, "Partial Intrinsic Reflectional Symmetry of 3D Shapes," ACM Trans. on Graphics (Proceeding of SIGGRAPH Asia 2009), Article 138. [PDF (16 MB) | PDF (reduced size: 7 MB) | Project page | bibtex] While many 3D objects around us exhibit various forms of global symmetries, prominent intrinsic symmetries which exist only on parts of an object are also well recognized ... In this paper, we introduce algorithms to extract and utilize partial intrinsic reflectional symmetries (PIRS) of a 3D shape ... 9. Hui Huang, Dan Li, Hao Zhang, Uri Ascher, and Daniel Cohen-Or, "Consolidation of Unorganized Point Clouds for Surface Reconstruction," ACM Trans. on Graphics (Proceeding of SIGGRAPH Asia 2009), Article 176. [PDF (8 MB) | PDF (reduced size: 2 MB) Project page with source code | bibtex] We consolidate an unorganized point cloud with noise, outliers, non-uniformities, and interference between close-by surface sheets as a preprocess to surface generation ... First, we present a weighted locally optimal projection operator ... Next, we introduce an iterative framework for robust normal estimation, ... 8. Kai Xu, Daniel Cohen-Or, Tao Ju, Ligang Liu, Hao Zhang, Shizhe Zhou, and Yueshan Xiong, "Feature-Aligned Shape Texturing," ACM Trans. on Graphics (Proceeding of SIGGRAPH Asia 2009), Article 108. [PDF (20 MB) | PDF (reduced size: 10 MB) | Project page | Source Code | bibtex] We explore the use of salient curves in synthesizing natural-looking, shape-revealing textures on surfaces. Our synthesis is guided by two principles: matching the direction of the texture patterns to those of the salient curves, and aligning the prominent feature lines in the texture to the salient curves exactly ... 7. Ramsay Dyer, Hao Zhang, and Torsten Moeller, "Gabriel meshes and Delaunay edge flips," Proc. of SIAM/ACM Joint Conf. on Geometric and Physical Modeling (GPM), pp. 295-300, 2009. [PDF | extended version with more proofs | bibtex] We undertake a study of the local properties of 2-Gabriel meshes. We show that, under mild constraints on the dihedral angles, such meshes are Delaunay meshes. The analysis is done by means of the Delaunay edge flipping algorithm and it reveals the details of the distinction between these two mesh structures ... 6. Andrea Tagliasacchi, Hao Zhang, and Daniel Cohen-Or, "Curve Skeleton Extraction from Incomplete Point Cloud," ACM Trans. on Graphics (Proceeding of SIGGRAPH 2009), Volume 28, Number 3, Article 71, 9 pages, DOI = 10.1145/1531326.1531377. [PDF | Project page | bibtex] We present an algorithm for curve skeleton extraction from imperfect point clouds where large portions of the data may be missing. Our construction is primarily based on a novel notion of generalized rotational symmetry axis (ROSA) of a point set with normals, via a variational formulation ... 5. Kai Xu, Hao Zhang, Daniel Cohen-Or, and Yueshan Xiong, "Dynamic Harmonic Fields for Surface Processing," Computers and Graphics (Special Issue of SMI), Vol. 33, pp. 391-398, 2009. [PDF | bibtex] We propose a method for fast updating of harmonic fields defined on polygonal meshes, enabling real-time insertion and deletion of constraints. Our approach utilizes the penalty method to enforce constraints in harmonic field computation. It maintains the symmetry of the Laplacian system ... 4. Xiaoxing Li, Tao Jia, and Hao Zhang, "Expression-Insensitive 3D Face Recognition using Sparse Representation," IEEE CS Conf. on Computer Vision and Pattern Recognition (CVPR 2009), pp. 2575-2582. [PDF | bibtex] We present a face recognition method based on sparse representation for recognizing 3D face meshes under expressions using low-level geometric features ... To handle facial expressions, we design a feature pooling and ranking scheme to collect various types of low-level geometric features and rank them ... 3. Kai Xu, Zhiquan Cheng, Yanzhen Wang, Yueshan Xiong, and Hao Zhang, "Quality Encoding for Tetrahedral Mesh Optimization," Computers and Graphics (Special Issue of SMI), Vol. 33, pp. 250-261, 2009. [PDF | bibtex ] We define quality differential coordinates (QDC) for per-vertex encoding of the quality of a tetrahedral mesh. Our formulation allows the incorporation of element quality metrics into QDC construction to penalize badly shaped and inverted tetrahedra ... 2. Rong Liu, Hao Zhang, Ariel Shamir, and Daniel Cohen-Or, "A Part-Aware Surface Metric for Shape Analysis," Computer Graphics Forum (Special Issue of Eurographics 2009), Vol. 28, No. 2, 397-406, 2009. [PDF | bibtex] The notion of parts in a shape plays an important role in many geometry problems. At the same time, many such problems utilize a surface metric to assist shape analysis and understanding. The main contribution of our work is to bring together these two fundamental concepts ... 1. Matt Olson and Hao Zhang, "Tangential Distance Fields for Mesh Silhouette Problems,," Computer Graphics Forum, Vol. 28, No. 1, pp. 84-100, 2009. [PDF | bibtex] We introduce a novel class of distance fields for a given surface defined by its tangent planes. At each point in space, we assign a scalar value which is a weighted sum of distances to these tangent planes. We use four applications to illustrate the benefit of using the resulting TDF scalar field: view point selection, ...

### 2008

 3. Ramsay Dyer, Hao Zhang, and Torsten Moeller, "Surface sampling and the intrinsic Voronoi diagram," Computer Graphics Forum (Special Issue of SGP), Volume 27, Number 5, pp. 1431-1439, 2008. (won Best Paper Award at SGP) [PDF | bibtex] We develop adaptive sampling criteria which guarantee a topologically faithful mesh and demonstrate an improvement and simplification over earlier results, albeit restricted to 2D surfaces. These sampling criteria are based on the strong convexity radius and the injectivity radius ... 2. Hao Zhang, Alla Sheffer, Daniel Cohen-Or, Qingnan Zhou, Oliver van Kaick, and Andrea Tagliasacchi, "Deformation-Driven Shape Correspondence," Computer Graphics Forum (Special Issue of SGP), Volume 27, Number 5, pp. 1393-1402, 2008. [PDF | bibtex | Project page (UBC | SFU)] We present an automatic feature correspondence algorithm capable of handling large, non-rigid shape variations, as well as partial matching ... The search is deformation-driven, prioritized by a self-distortion energy measured on meshes deformed according to a given correspondence ... 1. Rong Liu, Hao Zhang, and James Busby, "Convex Hull Covering of Polygonal Scenes for Accurate Collision Detection in Games," Proc. of Graphics Interface 2008, pp. 203-210. [PDF | bibtex] We look at a particular instance of the convex decomposition problem which arises from real-world game development. Given a collection of polyhedral surfaces (possibly with boundaries, holes, and complex interior structures) that model the scene geometry in a game environment, we wish to find a small set of convex hulls ...

### 2007

 8. Oliver van Kaick, Ghassan Hamarneh, Hao Zhang, and Paul Wighton, "Contour Correspondence via Ant Colony Optimization," Proc. of Pacific Graphics 2007, pp. 271-280. [Oliver's page with paper and MATLAB code | bibtex] We formulate contour correspondence as a Quadratic Assignment Problem (QAP), incorporating proximity information. By maintaining the neighborhood relation between points this way, we show that better matching results are obtained in practice. We propose the first Ant Colony Optimization (ACO) algorithm ... 7. Ramsay Dyer, Hao Zhang, and Torsten Moeller, "Delaunay Mesh Construction," Proc. of Eurographics Symposium on Geometry Processing (SGP), pp. 273-282. [PDF | bibtex] We present algorithms to produce Delaunay meshes from arbitrary triangle meshes by edge flipping and geometry-preserving refinement and prove their correctness. In particular we show that edge flipping serves to reduce mesh surface area, and that a poorly sampled input mesh may yield unflippable edges necessitating refinement ... 6. Hao Zhang, Oliver van Kaick, and Ramsay Dyer, "Spectral Methods for Mesh Processing and Analysis," Proc. of Eurographics 2007 State of the Art Report, pp. 1-22. [PDF | bibtex] Spectral methods for mesh processing and analysis rely on the eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks. This state-of-the-art report aims to provide a comprehensive survey on the spectral approach ... 5. Rong Liu and Hao Zhang, "Mesh Segmentation via Spectral Embedding and Contour Analysis," Computer Graphics Forum (Special Issue of Eurographics 2007), Vol. 26, pp. 385-394, 2007. [PDF | bibtex] We propose a mesh segmentation algorithm where at each step, a sub-mesh embedded in 3D is first spectrally projected into the plane with a contour extracted from the planar embedding. Transforming the shape analysis problem to the 2D domain facilitates our segmentability analysis and sampling tasks ... 4. Xiaoxing Li and Hao Zhang, "Adapting Geometric Attributes for Expression-Invariant 3D Face Recognition," Proc. of Shape Modeling International (SMI) 2007, pp. 21-32. [PDF | bibtex] We investigate the use of multiple intrinsic geometric attributes, including angles, geodesic distances, and curvatures, for 3D face recognition ... As invariance to facial expressions holds the key to improving recognition performance, we propose to train for the component-wise weights ... 3. Ramsay Dyer, Hao Zhang, and Torsten Moeller, "Voronoi-Delaunay Duality and Delaunay Meshes," Proc. of ACM Symposium on Solid and Physical Modeling (SPM) 2007, pp. 415-420. [PDF | bibtex] We define a Delaunay mesh to be a manifold triangle mesh whose edges form an intrinsic Delaunay triangulation or iDT of its vertices ... We show that meshes constructed from a smooth surface by taking an iDT or a restricted Delaunay triangulation, do not in general yield a Delaunay mesh ... 2. Varun Jain, Hao Zhang, and Oliver van Kaick, "Non-Rigid Spectral Correspondence of Triangle Meshes," International Journal on Shape Modeling (via invitation to Special Issue of SMI 2006), Volume 13, Number 1, pp. 101-124. [PDF | bibtex] We present an algorithm for finding a meaningful correspondence between two triangle meshes, which is designed to handle general non-rigid transformations. Our algorithm operates on embeddings of the two shapes in the spectral domain so as to normalize them with respect to uniform scaling and rigid-body transformation. 1. Varun Jain and Hao Zhang, "A Spectral Approach to Shape-Based Retrieval of Articulated 3D Models," Computer-Aided Design (via invitation to Special Issue of GMP 2006), Vol. 39, Issue 5, pp. 398-407, 2007. [PDF | DOI | bibtex] We present an approach for robust shape retrieval from databases containing articulated 3D models. Each shape is represented by the eigenvectors of an appropriately defined affinity matrix, forming a spectral embedding which achieves normalization against rigid-body transformations, shape articulation ...

### 2006

 8. John Li and Hao Zhang, "Nonobtuse Remeshing and Decimation," in Proc. of Symposium on Geometry Processing (SGP) 2006 (short paper), pp.235-238. [PDF | bibtex] We propose an algorithm for guaranteed nonobtuse remeshing and nonobtuse mesh decimation. Our strategy for the remeshing problem is to first convert an input mesh, using a modified Marching Cubes algorithm, into a rough approximate mesh that is guaranteed to be nonobtuse. We then apply iterative "deform-to-fit" ... 7. Matt Olson and Hao Zhang, "Silhouette Extraction in Hough Space," Computer Graphics Forum (Special Issue on Eurographics 2006), Volume 25, Number 3, pp. 273-282, 2006. [PDF | bibtex] We present an efficient silhouette extractor for triangle meshes under perspective projection in the Hough space. The more favorable point distribution in Hough space allows us to obtain significant performance gains over the traditional dual-space based techniques ... 6. Varun Jain and Hao Zhang, "Shape-Based Retrieval of Articulated 3D Models Using Spectral Embedding," in Proceeding of Geometric Modeling and Processing 2006, pp. 295-308. [PDF | bibtex] We present a spectral approach for robust shape retrieval from databases containing articulated 3D shapes. We show absolute improvement in retrieval performance when conventional shape descriptors are used in the spectral domain on the McGill database of articulated 3D shapes. We also propose a simple eigenvalue-based descriptor ... 5. Rong Liu, Hao Zhang, and Oliver van Kaick, "Spectral Sequencing based on Graph Distance," in Proceeding of Geometric Modeling and Processing 2006 (poster paper), pp. 632-638. [PDF | bibtex] In this paper, we treat optimal mesh layout generation as a problem of preserving graph distances and propose to use the subdominant eigenvector of a kernel (affinity) matrix for sequencing ... 4. Rong Liu, Varun Jain, and Hao Zhang, "Subsampling for Efficient Spectral Mesh Processing," in Proceeding of Computer Graphics International 2006, Lecture Notes in Computer Science 4035, H.-P. Seidel, T. Nishita, and Q. Peng, Eds., pp. 172-184, 2006. (acceptance rate: 10%) [PDF | bibtex] We apply Nystrom method, a sub-sampling and reconstruction technique, to speed up spectral mesh processing. We first relate this method to Kernel Principal Component Analysis (KPCA). This enables us to derive a novel measure in the form of a matrix trace, based soly on sampled data, to quantify the quality of Nystrom approximation ... 3. Varun Jain and Hao Zhang, "Robust 3D Shape Correspondence in the Spectral Domain," in Proceeding of International Conference on Shape Modeling and Applications (SMI) 2006, pp. 118-129, 2006. [PDF | bibtex] We present an algorithm for finding a meaningful correspondence between two 3D shapes given as triangle meshes. Our algorithm operates on embeddings of the two shapes in the spectral domain so as to normalize them with respect to uniform scaling, rigid-body transformation and shape bending ... 2. Andrew Clements and Hao Zhang, "Minimum Ratio Contours on Surface Meshes," in Proceeding of International Conference on Shape Modeling and Applications (SMI) 2006, pp. 26-37, 2006. [PDF | bibtex] We present a novel approach for discretely optimizing contours on the surface of a triangle mesh. This is achieved through the use of a minimum ratio cycle (MRC) algorithm, where we compute a contour having the minimal ratio between a novel contour energy term and the length of the contour ... 1. Xiaoxing Li, Greg Mori, and Hao Zhang, "Expression-Invariant Face Recognition with Expression Classification," in Proceeding of Canadian Conference on Computer and Robot Vision (CRV) 2006, pp. 77-83, 2006. [PDF | bibtex] Facial expression, which changes face geometry, usually has an adverse effect on the performance of a face recognition system. On the other hand, face geometry is a useful cue for recognition. Taking these into account, we utilize the idea of separating geometry and texture information in a face image ...

### 2005 -

 9. Hao Zhang and Rong Liu, "Mesh Segmentation via Recursive and Visually Salient Spectral Cuts," in Proceeding of Vision, Modeling, and Visualization 2005, pp. 429-436, 2005. [PDF | bibtex] 8. Varun Jain and Hao Zhang, "Robust 2D Shape Correspondence using Geodesic Shape Context," in Proceeding of Pacific Graphics 2005, (short paper), pp. 121-124, 2005. [bibtex] 7. Hao Zhang, "Discrete Combinatorial Laplacian Operators for Digital Geometry Processing," in Proc. of SIAM Conference on Geometric Design and Computing, pp. 575-592, 2004. [PDF | bibtex] 6. Rong Liu and Hao Zhang, "Segmentation of 3D Meshes through Spectral Clustering," in Proceeding of Pacific Graphics 2004, pp. 298-305. [PDF | bibtex] 5. Hao Zhang and Hendrik C. Blok, "Optimal Mesh Signal Transforms," in Proceeding of IEEE Geometric Modeling and Processing 2004 (poster paper), pp. 373-379. [bibtex] 4. Hao Zhang and Eugene Fiume, "Butterworth Filtering and Implicit Fairing of Irregular Meshes," in Proceedings of Pacific Graphics 2003 (short paper), pp. 502-506. [bibtex] 3. Hao Zhang and Eugene Fiume, "Mesh Smoothing with Shape or Feature Preservation," in Advances in Modeling, Animation, and Rendering, J. Vince and R. Earnshaw, editors, pp. 167-182, Springer 2002. Also as Proceeding of Computer Graphics International 2002. 2. Hao Zhang and Eugene Fiume, "Shape Matching of 3-D Contours using Normalized Fourier Descriptors," in Proceeding of International Conference on Shape Modeling and Applications (SMI), IEEE Computer Society, pp. 261-268, 2002. [PDF | bibtex] 1. John A. Brzozowski and Hao Zhang, "Delay-Insensitivity and Semi-Modularity," Formal Methods in System Design, Kluwer Academic Publishers, March 2000, vol. 16, pp. 191-218, 2000.

SIGGRAPH/TOG: 40; SIGGRAPH Courses: 6; SGP: 7; Eurographics: 8; EGSTAR: 3; CGF: 17; SMI: 11; PG: 5; ICCV+CVPR: 3.