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Tao Ju

Associate Professor
Department of Computer Science and Engineering
Washington University in St. Louis
Office: Jolley 406 (how to get here)
Phone: 314-935-6648
Email: taoju at cse.wustl.edu
Bio Sketch
I joined the faculty at Washington University in 2005. I finished my undergraduate study in 2000 at Tsinghua University (China) with a major in English and a minor in Computer Science, obtained my PhD degree in 2005 from Rice University in Computer Science under the supervision of Dr. Joe Warren, and pursued a short post-doctoral training in the summer of 2005 at the National Center for Macromolecular Imaging in Baylor College of Medicine directed by Dr. Wah Chiu.

My primary research area is computer graphics, with particular interests in geometric modeling, mesh processing, and shape understanding. The other focus of my research is on bio-medical applications, in particular geometric algorithms for analyzing bio-medical images and volumes. I have received a number of grant awards from NSF and NIH, including an NSF CAREER award in 2009.
Teaching
Advising
Current
  • Ming Zou (PhD)
  • Derek Burrows (PhD)
  • Michelle Vaughn (PhD, co-advised with Dr. Cindy Grimm)
  • Adam Steffen (MS)

Past
  • Lu Liu (PhD, graduated 2011, now at Google)
  • Sasakthi Abeysinghe (PhD, graduated 2010, now at Google)
  • Ruosi Li (MS, graduated 2011, now at Facebook)
  • Trung D. Nguyen (MS, graduated 2011, now at Microsoft)
  • Stephen Schuh (MS, graduated 2011, now at Google)
  • Tim Simpson (MS., graduated 2008)
Service
Journal Editorial Board
  • Computer-Aided Design, Associate Editor (2012-present)
  • Computer Graphics Forum, Associate Editor (2010-present)
  • Graphical Models, Associate Editor (2010-present)

Program Committee
  • Siggraph (2009,2010)
  • Siggraph Asia (2008,2012).
  • Eurographics (2007, 2009).
  • Symposium on Geometry Processing (2009, 2010, 2011, 2012).
  • Pacific Graphics (2006, 2007 (program co-chair), 2008, 2009, 2010, 2011).
  • ACM Symposium on Solid and Physical Modeling (2007, 2008, 2010, 2011, 2012).
  • Geometric Modeling and Processing (2006, 2008, 2010, 2012).
  • IEEE International Conference on Shape Modeling and Applications (2009, 2010, 2011)
  • Sketch-Based Interfaces and Modeling (2009, 2010, 2011, 2012)
  • International Symposium on Visual Computing (2006, 2007 (area co-chair), 2008, 2009, 2010, 2011, 2012).
  • Computer Graphics International Conference (2006)

Department Responsibilities
Research Directions
Here are some active projects that I am working on:

  Volumetric methods in mesh processing
  Barycentric coordinates and mesh deformation
  Protein structure identification using skeletons
  Deformable imaging using anatomical atlases
Research Software
Geometry processing
PolyMender: A robust, efficient program for removing cracks, holes, T-juctions and self-intersections from arbitrary polygonal models. Based on SIGGRAPH 2004 Paper "Robust Repair of Polygonal Models".
Ctr2Suf: A tool for smooth surface reconstruction from cross-section curves (or curve networks) that lie on either parallel or non-parallel planes. Based on Eurographics 2008 Paper "Surface Reconstruction From Non-parallel Curve Networks". (Developed by Lu Liu)

Bio-medical modeling
Gorgon: An interactive molecular modeling system specifically geared towards cryo-EM and other low resolution structures of macromolecular complexes.
GeneAtlas.org: A web-based spatial database of gene expression patterns in the mouse brain featuring fully-customized graphical query interface.
StackAligner: A graphical toolkit for reconstructing smooth 3D volumes from serially sectioned tissue images. Based on Journal of Neuroscience Methods paper "3D Volume Reconstruction of a Mouse Brain from Histological Sections using Warp Filtering".
Selected Publications
2012
Region-based Line Field Design Using Harmonic Functions
IEEE Transactions on Visualization and Computer Graphics, 18(6):902-913. (Paper, Supplementary material, Video)
C.-Y. Yao, M.-T. Chi, T.-Y. Lee, T. Ju

Field design has wide applications in graphics and visualization. One of the main challenges in field design has been how to provide users with both intuitive control over the directions in the field on one hand and robust management of its topology on the other hand. In this paper, we present a design paradigm for line fields that addresses this challenge. Rather than asking users to input all singularities as in most methods that offer topology control, we let the user provide a partitioning of the domain and specify simple flow patterns within the partitions. Represented by a selected set of harmonic functions, the elementary fields within the partitions are then combined to form continuous fields with rich appearances and well-determined topology. Our method allows a user to conveniently design the flow patterns while having precise and robust control over the topological structure. Based on the method, we developed an interactive tool for designing line fields from images, and demonstrated the utility of the fields in image stylization.
Feature correspondences using Morse Smale complex
The Visual Computer, DOI: 10.1007/s00371-012-0674-3. (Paper)
W. Feng, J. Huang, T. Ju, H-J Bao

Establishing corresponding features on two non-rigidly deformed 3D surfaces is a challenging and well-studied problem in computer graphics. Unlike previous approaches that constrain the matching between feature pairs using isometry-invariant distance metrics, we constrain the matching using a discrete connectivity graph derived from the Morse–Smale complex of the Auto Diffusion Function. We observed that the graph remains stable even for surfaces differing by topology or by significant deformation. This algorithm is simple to implement and efficient to run. When tested on a range of examples, our algorithm produces comparable results with state-of-art methods on surfaces with strong isometry but with greatly improved efficiency, and often gets better correspondences on surfaces with larger shape variances.
Similarity-Based Appearance-Prior for Fitting a Subdivision Mesh in Gene Expression Images
Proceedings of the 15th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI'12) (Paper)
Y-H. Le, U. Kurkure, N. Paragios, T. Ju, J. P. Carson, I. A. Kakadiaris

Automated segmentation of multi-part anatomical objects in images is a challenging task. In this paper, we propose a similarity-based appearance-prior to fit a compartmental geometric atlas of the mouse brain in gene expression images. A subdivision mesh which is used to model the geometry is deformed using a Markov Random Field (MRF) framework. The proposed appearance-prior is computed as a function of the similarity between local patches at corresponding atlas locations from two images. In addition, we introduce a similarity-saliency score to select the mesh points that are relevant for the computation of the proposed prior. Our method significantly improves the accuracy of the atlas fitting, especially in the regions that are influenced by the selected similarity-salient points, and outperforms the previous subdivision mesh fitting methods for gene expression images.
Gorgon and pathwalking: Macromolecular modeling tools for subnanometer resolution density maps
Biopolymers, 97(9):655-668 (Paper link)
M. L. baker, M. R. Baker, C. F. Hryc, T. Ju, W. Chiu.

The complex interplay of proteins and other molecules, often in the form of large transitory assemblies, are critical to cellular function. Today, X-ray crystallography and electron cryo-microscopy (cryo-EM) are routinely used to image these macromolecular complexes, though often at limited resolutions. Despite the rapidly growing number of macromolecular structures, few tools exist for modeling and annotating structures in the range of 3-10A resolution. To address this need, we have developed a number of utilities specifically targeting subnanometer resolution density maps. As part of the 2010 Cryo-EM Modeling Challenge, we demonstrated two of our latest de novo modeling tools, Pathwalking and Gorgon, as well as a tool for secondary structure identification (SSEHunter) and a new rigid-body/flexible fitting tool in Gorgon. In total, we submitted 30 structural models from ten different subnanometer resolution data sets in four of the six challenge categories. Each of our utilities produced accurate structural models and annotations across the various density maps. In the end, the utilities that we present here offer users a robust toolkit for analyzing and modeling protein structure in macromolecular assemblies at non-atomic resolutions.
2011
Extended Grassfire Transform on Medial Axes of 2D Shapes
Computer Aided Design (Proceedings of SPM 2011), 43(11):1496-1505 (Paper, Slides (168MB), Slides without video)
Lu Liu, Erin Chambers, David Letscher, Tao Ju

The medial axis is an important shape descriptor first introduced by Blum via a grassfire burning analogy. However, the medial axes are sensitive to boundary perturbations, which calls for global shape measures to identify meaningful parts of a medial axis. On the other hand, a more compact shape representation than the medial axis, such as a "center point", is needed in various applications ranging from shape alignment to geography. In this paper, we present a uniform approach to define a global shape measure (called extended distance function, or EDF) along the 2D medial axis as well as the center of a 2D shape (called extended medial axis, or EMA). We reveal a number of properties of the EDF and EMA that resemble those of the boundary distance function and the medial axis, and show that EDF and EMA can be generated using a fire propagation process similar to Blum's grassfire analogy, which we call the extended grassfire transform. The EDF and EMA are demonstrated on many 2D examples, and are related to and compared with existing formulations. Finally, we demonstrate the utility of EDF and EMA in pruning medial axes, aligning shapes, and shape description.
Isotopic Frechet Distance
Proceedings of 23rd Canadian Conference on Computational Geometry, accepted (Paper)
Erin Chambers, Tao Ju, David Letscher, Lu Liu

We are interested in defining a distance measure between two (homeomorphic) shapes, which has a number of potential applications in computer graphics and vision. We propose a new distance measure which intuitively is the least effort of morphing a source shape into a target shape, such that each intermediate shape during the morph is homeomorphic to the source. For a given morph, this "effort" is measured as the maximum distance traveled by any point on the source shape. Our measure is closely related to Frechet distance as well as the homotopic Frechet distance, yet can better characterize the dissimilarity between two curves. This paper discusses the formulation of the distance measure, compares with previous measures, and touches on the challenges in computing the measure.
A Geometric Study of V-style Pop-ups: Theories and Algorithms
ACM Transactions on Graphics (Proceedings of Siggraph 2011), 30(4), article 98. (Paper, Video, Project)
X-Y. Li, T. Ju, Y. Gu, S-M. Hu

Pop-up books are a fascinating form of paper art with intriguing geometric properties. In this paper, we present a systematic study of a simple but common class of pop-ups consisting of patches falling into four parallel groups, which we call v-style pop-ups. We give sufficient conditions for a v-style paper structure to be pop-uppable. That is, it can be closed flat while maintaining the rigidity of the patches, the closing and opening do not need extra force besides holding two patches and are free of intersections, and the closed paper is contained within the page border. These conditions allow us to identify novel mechanisms for making pop-ups. Based on the theory and mechanisms, we developed an interactive tool for designing v-style pop-ups and an automated construction algorithm from a given geometry, both of which guaranteeing the popuppability of the results.
View-independent Contour Culling of 3D Density Maps for Far-field Viewing of Iso-surfaces
Computer and Graphics (Proceedings of SMI'11), 35(3):561-568 (Paper)
P. Feng, T. Ju, J. Warren

In many applications, iso-surface is the primary method for visualizing the structure of 3D density maps. We consider a common scenario where the user views the iso-surfaces from a distance and varies the level associated with the iso-surface as well as the view direction to gain a sense of the general 3D structure of the density map. For many types of density data, the iso-surfaces associated with a particular threshold may be nested and never visible during this type of viewing. In this paper, we discuss a simple, conservative culling method that avoids the generation of interior portions of iso-surfaces at the contouring stage. Unlike existing methods that perform culling based on the current view direction, our culling is performed once for all views and requires no additional computation as the view changes. By pre-computing a single visibility map, culling is done at any iso-value with little overhead in contouring. We demonstrate the effectiveness of the algorithm on a range of bio-medical data and discuss a practical application in online visualization.
Modeling protein structure at near atomic resolutions with Gorgon
Journal of Structural Biology, 174(2):360-373 (Paper, Journal cover, Project)
M. Baker, S. Abeysinghe, S. Schuh, R. Coleman, A. Abrams, M. Marsh, C. Hryc, T. Ruths, W. Chiu, T. Ju

Electron cryo-microscopy (cryo-EM) has played an increasingly important role in elucidating the structure and function of macromolecular assemblies in near native solution conditions. Typically, however, only non-atomic resolution reconstructions have been obtained for these large complexes, necessitating computational tools for integrating and extracting structural details. With recent advances in cryo-EM, maps at near-atomic resolutions have been achieved for several macromolecular assemblies from which models have been manually constructed. In this work, we describe a new interactive modeling toolkit called Gorgon targeted at intermediate to near-atomic resolution density maps (10-3.5A), particularly from cryo-EM. Gorgon's de novo modeling procedure couples sequence-based secondary structure prediction with feature detection and geometric modeling techniques to generate initial protein backbone models. Beyond model building, Gorgon is an extensible interactive visualization platform with a variety of computational tools for annotating a wide variety of 3D volumes. Examples from cryo-EM maps of Rotavirus and Rice Dwarf Virus are used to demonstrate its applicability to modeling protein structure.
Landmark/Image-based Deformable Registration of Gene Expression Data
IEEE Computer Vision and Pattern Recognition (CVPR'11), 1089-1096 (Paper)
U. Kurkure, Y.-H. Le, N. Paragios, J. Carson, T. Ju, I. Kakadiaris

Analysis of gene expression patterns in brain images obtained from high-throughput in situ hybridization requires accurate and consistent annotations of anatomical regions/subregions. Such annotations are obtained by mapping an anatomical atlas onto the gene expression images through intensity- and/or landmark-based registration methods or deformable model-based segmentation methods. Due to the complex appearance of the gene expression images, these approaches require a pre-processing step to determine landmark correspondences in order to incorporate landmark-based geometric constraints. In this paper, we propose a novel method for landmark-constrained, intensity-based registration without determining landmark correspondences a priori. The proposed method performs dense image registration and identifies the landmark correspondences, simultaneously, using a single higher-order Markov Random Field model. In addition, a machine learning technique is used to improve the discriminating properties of local descriptors for landmark matching by projecting them in a Hamming space of lower dimension. We qualitatively show that our method achieves promising results and also compares well, quantitatively, with the expert's annotations, outperforming previous methods.
A semi-automated approach for artifact removal in serial tissue cryosections
Journal of Microscopy, 241(2):200-206
L. Kindle, I. Kakadiaris, T. Ju, J. Carson

Thinly sliced serial tissue sections of an organ can be imaged using optical microscopy and then reconstructed into three dimensional datasets with a resolution detailing individual cells. When the tissue sections are first subjected to in situ hybridization or immunohistochemistry, these datasets can be analyzed for changes in gene expression and gene products. Such spatial information is important for understanding the functional effects of experimental or environmental challenges to the organism. However, a critical step in processing these 3D datasets is mitigating artifacts and defects that occur to the tissue during the sectioning process. Here we describe a new method for detecting and addressing such artifacts including dust particles, air bubbles, and tears.
Volumetric Quantitative Computed Tomography Measurement Precision for Volumes and Densities of Tarsal and Metatarsal Bones
Journal of Clinical Densitometry, 14(3):313-320 (Paper Link)
Paul Commean, Jared Kennedy, Karen Bahow, Charles Hildebolt, Lu Liu, Kirk Smith, Mary Hastings, Tao Ju, Fred Prior, David Sinacore

Diabetic foot diseases, such as ulcerations, infections, and neuropathic (Charcot's) arthropathy, are major complications of diabetes mellitus (DM) and peripheral neuropathy (PN) and may cause osteolysis (bone loss) in foot bones. The purposes of our study were to make computed tomography (CT) measurements of foot-bone volumes and densities and to determine measurement precision (percent coefficients of variation for root-mean-square standard deviations) and least significant changes (LSCs) in these percentages that could be considered biologically real with 95% confidence. Our study shows that volumetric quantitative CT provides precise measurements of volume and BMD for metatarsal and tarsal bones, where diabetic foot diseases commonly occur.
2010
A simple and robust thinning algorithm on cell complexes
Computer Graphics Forum (Proceedings of Pacific Graphics 2010), 29(7):2253-2260 (Paper, Video, Project)
L. Liu, E. Chambers, D. Letscher, T. Ju

Thinning is a commonly used approach for computing skeleton descriptors. Traditional thinning algorithms often have a simple, iterative structure, yet producing skeletons that are overly sensitive to boundary perturbations. We present a novel thinning algorithm, operating on objects represented as cell complexes, that preserves the simplicity of typical thinning algorithms but generates skeletons that more robustly capture global shape features. Our key insight is formulating a skeleton significance measure, called medial persistence, which identify skeleton geometry at various dimensions (e.g., curves or surfaces) that represent object parts with different anisotropic elongations (e.g., tubes or plates). The measure is generally defined in any dimensions, and can be easily computed using a single thinning pass. Guided by medial persistence, our algorithm produces a family of topology and shape preserving skeletons whose shape and composition can be flexible controlled by desired level of medial persistence.
Semi-isometric registration of line features for flexible fitting of protein structures
Computer Graphics Forum (Proceedings of Pacific Graphics 2010), 29(7):2243-2252 (Paper)
S. Abeysinghe, M. Baker, W. Chiu, T. Ju

In this paper, we study a registration problem that is motivated by a practical biology problem - fitting protein structures to low-resolution density maps. We consider registration between two sets of lines features (e.g., helices in the proteins) that have undergone not a single, but multiple isometric transformations (e.g., hinge-motions). The problem is further complicated by the presence of symmetry in each set. We formulate the problem as a clique-search problem in a product graph, and propose a heuristic solution that includes a fast clique-finding algorithm unique to the structure of this graph. When tested on a suite of real protein structures, the algorithm achieved high accuracy even for very large inputs containing hundreds of helices.
Instant Propagation of Sparse Edits on Images and Videos
Computer Graphics Forum (Proceedings of Pacific Graphics 2010), 29(7):2049-2054 (Paper)
Y. Li, T. Ju, S-M. Hu

The ability to quickly and intuitively edit digital contents has become increasingly important in our everyday life. We propose a novel method for propagating a sparse set of user edits (e.g., changes in color, brightness, contrast, etc.) expressed as casual strokes to nearby regions in an image or video with similar appearances. Existing methods for edit propagation are typically based on optimization, whose computational cost can be prohibitive for large inputs. We re-formulate propagation as a function interpolation problem in a high-dimensional space, which we solve very efficiently using radial basis functions. While simple to implement, our method significantly improves the speed and space cost of existing methods, and provides instant feedback of propagation results even on large images and videos.
Polygonizing Extremal Surfaces with Manifold Guarantees
Proceedings of Symposium of Solid and Physical Modeling (SPM) 2010, 189-194 (Paper)
R-S. Li, L. Liu, L. Phan, S. Abeysinghe, C. Grimm, T. Ju

Extremal surfaces are a class of implicit surfaces that have been found useful in a variety of geometry reconstruction applications. Compared to iso-surfaces, extremal surfaces are particularly challenging to construct in part due to the presence of boundaries and the lack of a consistent orientation. We present a novel, grid-based algorithm for constructing polygonal approximations of extremal surfaces that may be open or unorientable. The algorithm is simple to implement and applicable to both uniform and adaptive grid structures. More importantly, the resulting discrete surface preserves the structural property of the extremal surface in a grid-independent manner. The algorithm is applied to extract ridge surfaces from intensity volumes and reconstruct surfaces from point set with unoriented normals.
Piecewise Tri-linear Contouring for Multi-Material Volumes
Proceedings of Geometry Modeling and Processing (GMP) 2010, 43-56 (Paper)
P. Feng, T. Ju, J. Warren

The ability to model objects composed of multiple materials has become increasingly more demanded in scientific applications. The visualization of a discrete multi-material volume often suffers from voxelization of the boundary between materials. We propose a contouring method that can be efficiently implemented on the GPU to reduce the artifacts and jaggedness along the material boundaries. Our method extends naturally from the standard tri-linear contouring in a signed volume, and further provides sub-voxel accuracy for representing three or more materials.
Subdivision meshes for organizing spatial biomedical data
Method, 50(2):70-76 (Paper)
T. Ju, J. Carson, L. Liu, J. Warren, M. Bello, I. Kakadiaris

As biomedical images and volumes are being collected at an increasing speed, there is a growing demand for efficient means to organize spatial information for comparative analysis. In many scenarios, such as determining gene expression patterns by in situ hybridization, the images are collected from multiple subjects over a common anatomical region, such as the brain. A fundamental challenge in comparing spatial data from different images is how to account for the shape variations among subjects, which make direct image-to-image comparisons meaningless. In this paper, we describe subdivision meshes as a geometric means to efficiently organize 2D images and 3D volumes collected from different subjects for comparison. The key advantages of a subdivision mesh for this purpose are its light-weight geometric structure and its explicit modeling of anatomical boundaries, which enable efficient and accurate registration. The multi-resolution structure of a subdivision mesh also allows development of fast comparison algorithms among registered images and volumes.
Automated pipeline for atlas-based annotation of gene expression patterns: Application to postnatal day 7 mouse brain
Method, 50(2):85-95 (Paper)
J. Carson, T. Ju, M. Bello, C. Thaller, J. Warren, I. A. Kakadiaris, W. Chiu, G. Eichele

Massive amounts of image data have been collected and continue to be generated for representing cellular gene expression throughout the mouse brain. Critical to exploiting this key effort of the post-genomic era is the ability to place these data into a common spatial reference that enables rapid interactive queries, analysis, data sharing, and visualization. In this paper, we present a set of automated protocols for generating and annotating gene expression patterns suitable for the establishment of a database. The steps include imaging tissue slices, detecting cellular gene expression levels, spatial registration with an atlas, and textual annotation. Using high-throughput in situ hybridization to generate serial sets of tissues displaying gene expression, this process was applied toward the establishment of a database representing over 200 genes in the postnatal day 7 mouse brain. These data using this protocol are now well-suited for interactive comparisons, analysis, queries, and visualization.
2009
Feature-Aligned Shape Texturing
ACM Transactions on Graphics (Proceedings of Siggraph Asia 2009), 28(5): article 108 (Paper, Project)
K. Xu, D. Cohen-Or, T. Ju, L-G. Liu, H. Zhang, S-Z. Zhou, Y-S. Xiong

The essence of a 3D shape can often be well captured by its salient feature curves. In this paper, we explore the use of salient curves in synthesizing intuitive, shape-revealing textures on surfaces. Our texture 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. We have observed that textures synthesized by these principles not only fit naturally to the surface geometry, but also visually reveal, even reinforce, the shape's essential characteristics. We call these feature-aligned shape texturing. Our technique is fully automatic, and introduces two novel technical components in vector-field- guided texture synthesis: an algorithm that orients the salient curves on a surface for constrained vector field generation, and a feature-to-feature texture optimization.
Efficient Affinity-based Edit Propagation using K-D Tree
ACM Transactions on Graphics (Proceedings of Siggraph Asia 2009), 28(5): article 118 (Paper)
K. Xu, Y. Li, T. Ju, S-M. Hu, T-Q. Liu

Image/video editing by strokes has become increasingly popular due to the ease of interaction. Propagating the user inputs to the rest of the image/video, however, is often time and memory consuming especially for large data. We propose here an efficient scheme that allows affinity-based edit propagation to be computed on data containing tens of millions of pixels at interactive rate (in matter of seconds). The key in our scheme is a novel means for approximately solving the optimization problem involved in edit propagation, using adaptive clustering in a high-dimensional, affinity space. Our approximation significantly reduces the cost of existing affinity-based propagation methods while maintaining visual fidelity, and enables interactive stroke-based editing even on high resolution images and long video sequences using commodity computers.
Compatible quadrangulation by sketching
Computer Animation And Virtual Worlds (Proceedings of CASA'09), 23(2-3):101-109 (Paper, Video)
C.-Y. Yao, H.-K. Chu, T. Ju and T.-Y. Lee.

Mesh quadrangulation has received increasing attention in the past decade. While previous works have mostly focused on producing a high quality quad mesh of a single model, the connectivity of the quadrangulation is typically difficult to control and varies among models even with similar shapes. In this paper, we propose a novel interactive framework for quadrangulating a set of models collectively with compatible connectivity. Furthermore, we demonstrate its application to 3D mesh morphing. In our approach, the user interactively sketches a skeleton within each model, and our method automatically computes compatible base domains for all models from these skeletons, on which the models are parameterized. With this novel parameterization, it is very easy to generate a pleasing and smooth 3D morphing sequence among these compatible models. The method yields quadrangulation with comparable quality to existing approaches, but greatly simplifies compatible re-meshing among a group of topologically equivalent models, in particular characters and animals models, with direct applications in shape blending and morphing.
VolumeViewer: An Interactive Tool for Fitting Surfaces to Volume Data
Sixth Eurographics Workshop on Sketch Based Interfaces and Modeling, 141-148 (Paper, Video, Project)
R. Sowell, L. Liu, T. Ju, C. Grimm, C. Abraham, G. Gokhroo, D. Low.

Recent advances in surface reconstruction algorithms allow surfaces to be built from contours lying on non-parallel planes. Such algorithms allow users to construct surfaces of similar quality more efficiently by using a small set of oblique contours, rather than many parallel contours. However, current medical imaging systems do not provide tools for sketching contours on oblique planes. In this paper, we take the first steps towards bridging the gap between the new surface reconstruction technologies and putting those methods to use in practice. We develop a novel interface for modeling surfaces from volume data by allowing the user to sketch contours on arbitrarily oriented cross-sections of the volume, and we examine the users' ability to contour the same structures using oblique cross-sections with similar consistency as they can using parallel cross-sections. We measure the inter-observer and intra-observer variability of trained physicians contouring on oblique cross-sections of real patient data as compared to the traditional parallel cross-sections, and show that the variation is much higher for oblique contouring. We then show that this variability can be greatly reduced by integrating a collection of training images into the interface.
Interactive skeletonization of intensity volumes
The Visual Computer (Proceedings of CGI'09), 25(5-7):627-635 (Paper, Video, Download)
S. Abeysinghe, T. Ju.

We present an interactive approach for identifying skeletons (i.e. centerlines) in intensity volumes, such as those produced by biomedical imaging. While skeletons are very useful for a range of image analysis tasks, it is extremely difficult to obtain skeletons with correct connectivity and shape from noisy inputs using automatic skeletonization methods. In this paper we explore how easy-to-supply user inputs, such as simple mouse clicking and scribbling, can guide the creation of satisfactory skeletons. Our contributions include formulating the task of drawing 3D centerlines given 2D user inputs as a constrained optimization problem, solving this problem on a discrete graph using a shortest-path algorithm, building a graphical interface for interactive skeletonization and testing it on a range of biomedical data.
Adaptive smooth surface fitting with manifolds
The Visual Computer (Proceedings of CGI'09), 25(5-7):589-597 (Paper)
C. Grimm, T. Ju, L. Phan, J. Hughes.

We present a smooth, everywhere C^k, analytic surface representation for closed surfaces of arbitrary topology. We demonstrate fitting this representation to meshes of varying resolutions and sampling quality. The fitting process is adaptive and provides controls for both the average and the maximum allowable error. The representation is suitable for applications which require consistent parameterizations across different surfaces.
Fixing Geometric Errors on Polygonal Models: A Survey
Journal of Computer Science and Technology, 24(1):19-29 (Paper)
T. Ju

Polygonal models are popular representations of 3D objects. The use of polygonal models in computational applications often requires a model to properly bound a 3D solid. That is, the polygonal model needs to be closed, manifold, and free of self-intersections. This paper surveys a sizeable literature for repairing models that do not satisfy this criteria, focusing on categorizing them by their methodology and capability. We hope to offer pointers to further readings for researchers and practitioners, and suggestions of promising directions for future research endeavors.

2008
Reusable Skinning Templates Using Cage-based Deformations
ACM Transactions on Graphics (Proceedings of Siggraph Asia 2008), 27(5):1-10 (Paper, Video)
T. Ju, Q.-Y. Zhou, M. van de Panne, D. Cohen-Or, U. Neumann

Character skinning determines how the shape of the surface geometry changes as a function of the pose of the underlying skeleton. In this paper we describe skinning templates, which define common deformation behaviors for common joint types. This abstraction allows skinning solutions to be shared and reused, and they allow a user to quickly explore many possible alternatives for the skinning behavior of a character. The skinning templates are implemented using cage-based deformations, which offer a flexible design space within which to develop reusable skinning behaviors. We demonstrate the interactive use of skinning templates to quickly explore alternate skinning behaviors for 3D models.
Interactive Separation of Segmented Bones in CT Volumes Using Graph Cut
Lecture Notes in Computer Science (Proceedings of MICCAI 2008), 5241:296-304 (Paper, Poster)
L. Liu, D. Raber, D. Nopachai, P. Commean, D. Sinacore, F. Prior, R. Pless, and T. Ju

We present a fast, interactive method for separating bones that have been collectively segmented from a CT volume. Given userprovided seed points, the method computes the separation as a multiway cut on a weighted graph constructed from the binary, segmented volume. By properly designing and weighting the graph, we show that the resulting cut can accurately be placed at bone-interfaces using only a small number of seed points even when the data is noisy. The method has been implemented with an interactive graphical interface, and used to separate the 12 human foot bones in 10 CT volumes. The interactive tool produced compatible result with a ground-truth separation, generated by a completely manual labelling procedure, while reducing the human interaction time from a mean of 2.4 hours per volume in manual labelling down to approximately 18 minutes.
Segmentation-free skeletonization of grayscale volumes for shape understanding.
IEEE International Conference on Shape Modeling and Applications 2008, pp. 63-71 (Paper)
S. Abeysinghe, M. Baker, W. Chiu, T. Ju

Medical imaging has produced a large number of volumetric images capturing biological structures in 3D. Computer-based understanding of these structures can often benefit from the knowledge of shape components, particularly rod-like and plate-like parts, in such volumes. Previously, skeletons have been a common tool for identifying these shape components in a solid object. However, obtaining skeletons of a grayscale volume poses new challenges due to the lack of a clear boundary between object and background. In this paper, we present a new skeletonization algorithm on grayscale volumes typical to medical imaging (e.g., MRI, CT and EM scans), for the purpose of identifying shape components. Our algorithm does not require an explicit segmentation of the volume into object and background, and is capable of producing skeletal curves and surfaces that lie centered at rod-shaped and plate-shaped parts in the grayscale volume. Our method is demonstrated on both synthetic and medical data.
Surface Reconstruction From Non-parallel Curve Networks.
Computer Graphics Forum (Proceedings of Eurographics 2008), 27(2):155-163 (Paper, Project)
L. Liu, C. Bajaj, J.O. Deasy, D.A. Low, T. Ju

Building surfaces from cross-section curves has wide applications including bio-medical modeling. Previous work in this area has mostly focused on connecting simple closed curves on parallel cross-sections. Here we consider the more general problem where input data may lie on non-parallel cross-sections and consist of curve networks that represent the segmentation of the underlying object by different material or tissue types (e.g., skin, muscle, bone, etc.) on each cross-section. The desired output is a surface network that models both the exterior surface and the internal partitioning of the object. We introduce an algorithm that is capable of handling curve networks of arbitrary shape and topology on cross-section planes with arbitrary orientations. Our algorithm is simple to implement and is guaranteed to produce a closed surface network that interpolates the curve network on each cross-section. Our method is demonstrated on both synthetic and bio-medical examples.
Geometric interpretation of the Gamma dose distribution comparison technique: interpolation-free calculation
Medical Physics, 35(3):879-887 (Paper, Program, Code)
T. Ju, T. Simpson, J.O. Deasy, D.A. Low

The Gamma dose distribution comparison tool has been used by numerous investigators to quantitatively compare multidimensional dose distributions. The tool simultaneously evaluates the dose difference and distance-to-agreement of two dose distributions. One of the weaknesses of the tool is that the comparison requires one of the dose distributions to have a relatively high spatial resolution, due to the fact that the Gamma tool measures the closest pixel in one of the dose distributions with individual pixels of another, and this closest distance can not be accurately measured unless the pixels are finely spaced, which requires time-consuming interpolation. We provide a reinterpretation of the Gamma distance as the geometric distance between two 3D or 4D meshes representing the two 2D or 3D dose distributions. The geometric approach avoids the drastic growth of calculation time incurred by interpolation and makes the Gamma tool more practical and more accurate.
Shape modeling and matching in identifying 3D protein structures.
Computer Aided-Design, 40:708-720 (Paper)
S. Abeysinghe, T. Ju, M. L. Baker, W. Chiu

In this paper, we describe a novel geometric approach in the process of recovering 3D protein structures from scalar volumes. The input to our method is a sequence of alpha-helices that make up a protein, and a low-resolution protein density volume where possible locations of alpha-helices have been detected. Our task is to identify the correspondence between the two sets of helices, which will shed light on how the protein folds in space. The central theme of our approach is to cast the correspondence problem as that of shape matching between the 3D volume and the 1D sequence. We model both shapes as attributed relational graphs, and formulate a constrained inexact graph matching problem. To compute the matching, we developed an optimal algorithm based on the A*-search with several choices of heuristic functions. As demonstrated in a suite of synthetic and authentic inputs, the shape-modeling approach is capable of identifying helix correspondences in noise-abundant volumes at high accuracy with minimal or no user intervention.
Tarsal and Metatarsal Bone Mineral Density Measurement using Volumetric Quantitative Computed Tomography.
Journal of Digital Imaging, 22(5): 492-502 (Paper)
P. K. Commean, T. Ju, L. Liu, D. R. Sinacore, M. K. Hastings, M. J. Mueller

A new method for measuring bone mineral density (BMD) of the tarsal and metatarsals is described using volumetric quantitative computed tomography (VQCT) in conjunction with geometric subdivision in subjects with diabetes mellitus and peripheral neuropathy. In addition to whole-bone segmentation and measurement, we performed atlas-based partitioning of sub-regions within the second metatarsal for all subjects, from which the volumes and BMDs were obtained for each sub-region. The sub-region measurement BMD errors (root mean square coefficient of variation) within the shaft, proximal end and distal end were shown to vary by approximately 1% between the two scans of each subject. These methods can provide an important outcome measure for clinical research trials investigating the effects of interventions, aging or disease progression on bone loss or gain in individual foot bones.
2007
Editing The Topology of 3D Models by Sketching.
ACM Transactions on Graphics (Proceedings of SIGGRAPH 2007), 26(3): 42 (Paper, Video (33MB), Project)
T. Ju, Q-Y Zhou, S-M Hu

We present a method for modifying the topology of a 3D model with user control. The heart of our method is a guided topology editing algorithm. Given a source model and a user-provided target shape, the algorithm modifies the source so that the resulting model is topologically consistent with the target. Our algorithm permits removing or adding various topological features (e.g., handles, cavities and islands) in a common framework and ensures that each topological change is made by minimal modification to the source model. To create the target shape, we have also designed a convenient 2D sketching interface for drawing 3D line skeletons. As demonstrated in a suite of examples, the use of sketching allows more accurate removal of topological artifacts than previous methods, and enables creative designs with specific topological goals.
Real-time homogenous translucent material editing.
Computer Graphics Forum (Proceedings of Eurographics 2007), 26(3):545-552 (Paper)
K. Xu, Y. Gao, Y. Li, T. Ju, S.-M. Hu

This paper presents a novel method for real-time homogenous translucent material editing under fixed illumination. We consider the complete analytic BSSRDF model proposed by Jensen et al. [JMLH01], including both multiple scattering and single scattering. Our method allows the user to adjust the analytic parameters of BSSRDF and provides high-quality, real-time rendering feedback. Inspired by recently developed Precomputed Radiance Transfer (PRT) techniques, we approximate both the multiple scattering diffuse reflectance function and the single scattering exponential attenuation function in the analytic model using basis functions, so that re-computing the outgoing radiance at each vertex as parameters change reduces to simple dot products. In addition, using a non-uniform piecewise polynomial basis, we are able to achieve smaller approximation error than using bases adopted in previous PRT-based works, such as spherical harmonics and wavelets. Using hardware acceleration, we demonstrate that our system generates images comparable to [JMLH01] at real-time frame-rates.
Shape modeling and matching in identifying protein structure from low-resolution images.
ACM Symposium on Solid and Physical Modeling 2007 (Paper,Talk)
S. Abeysinghe, T. Ju, M. Baker, W. Chiu

In this paper, we describe a novel, shape-modeling approach to recovering 3D protein structures from volumetric images. The input to our method is a sequence of a-helices that make up a protein, and a low-resolution volumetric image of the protein where possible locations of a-helices have been detected. Our task is to identify the correspondence between the two sets of helices, which will shed light on how the protein folds in space. The central theme of our approach is to cast the correspondence problem as that of shape matching between the 3D volume and the 1D sequence. We model both the shapes as attributed relational graphs, and formulate a constrained inexact graph matching problem. To compute the matching, we developed an optimal algorithm based on the A*-search with several choices of heuristic functions. As demonstrated in a suite of real protein data, the shape-modeling approach is capable of correctly identifying helix correspondences in noise-abundant volumes with minimal or no user intervention.
Computing a family of skeletons of volumetric models for shape description
Computer-Aided Design, 39(5):352-360 (Paper)
T. Ju, M. Baker, W. Chiu

Skeletons are important shape descriptors in object representation and recognition. Typically, skeletons of volumetric models are computed using iterative thinning. However, traditional thinning methods often generate skeletons with complex structures that are unsuitable for shape description, and appropriate pruning methods are lacking. In this paper, we present a new method for computing skeletons of volumetric models by alternating thinning and a novel skeleton pruning routine. Our method creates a family of skeletons parameterized by two user-specified numbers that determine respectively the size of curve and surface features on the skeleton. As demonstrated on both real-world models and protein images in bio-medical research, our method generates skeletons with simple and meaningful structures that are particularly suitable for describing cylindrical and plate-like shapes.
Learning-based Segmentation Framework for Tissue Images Containing Gene Expression Data
IEEE Transactions on Medical Imaging, 26(5):728-744 (Paper)
M. Bello, T. Ju, J. Carson, J. Warren, W. Chiu, I.A. Kakadiaris

Associating specific gene activity with functional locations in the brain results in a greater understanding of the role of the gene. To perform such an association for the over 20,000 genes in the mammalian genome, reliable automated methods that characterize the distribution of gene expression in relation to a standard anatomical model are required. In this paper, we propose a new automatic method that results in the segmentation of gene expression images into distinct anatomical regions in which the expression can be quantified and compared with other images. Our contribution is a novel hybrid atlas that utilizes a statistical shape model based on a subdivision mesh, texture differentiation at region boundaries, and features of anatomical landmarks to delineate boundaries of anatomical regions in gene expression images. This atlas, which provides a common coordinate system for internal brain data, is being used to create a searchable database of gene expression patterns in the adult mouse brain. Our framework annotates the images about four times faster and has achieved a median spatial overlap of up to 0.92 compared with expert segmentation in 64 images tested. This tool is intended to help scientists interpret large-scale gene expression patterns more efficiently.
Topology Repair of Solid Models Using Skeletons
IEEE Transactions on Visualization and Computer Graphics, 13(4):675-685 (Paper, Project)
Q-Y Zhou, T. Ju, S-M. Hu

We present a method for repairing topological errors on solid models in the form of small surface handles, which often arise from surface reconstruction algorithms. We utilize a skeleton representation that offers a new mechanism for identifying and measuring handles. Our method presents two unique advantages over previous approaches. First, handle removal is guaranteed not to introduce invalid geometry or additional handles. Second, by using an adaptive grid structure, our method is capable of processing huge models efficiently at high resolutions.
A general geometric construction of coordinates in a convex simplicial polytope
Computer Aided Geometric Design, 24(3): 161-178 (Paper, Talk)
T. Ju, P. Liepa, J. Warren

Barycentric coordinates are a fundamental concept in computer graphics and geometric modeling. We extend the geometric construction of Floater's mean value coordinates to a general form that is capable of constructing a family of coordinates in a convex 2D polygon, 3D triangular polyhedron, or a higher-dimensional simplicial polytope. This family unifies previously known coordinates, including Wachspress coordinates, mean value coordinates and discrete harmonic coordinates, in a simple geometric framework. Using the construction, we are able to create a new set of coordinates in 3D and higher dimensions and study its relation with known coordinates. We show that our general construction is complete, that is, the resulting family includes all possible coordinates in any convex simplicial polytope.
Manifold Dual Contouring
IEEE Transactions on Visualization and Computer Graphics, 13(3):610-619 (Paper)
S. Schaefer, T. Ju, J. Warren

Dual Contouring is a feature-preserving iso-surfacing method that extracts crack-free surfaces from both uniform and adaptive octree grids. We present an extension of Dual Contouring that further guarantees that the mesh generated is a manifold even under adaptive simplification. Our main contribution is an octree-based, topology-preserving vertex clustering algorithm for adaptive contouring. The contoured surface generated by our method contains only manifold vertices and edges, preserves sharp features, and possesses much better adaptivity than those generated by other iso-surfacing methods under topologically safe simplification.
Identification of Secondary Structure Elements in Intermediate Resolution Density Maps
Structure, 15(1):7-19, 2007 (Paper)
M. L. Baker, T. Ju, W. Chiu

An increasing number of structural studies of large macromolecular complexes, both in X-ray crystallography and electron cryomicroscopy, have resulted in intermediate resolution (5-10 A) structures. Despite being limited in resolution, significant structural and functional information may be extractable from these maps. To aid in the analysis and annotation of these complexes, we have developed SSEhunter, a tool for the quantitative detection of alpha-helices and beta-sheets. Based on density skeletonization, local geometry calculations and a template-based search, SSEhunter has been tested and validated on a variety of simulated and authentic subnanometer resolution density maps. The result is a robust, user-friendly approach that allows users to quickly visualize, assess and annotate intermediate resolution density maps. Beyond secondary structure element identification, the skeletonization algorithm in SSEhunter provides secondary structure topology, potentially useful in leading to structural models of individual molecular components directly from the density.
2006
A Unified, Integral Construction For Coordinates Over Closed Curves
Computer-Aided Geometric Design, 24(8-9):481-493 (Paper)
S. Schaefer, T. Ju and J. Warren

We propose a simple generalization of Shephard's interpolation to piecewise smooth, convex closed curves that yields a family of boundary interpolants with linear precision. Two instances of this family reduce to previously known interpolants: one based on a generalization of Wachspress coordinates to smooth curves and the other an integral version of mean value coordinates for smooth curves. A third instance of this family yields a previously unknown generalization of discrete harmonic coordinates to smooth curves. For closed, piecewise linear curves, we prove that our interpolant reproduces a general family of barycentric coordinates considered by Floater, Hormann and Kos that includes Wachspress coordinates, mean value coordinates and discrete harmonic coordinates.
Probing 3'-ssDNA Loop Formation in E. coli RecBCD/RecBC-DNA Complexes using Non-natural DNA: A Model for "Chi" Recognition Complexes
Journal of Molecular Biology, 362(1):26-43 (Paper)
C. Jason Wong, Rachel L. Rice, Nathan A. Baker, Tao Ju and Timothy M. Lohman

The equilibrium binding of E. coli RecBC and RecBCD helicases to duplex DNA ends containing varying lengths of polyethylene glycol (PEG) spacers within pre-formed 3'-single-stranded (ss) DNA ((dT)n) tails were studied. These studies were designed to test a previous proposal that the 3'-(dT)n tail can be looped out upon binding RecBC and RecBCD for 3'-ssDNA tails with n>=6 nucleotides. Equilibrium binding of protein to unlabeled DNA substrates with ends containing PEG-substituted 3'-ssDNA tails was examined by competition with a Cy3-labeled reference DNA which undergoes a Cy3 fluorescence enhancement upon protein binding. We find that the binding affinities of both RecBC and RecBCD for a DNA end are unaffected upon substituting PEG for the ssDNA between the sixth and the final two nucleotides of the 3'-(dT)n tail. However, placing PEG at the end of the 3'-(dT)n tail increases the binding affinities to their maximum values (i.e. the same as binding constants for RecBC or RecBCD to a DNA end with only a 3'-(dT)6 tail). Equilibrium binding studies of a RecBC mutant containing a nuclease domain deletion, RecBC suggest that looping of the 3'-tail (when n>=6 nucleotides) occurs even in the absence of the RecB nuclease domain, the nuclease domain stabilizes such loop formation. Computer modeling of the RecBCD-DNA complexes suggests that the loop in the 3'-ssDNA tail may form at the RecB/RecC interface. Based on these results we suggest a model for how a loop in the 3'-ssDNA tail might form upon encounter of a "Chi" recognition sequence during unwinding of DNA by the RecBCD helicase.
Intersection-free Contouring on An Octree Grid
Proceedings of Pacific Graphics, 2006 (Paper, Code on Sourceforge)
T. Ju and T. Udeshi

A method for extracting intersection-free iso-surfaces from volumetric data with an octree structure is presented. Unlike contouring techniques designed for uniform grids (such as Marching Cubes), adaptive contouring methods (such as Dual Contouring) can and do often generate intersecting polygons. Our main contribution is a polygon generation algorithm that produces triangles enclosed in nonoverlapping volumes, which guarantees an intersection-free mesh. Like other adaptive contouring methods, this new method generates crack-free and feature-preserving surfaces on both uniform and octree grids. We demonstrate the method on both scanned objects and industrial models.
Computing a family of skeletons of volumetric models for shape description
Proceedings of Geometric Modeling and Processing 2006, pp. 235 - 247 (Paper,Talk)
T. Ju, M. Baker, and W. Chiu

Skeletons are important shape descriptors in object representation and recognition. Typically, skeletons of volumetric models are computed via an iterative thinning process. However, traditional thinning methods often generate skeletons with complex structures that are unsuitable for shape description, and appropriate pruning methods are lacking. In this paper, we present a new method for computing skeletons on volumes by alternating thinning and a novel skeleton pruning routine. Our method creates a family of skeletons parameterized by two user-specified numbers that determine respectively the size of curve and surface features on the skeleton. As demonstrated on both real-world models and medical images, our method generates skeletons with simple and meaningful structures that are particularly suitable for describing cylindrical and plate-like shapes.
3D Volume Reconstruction of a Mouse Brain from Histological Sections using Warp Filtering
Journal of Neuroscience Methods, 156(1-2):84-100 (Paper,Program)
T. Ju, J. Warren, J. Carson, M. Bello, I. Kakadiaris, W. Chiu, C. Thaller and G. Eichele

Sectioning tissues for optical microscopy often introduces upon the resulting sec- tions distortions that make 3d reconstruction di??cult. Here we present an automatic method for producing a smooth 3D volume from distorted 2D sections in the ab- sence of any undistorted references. The method is based on pairwise elastic image warps between successive tissue sections, which can be computed by 2D image reg- istration. Using a Gaussian ??lter, an average warp is computed for each section from the pairwise warps in a group of its neighboring sections. The average warps deform each section to match its neighboring sections, thus creating a smooth vol- ume where corresponding features on successive sections lie close to each other. The proposed method can be used with any existing 2D image registration method for 3D reconstruction. In particular, we present a novel image warping algorithm based on dynamic programming that extends Dynamic Time Warping in 1D speech recog- nition to compute pairwise warps between high-resolution 2D images. The warping algorithm e??ciently computes a restricted class of 2D local deformations that are characteristic between successive tissue sections. Finally, a validation framework is proposed and applied to evaluate the quality of reconstruction using both real sections and a synthetic volume.
2005
Building 3D surface networks from 2D curve networks with application to anatomical modeling
Proceedings of Pacific Graphics 2005, 21(8-10):764-773
The Visual Computer, (Paper)
T. Ju, J. Warren, J. Carson, G. Eichele, C. Thaller, W. Chiu, M. Bello and I. Kakadiaris

We present a novel method that automatically constructs a surface network from curve networks with arbitrary topology and partitioning an arbitrary number of materials. The surface network exactly interpolates the curve network on each plane and is guaranteed to be free of gaps or self-intersections. In addition, our method provides a flexible framework for user interaction so that the surface topology can be modified conveniently when necessary. As an application, we applied the method to build a high-resolution 3D model of the mouse brain from 2D anatomical boundaries defined on 350 tissue sections.
A Digital Atlas to Characterize the Mouse Brain Transcriptome
PLoS Computational Biology, 1(4): e41, 2005 (Paper)
J. Carson, T. Ju, H. Lu, C. Thaller, M. Xu, S. Pallas, M. C. Crair, J. Warren, W. Chiu and G. Eichele

Here we have developed a computational method for annotating gene expression patterns in the context of a digital atlas to facilitate custom user-queries and comparisons of this type of data. This procedure has been applied to 200 genes in the postnatal mouse brain. As an illustration of utility, we identify candidate genes that may be related to Parkinson's disease by using the expression of a dopamine transporter in the substantia nigra as a search query pattern. In addition, we discover that transcription factor Rorb is down-regulated in the barrelless mutant relative to control mice by quantitative comparison of expression patterns in layer IV somatosensory cortex.
Hybrid Segmentation Framework for Tissue Images Containing Gene Expression Data
Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), p254-261, 2005 (Paper)
M. Bello, T. Ju, J. Warren, J. Carson, W. Chiu, C. Thaller, G. Eichele and I. Kakadiaris

In this work, we propose a new automatic method that results in the segmentation of gene expression images into distinct anatomical regions in which the expression can be quantified and compared with other images. Our method utilizes models of shape of training images, texture differentiation at region boundaries, and features of anatomical landmarks to deform a subdivision mesh-based atlas to fit gene expression images.
Geometric Construction of Coordinates for Convex Polyhedra using Polar Duals
Proceedings of Eurographics Symposium on Geometry Processing, p181-186, 2005 (Paper)
T. Ju, S. Schaefer, J. Warren, M.Desbrun

A fundamental problem in geometry processing is that of expressing a point inside a convex polyhedron as a combination of the vertices of the polyhedron. In this paper, we present a uned geometric construction for building these weighted combinations using the notion of polar duals. We show that our method yields a simple geometric construction for Wachspress's barycentric coordinates, as well as for constructing Colin de Verdire matrices from convex polyhedra, critical step in Lovasz's method with applications to parameterizations.
Mean value coordinates for closed triangular meshes
Proceedings of ACM SIGGRAPH, 2005
ACM Transactions on Graphics, 24(3):561-566 (Paper)
T. Ju, S. Schaefer, J. Warren

In this paper, we generalize mean value coordinates from closed 2D polygons to closed triangular meshes. Given such a mesh P, we show that these coordinates are continuous everywhere and smooth on the interior of P. The coordinates are linear on the triangles of P and can reproduce linear functions on the interior of P. To illustrate their usefulness, we conclude by considering several interesting applications including constructing volumetric textures and surface deformation.


2004
Robust Repair of Polygonal Models
Proceedings of ACM SIGGRAPH, 2004
ACM Transactions on Graphics, 23(3):888-895 (Paper, Slides, Program)
Tao Ju

We present a robust method for repairing arbitrary polygon models. The method is guaranteed to produce a closed surface that partitions the space into disjoint internal and external volumes. Our novel algorithm can efficiently process large models containing millions of polygons and is capable of reproducing sharp features in the original geometry.
Automated Characterization of Gene Expression Patterns with an Atlas of the Mouse Brain
Proceedings of IEEE International Conference of the Engineering in Medicine and Biology Society (EMBS), p2917-2920, 2004 (Paper)
J. P. Carson, T. Ju, C. Thaller, J. Warren, M. Bello, I. Kakadiaris, W. Chiu, G. Eichele

A spatio-temporal map of gene activity in the brain would be an important contribution to the understanding of brain development, disease, and function. Such a resource is now possible using high-throughput in situ hybridization, a method for transcriptome-wide acquisition of cellular resolution gene expression patterns in serial tissue sections. However, querying an enormous quantity of image data requires computational methods for describing and organizing gene expression patterns in a consistent manner. In addressing this, we have developed procedures for automated annotation of gene expression patterns in the postnatal mouse brain.
Landmark-driven, Atlas-based Segmentation of Mouse Brain Tissue Images Containing Gene Expression Data
Proceedings of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), p192-199, 2004 (Paper)
Ioannis A. Kakadiaris, Musodiq Bello, Shiva Arunachalam, Wei Kang, Tao Ju, Joe Warren, James Carson, Wah Chiu, Christina Thaller, and Gregor Eichele

In this paper, we present an anatomical landmark detection method that has been incorporated into an atlasbased segmentation. The addition of this technique significantly increases the accuracy of automated atlas-deformation. The resulting large-scale annotation will help scientists interpret gene expression patterns more rapidly and accurately.
Turtle Geometry in Computer Graphics and Computer Aided Design
Computer-Aided Design, 36(14): 1471-1482, 2004 (Paper)
Ron Goldman, Scott Schaefer, and Tao Ju

LOGO is a programming language incorporating turtle graphics, originally devised for teaching computing to young children in elementary and middle schools. Here we advocate the use of LOGO to help introduce some of the basic concepts of computer graphics and computer aided design to undergraduate and graduate students in colleges and universities. We shall show how to motivate affine coordinates and affine transformations, fractal curves and iterated function systems, relaxation methods and subdivision schemes from elementary notions in turtle geometry and turtle programming.
Recursive Turtle Programs and Iterated Affine Transformations
Computer and Graphics, 28(6): 991-1004, 2004. (Paper)
Tao Ju, Scott Schaefer and Ron Goldman.

Recursive turtle programs (RTP) and iterated affine transformations (IAT) are two popular methods for generating fractals. We show that these two models are equivalent in their expressive power. Conversion algorithms in both directions are presented explicitly from the structure of the RTP and the affine transformations in the IAT.
2003
A geometry database for gene expression data
Proceedings of Eurographics Symposium on Geomtry Processing, 2003. (Paper, Slides)
Tao Ju, Joe Warren, Gregor Eichele, Christina Thaller, Wah Chiu and James Carson

In this paper, we describe the structure of a geometric database for the mouse brain that allows biologists to organize and search gene expression data in the mouse brain. The central component of this database is a standard atlas, represented as a subdivision mesh, that explicitly partitions the mouse brain into key anatomical subregions. Due to this partitioning, user queries comparing expression data between various genes can be restricted to anatomical subregions without difficulty while the multi-resolution structure of the subdivision mesh allows these queries to be processed efficiently. The database and searching tools are available at www.geneatlas.org.
Morphing of rational b-spline curves and surfaces using mass distributions
Proceedings of Eurographics, short papers, 2003. (Paper, Slides)
Tao Ju and Ron Goldman.

A rational B-spline curve or surface is a collection of points associated with a mass (weight) distribution. These mass distributions can be used to exert local control over the morph between two rational B-spline curves or surfaces. Here we propose a technique for designing customized morphs by attaching appropriate mass distributions to target B-spline curves and surfaces. We also develop a user interface for this morphing method that is easy to use and requires no knowledge of B-splines on the part of the user.
Convex Contouring on Volumetric Data
The Visual Computer, 19: 513-525, 2003. (Paper, Slides)
Tao Ju, Scott Schaefer, Joe Warren.

In this paper we present a fast, table-driven isosurface extraction technique on volumetric data. Unlike Marching Cubes or other cell-based algorithms, the proposed polygonization generates convex negative space inside individual cells, enabling fast collision detection on the triangulated isosurface. In our implementation, we are able to perform over 2 million point classifications per second. The algorithm is driven by an automatically constructed look-up table that stores compact decision trees by sign configurations. Using the same technique, we can perform fast, crack-free multi-resolution contouring on nested grids of volumetric data.
2002
Dual Contouring on Hermite Data
Proceedings of ACM SIGGRAPH, 2002. (Paper, Code on Sourceforge)
Tao Ju, Frank Losasso, Scott Schaefer and Joe Warren

This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (i.e; exact intersection points and normals). We extend this contouring method to the case of multi-signed functions and demonstrate how to model textured contours using multi-signed functions. Using a new, numerically stable representation for quadratic error functions, we develop an octreebased method for simplifying these contours and their textured regions. We next extend our contouring method to these simplified octrees.
2001
Modifying the shape of NURBS surfaces with geometric constraints
Computer Aided Design, 33(12): 903-912, 2001. (Paper)
Shi-Min Hu, You-Fu Li, Tao Ju and Xiang Zhu

NURBS surfaces are among the most commonly used parametric surfaces in CAGD and Computer Graphics. This paper investigates shape modification of NURBS surfaces with geometric constraints, such as point, normal vector, and curve constraints. Two new methods are presented by constrained optimization and energy minimization. The former is based on minimizing changes in control net of surfaces, whereas the latter is based on strain energy minimization. By these two methods, we change control points and weights of an original surface, such that the modified surface satisfies the given constraints. Comparison results and practical examples are also given.
Approximate merging of a pair of Bezier curves
Computer Aided Design, 33(2): 125-136, 2001. (Paper)
Hu Shi-Min, Tong Ruo-Feng, Ju Tao and Sun Jia-Guang

This paper deals with the merging problem, i.e. to approximate two adjacent Bezier curves by a single Bezier curve. A novel approach for approximate merging is introduced in the paper by using the constrained optimization method. The basic idea of this method is to find conditions for the precise merging of Bezier curves first, and then compute the constrained optimization solution by moving the control points. "Discrete" coefficient norm in L2 sense and "squared difference integral" norm are used in our method. Continuity at the endpoints of curves are considered in the merging process, and approximate merging with points constraints are also discussed. Further, it is shown that the degree elevation of original Bezier curves will reduce the merging error.

Comments or suggestions: taoju at cs.wustl.edu