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and (95), the (80), shape (55), funkhouser (45), thomas (44), for (44), graphics (24), model (21), acm (19), models (18), symmetry (18), transactions (17), are (17), kazhdan (16), search (16), siggraph (16), princeton (15), michael (15), with (15), based (14), analysis (13), that (13), min (12), benchmark (12), geometry (11), patrick (11), chen (11), david (11), shilane (10), 2004 (10), aleksey (10), golovinskiy (10), shapes (10), matching (10), june (10), retrieval (10), from (10), dobkin (9), file (9), philip (9), szymon (9), rusinkiewicz (9), reflective (9), processing (9), computer (9), august (9), segmentation (9), yaron (9), lipman (9), vladimir (9), kim (9), engine (8), modeling (8), july (8), descriptor (8), symposium (8), descriptors (8), using (8), 2009 (8), proc (8), each (8), this (8), have (8), example (7), mesh (7), text (7), xiaobai (7), which (7), user (7), university (6), 2006 (6), international (6), distributions (6), 2002 (6), algorithms (6), curves (6), data (6), 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ain research issues are to develop effective shape representations and query interfaces the princeton shape benchmark and princeton segmentation benchmark provide data for evaluation of shape based retrieval and analysis algorithms this web page provides an overview of some projects on these topics our publications provide more details shape representations a key issue in developing a shape based retrieval and analysis system is to find a computational representation of shape a shape descriptor for which an index can be built similarity queries can be answered efficiently we are studying a spectrum of shape descriptors ranging from ones that are simple to compute but perhaps not very discriminating to ones that require expensive computations but provide sophisticated shape analysis shape distributions on the low end of the spectrum we have been investigating shape distributions that represent the shape of a 3d model as a probability distribution sampled from a shape function measuring geometric properties of a 3d model the motivation for this approach is that samples can be computed quickly and easily and the shape of the resulting distributions are invariant to similarity transformations noise tessellation cracks etc with a normalization step for scale invariance for example one such shape distribution which we call d2 represents the global shape of an object by the probability distribution of euclidean distances between pairs of randomly selected points on its surface the figure below shows the d2 distributions for 5 tanks gray curves and 6 cars black curves note how the classes are distinguishable reflective symmetry descriptors computing reflective symmetries of 2d and 3d shapes is a classical problem in computer vision and computational geometry most prior work has focused on finding the main axes of symmetry or determining that none exists we have studied a new shape descriptor that represents a measure of reflective symmetry for an arbitrary 3d voxel model for all planes through the model s center of mass even if they are not planes of symmetry for example the figure to the right shows a car cube and chair top and their corresponding reflective symmetry descriptors bottom the descriptors are drawn by scaling unit vectors on the sphere in proportion to the measure of reflective symmetry about the plane through the center of mass and normal to the vector the main benefits of this new shape descriptor are that it is defined over a canonical parameterization the sphere which makes comparison simple and it describes global symmetry properties of a 3d shape which capture significant semantic features of many objects spherical harmonics one of the main challenges in matching and indexing shapes is accounting for arbitrary rotations previous methods that require alignment into a common coordinate system e g with principal axes are not robust other methods that rely upon rotationally invariant shape descriptors are usually not very discriminating we propose a novel rotation invariant shape descriptor based on spherical harmonics the main idea is to decompose a 3d model into a collection of functions defined on concentric spheres and to use spherical harmonics to discard orientation information phase for each one this yields a shape descriptor that is both orientation invariant and descriptive skeletal graphs on the high end of the spectrum we are investigating skeletons as a descriptor of shape the general idea is to derive 1d skeletal curves from a 3d object such that each curve represents a significant part of the object these curves are then converted to an attributed graph representation a skeletal graph which can be used for indexing matching segmentation correspondence finding etc as an example the figure below shows a plane model its medial axis as computed using the powercrust algorithm 3 our voxelized centerline representation and the resulting skeletal graph note that the medial axis comprises a multitude of noisy curves and sheets while our centerline representation nicely segments the plane into its salient parts query interfaces another issue is how should people specify shape based queries for instance consider a person who wants to build a 3d virtual world representing a city scene she will need cars street lamps stop signs etc what input should be given to a search engine to retrieve objects of these types from the world wide web we have investigated several options text the simplest query interface is to search for 3d models based on textual keywords to support this feature we construct for each 3d model a representative document containing the model filename the anchor and nearby text parsed from its referring web page and ascii labels parsed from inside the model file for each document stop words are removed verbs are stemmed to remove inflectional changes and synonyms are added using wordnet miller95 we match documents to user specified keywords using the tf idf rocchio method rocchio71 a popular weighting and classification scheme for text documents 3d model we also support shape based queries for instance the user can provide an existing 3d model and ask our search engine to retrieve similar ones alternately the user may search for models with shapes like one returned in a previous search by clicking on the find similar shape link under its image on a results page blue text in the figure below 3d sketches of course shape similarity queries are only possible when the user already has a representative 3d model in some cases he will be able to find one by using a text search however in other cases he will have to create it from scratch at least to seed the search to investigate this option we have developed a query interface in which the user creates a simple 3d model with teddy igarashi99 and then the system returns objects with similar shapes for example the figure below shows a cup sketched in teddy and its five closest matches 2d sketches an alternative approach is to allow the user to draw one or more 2d shapes with a pixel paint program and then have the system match the resulting image s to 2d projections of 3d objects for example in the figures below the user has drawn outline contours specifying a shape and the system has returned a set of matching objects princeton shape benchmark the princeton shape benchmark provides a repository of 3d models and software tools for evaluating shape based retrieval and analysis algorithms the motivation is to promote the use of standardized data sets and evaluation methods for research in matching classification clustering and recognition of 3d models researchers are encouraged to use these resources to produce comparisons of competing algorithms in future publications the benchmark contains a database of 3d polygonal models collected from the world wide web for each 3d model there is a object file format off file with the polygonal geometry of the model an ascii text file with information about the model e g the url from whence it came and a jpeg image file with a thumbnail view of the model version 1 of the benchmark contains 1 814 models source code for parsing the files viewing the models and creating overview web pages is provided princeton segmentation benchmark the princeton segmentation benchmark provides data for quantitative analysis of how people decompose objects into parts and for comparison of automatic mesh segmentation algorithms to build the benchmark we recruited eighty people to manually segment surface meshes into functional parts yielding an average of 11 human generated segmentations for each of 380 meshes across 19 object categories shown in the figure above this data set provides a sampled distribution over how humans decompose each mesh into functional parts which we treat as a probabilistic ground truth darker lines in the image above show places where more people placed a segmentation boundary given this data set it is possible to analyze properties of the human generated segmentations to learn about what they have in common with each other and with computer generated segmentations and to compute evaluation metrics that measure how well the human generated segmentations match computer generated ones for the same mesh publications vladimir g kim siddhartha chaudhuri leonidas guibas and thomas funkhouser shape2pose human centric shape analysis acm transactions on graphics proc siggraph august 2014 xiaobai chen shape analysis with crowd sourced data ph d thesis princeton university may 2014 vladimir g kim wilmot li niloy j mitra siddhartha chaudhuri stephen diverdi and thomas funkhouser learning part based templates from large collections of 3d shapes acm transactions on graphics proc siggraph july 2013 vladimir g kim wilmot li niloy mitra stephen diverdi and thomas funkhouser exploring collections of 3d models using fuzzy correspondences acm transactions on graphics proc siggraph august 2012 tianqiang liu vladimir g kim thomas funkhouser finding surface correspondences using symmetry axis curves computer graphics forum proc symposium on geometry processing july 2012 vladimir g kim yaron lipman thomas funkhouser symmetry guided texture synthesis and manipulation acm transactions on graphics 31 3 may 2012 doug m boyer yaron lipman elizabeth st clair jesus puente biren a patel thomas funkhouser jukka jernvall and ingrid daubechies algorithms to automatically quantify the geometric similarity of anatomical surfaces pnas october 2011 vladimir g kim yaron lipman and thomas funkhouser blended intrinsic maps acm transactions on graphics proc siggraph august 2011 yaron lipman xiaobai chen ingrid daubechies and thomas funkhouser symmetry factored embedding and distance acm transactions on graphics siggraph 2010 august 2010 xiaobai chen abulhair saparov bill pang and thomas funkhouser schelling points on 3d surface meshes acm transactions on graphics proc siggraph august 2012 vladimir kim yaron lipman xiaobai chen and thomas funkhouser mobius transformations for global intrinsic symmetry analysis computer graphics forum symposium on geometry processing july 2010 jian sun xiaobai chen and thomas funkhouser fuzzy geodesics and consistent sparse correspondences for deformable shapes computer graphics forum symposium on geometry processing july 2010 yaron lipman raif rustamov and thomas funkhouser biharmonic distance acm transactions on graphics 29 3 june 2010 aleksey golovinskiy and thomas funkhouser min cut based segmentation of point clouds search in 3d and video s3dv september 2009 raif rustamov yaron lipman and thomas funkhouser interior distance using barycentric coordinates computer graphics forum symposium on geometry processing 2009 aleksey golovinskiy joshua podolak and thomas funkhouser symmetry aware mesh processing mathematics of surfaces 2009 invited paper lncs 5654 september 2009 previously princeton university tech report tr 782 07 aleksey golovinskiy vladimir kim and thomas funkhouser shape based recognition of 3d point clouds in urban environments international conference on computer vision iccv september 2009 yaron lipman and thomas funkhouser mobius voting for surface correspondence acm transactions on graphics proc siggraph 28 3 august 2009 xiaobai chen aleksey golovinskiy and thomas funkhouser a benchmark for 3d mesh segmentation acm transactions on graphics proc siggraph 28 3 august 2009 aleksey golovinskiy and thomas funkhouser consistent segmentation of 3d models computers and graphics shape modeling international beijing june 2009 aleksey golovinskiy and thomas funkhouser randomized cuts for 3d mesh analysis acm transactions on graphics siggraph asia 2008 december 2008 jeehyung lee and thomas funkhouser sketch based search and composition of 3d models eurographics workshop on sketch based interfaces and modeling june 2008 philip shilane and thomas funkhouser distinctive regions of 3d surfaces acm transactions on graphics volume 26 number 2 june 2007 joshua podolak philip shilane aleksey golovinskiy szymon rusinkiewicz and thomas funkhouser a planar reflective symmetry transform for 3d shapes acm transactions on graphics siggraph 2006 25 3 july 2006 thomas funkhouser and philip shilane partial matching of 3d shapes with priority driven search symposium on geometry processing june 2006 zafer barutcuoglu and christopher decoro hierarchical shape classification using bayesian aggregation shape modeling international june 2006 philip shilane and thomas funkhouser selecting distinctive 3d shape descriptors for similarity retrieval shape modeling international june 2006 thomas funkhouser michael kazhdan patrick min and philip shilane shape based retrieval and analysis of 3d models communications of the acm 48 6 58 64 june 2005 patrick min michael kazhdan and thomas funkhouser a comparison of text and shape matching for retrieval of online 3d models european conference on digital libraries september 2004 thomas funkhouser michael kazhdan philip shilane patrick min william kiefer ayellet tal szymon rusinkiewicz and david dobkin modeling by example acm transactions on graphics siggraph 2004 los angeles ca august 2004 michael kazhdan thomas funkhouser and szymon rusinkiewicz shape matching and anisotropy acm transactions on graphics siggraph 2004 los angeles ca august 2004 michael kazhdan thomas funkhouser and szymon rusinkiewicz symmetry descriptors and 3d shape matching symposium on geometry processing july 2004 michael kazhdan shape representations and algorithms for 3d model retrieval phd thesis princeton university june 2004 philip shilane patrick min michael kazhdan and thomas funkhouser the princeton shape benchmark shape modeling international genova italy june 2004 patrick min a 3d model search engine ph d thesis january 2004 michael kazhdan bernard chazelle david dobkin thomas funkhouser and szymon rusinkiewicz a reflective symmetry descriptor for 3d models algorithmica 38 2 november 2003 pp 201 225 michael kazhdan thomas funkhouser and szymon rusinkiewicz rotation invariant spherical harmonic representation of 3d shape descriptors symposium on geometry processing 2003 patrick min john a halderman michael kazhdan and thomas a funkhouser early experiences with a 3d model search engine web3d symposium pp 7 18 saint malo france march 2003 thomas funkhouser patrick min michael kazhdan joyce chen alex halderman david dobkin and david jacobs a search engine for 3d models acm transactions on graphics 22 1 pp 83 105 january 2003 robert osada thomas funkhouser bernard chazelle and david dobkin shape distributions acm transactions on graphics 21 4 pp 807 832 october 2002 michael kazhdan bernard chazelle david dobkin adam finkelstein and thomas funkhouser a reflective symmetry descriptor european conference on computer vision eccv may 2002 michael kazhdan and thomas funkhouser harmonic 3d shape matching siggraph 2002 technical sketches p 191 july 2002 patrick min joyce chen and thomas funkhouser a 2d sketch interface for a 3d ...