Teaching Activities
I teach the following modules in the academic year 2015/16:
 CM1208 Maths for Computer Science
 CM2104 Computational Mathematics (shared with Prof. A. D. Marshall)
 CM2208 Scientific Computing (shared with Prof. A. D. Marshall)
 CMT205 Object Oriented Development with Java (shared with Prof. A. D. Marshall)
2016
Efficient and Flexible Deformation Representation for DataDriven Surface Modeling
ACM Transactions on Graphics, to appear. (to be presented at SIGGRAPH 2016)
Lin Gao, YuKun Lai, Dun Liang, ShuYu Chen and Shihong Xia
Effectively characterizing the behavior of deformable objects has wide applicability
but remains challenging. We present a new rotation invariant
deformation representation and a novel reconstruction algorithm to accurately
reconstruct the positions and local rotations simultaneously. Meshes
can be very efficiently reconstructed from our representation by matrix predecomposition,
while at the same time, hard or soft constraints can be flexibly
specified with only positions of handles needed. Our approach is thus
particularly suitable for constrained deformations guided by examples, providing
significant benefits over stateoftheart methods. Based on this, we
further propose novel datadriven approaches to mesh deformation and nonrigid
registration of deformable objects. Both problems are formulated consistently
as finding an optimized model in the shape space that satisfies
boundary constraints, either specified by the user, or according to the scan.
By effectively exploiting the knowledge in the shape space, our method
produces realistic deformation results in realtime and produces high quality
registrations from a template model to a single noisy scan captured using
a lowquality depth camera, outperforming stateoftheart methods.
Other Publications:
 S. Lin, Y. Chen, Y.K. Lai, R. R. Martin, Z.Q. Cheng. Fast Capture of Textured FullBody Avatar with RGBD Cameras, The Visual Computer, vol. 32(68), pp. 681691, 2016.
 S. Lin, Y.K. Lai, R. R. Martin, S. Jin, Z.Q. Cheng. Coloraware surface registration, Computers & Graphics, vol. 58, pp. 3142, 2016.
 K. Li, J. Yang, L. Liu, R. Boulic, YK. Lai, Y. Liu, Y. Li, E. Molla. SPA: Sparse Photorealistic Animation Using a Single RGBD Camera, IEEE Transactions on Circuits and Systems for Video Technology, to appear.
 F. M. Anuar, R. Setchi, Y.K. Lai. Semantic retrieval of trademarks based on conceptual similarity, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 46(2), pp. 220233, 2016. doi:10.1109/TSMC.2015.2421878
 A. Abdulmunem, Y.K. Lai, X. Sun. Saliency guided local and global descriptors for effective action recognition, Computational Visual Media, vol. 2(1), pp. 97106, 2016. doi:10.1007/s4109501600339
 L. Gao, S.Y. Chen, Y.K. Lai, S. Xia. Datadriven shape interpolation and morphing editing, Computer Graphics Forum, to appear.
2015
Active Exploration of Large 3D Model Repositories
IEEE Transactions on Visualization and Computer Graphics, vol. 21(12), pp. 13901402, 2015 (doi:10.1109/TVCG.2014.2369039).
Lin Gao, YanPei Cao, YuKun Lai, HaoZhi Huang, Leif Kobbelt, ShiMin Hu
With broader availability of largescale 3D model repositories, the need for efficient and effective exploration becomes
more and more urgent. Existing model retrieval techniques do not scale well with the size of the database since often a large
number of very similar objects are returned for a query, and the possibilities to refine the search are quite limited. We propose an
interactive approach where the user feeds an active learning procedure by labeling either entire models or parts of them as "like"
or "dislike" such that the system can automatically update an active set of recommended models. To provide an intuitive user
interface, candidate models are presented based on their estimated relevance for the current query. From the methodological
point of view, our main contribution is to exploit not only the similarity between a query and the database models but also the
similarities among the database models themselves. We achieve this by an offline preprocessing stage, where global and local
shape descriptors are computed for each model and a sparse distance metric is derived that can be evaluated efficiently even
for very large databases. We demonstrate the effectiveness of our method by interactively exploring a repository containing over
100K models.
Other Publications:
 Y. Xiao, L. Wan, C. S. Leung, Y.K. Lai, T.T. Wong. Optimizationbased gradient mesh colour transfer, Computer Graphics Forum, to appear, doi:10.1111/cgf.12524, 2015.
 J. Yang, K. Li, K. Li, Y.K. Lai. Sparse nonrigid registration of 3D shapes, Computer Graphics Forum, vol. 34(5), pp. 8999, doi:10.1111/cgf.12699, 2015.
 K. Chen, YK. Lai, S.M. Hu. 3D indoor scene modeling from RGBD data: a survey, Computational Visual Media, vol. 1(4), pp. 267278, 2015 (doi:10.1007/s410950150029x).
 P. L. Rosin, Y.K. Lai. Nonphotorealistic rendering of portraits, Proc. Computational Aesthetics, doi:10.2312/exp.20151189, 2015.
 C. Liu, P. L. Rosin, Y.K. Lai, W. Hu. Robust segmentation of historical parchment XMT images for virtual unrolling, Proc. Digital Heritage, 2015.
2014
Automatic Semantic Modeling of Indoor Scenes from Lowquality RGBD Data using Contextual Information
ACM Transactions on Graphics, vol. 33(6), 208:112, 2014 (SIGGRAPH Asia 2014). Project
Kang Chen, YuKun Lai, YuXin Wu, Ralph R. Martin, ShiMin Hu
We present a novel solution to automatic semantic modeling of indoor scenes from a sparse set of lowquality RGBD images. We exploit the knowledge in a scene database containing hundreds of indoor scenes and over 10,000 objects represented as manually segmented and labeled mesh models. Within a few seconds, we output a visually plausible 3D scene, based on models and parts from the database adapted to fit the input scans. Using lowquality RGBD data is challenging due to noise, low resolution, occlusion and missing depth information. Contextual relationships learned from the 3D database are used to constrain reconstruction, ensuring semantic compatibility between both object models and parts. Small objects and objects with incomplete depth information are difficult to recover reliably. We do so with a twostage approach: major objects are recognized first to provide a known scene structure. We then apply 2D contourbased model retrieval to recover the smaller objects. An evaluation on our own data and two public RGBD datasets shows that our approach can model typical realworld indoor scenes efficiently and robustly.
BiggerPicture: Datadriven Image Extrapolation Using Graph Matching
ACM Transactions on Graphics, vol. 33(6), 173:113, 2014 (SIGGRAPH Asia 2014). Project
Miao Wang, YuKun Lai, Yuan Liang, Ralph R. Martin, ShiMin Hu
Filling a small hole in an image with plausible content is well studied. Extrapolating an image to give a distinctly larger one is much more challenginga significant amount of additional content is needed which matches the original image, especially near its boundaries. We propose a datadriven approach to this problem. Given a source image, and the amount and direction(s) in which it is to be extrapolated, our system determines visually consistent content for the extrapolated regions using library images. As well as considering lowlevel matching, we achieve consistency at a higher level by using graph proxies for regions of source and library images. Treating images as graphs allows us to find candidates for image extrapolation in a feasible time. Consistency of subgraphs in source and library images is used to find good candidates for the additional content; these are then further filtered. Region boundary curves are aligned to ensure consistency where image parts are joined using a photomontage method. We demonstrate the power of our method in image editing applications.
Diffusion Pruning for Rapidly and Robustly Selecting Global Correspondences using Local Isometry
ACM Transactions on Graphics, vol. 33(1), Article No. 4, pp. 117, 2014.
Gary K.L. Tam, Ralph R. Martin, Paul L. Rosin and YuKun Lai
Finding correspondences between two surfaces is a fundamental operation in various applications in computer graphics and related fields. Candidate
correspondences can be found by matching local signatures, but as they only consider local geometry, many are globally inconsistent. We provide a novel
algorithm to prune a set of candidate correspondences to those most likely to be globally consistent. Our approach can handle articulated surfaces, and
ones related by a deformation which is globally nonisometric, provided that the deformation is locally approximately isometric. Our approach uses
an efficient diffusion framework, and only requires geodesic distance calculations in small neighbourhoods, unlike many existing techniques which
require computation of global geodesic distances. We demonstrate that, for typical examples, our approach provides significant improvements in accuracy,
yet also reduces time and memory costs by a factor of several hundred compared to existing pruning techniques. Our method is furthermore insensitive to holes, unlike many other methods.
Parametric MetaFilter Modeling from a Single Example Pair
The Visual Computer, vol. 30(68), pp. 673684, 20014 Project
ShiSheng Huang, GuoXin Zhang, YuKun Lai, Johannes Kopf, Daniel CohenOr, ShiMin Hu
We present a method for learning a metaFilter from an example pair comprising an original image A and its Filtered version A0 using an unknown image Filter. A metaFilter is a parametric model, consisting of a spatially varying linear combination of simple basis Filters. We introduce a technique for learning the parameters of the metaFilter f such that it approximates the effects of the unknown Filter, i.e., f(A) approximates A0. The metaFilter can be transferred to novel input images, and its parametric representation enables intuitive tuning of its parameters to achieve controlled variations. We show that our technique successfully learns and models metaFilters that approximate a large variety of common image Filters with high accuracy both visually and quantitatively.
Efficient Circular Thresholding
IEEE Transactions on Image Processing, vol. 23(3), pp. 9921001, 20014
YuKun Lai and Paul L. Rosin
Otsu's algorithm for thresholding images is widely used, and the computational complexity of determining the
threshold from the histogram is O(N) where N is the number of histogram bins. When the algorithm is adapted to circular rather
than linear histograms then two thresholds are required for binary thresholding. We show that, surprisingly, it is still possible to
determine the optimal threshold in O(N) time. The efficient optimal algorithm is over 300 times faster than traditional approaches
for typical histograms and is thus particularly suitable for realtime applications. We further demonstrate the usefulness of circular
thresholding using the adapted Otsu criterion for various applications, including analysis of optical flow data, indoor/outdoor
image classification and nonphotorealistic rendering. In particular, by combining circular Otsu feature with other colour/texture
features, a 96.9% correct rate is obtained for indoor/outdoor classification on the well known IITMSCID2 dataset, outperforming
the stateoftheart result by 4.3%.
Other Publications:
 O. Samko, Y.K. Lai, A. D. Marshall, P. L. Rosin. Virtual unrolling and information recovery from scanned historical documents, Pattern Recognition, vol. 47(1), pp. 248259, 2014.
 Y.K. Lai, P. L. Rosin. Artistic rendering enhancing global structure, The Visual Computer, vol. 30(10), pp. 11791193, 2014.
 J. Wu, R. R. Martin, P. L. Rosin, X. Sun, Y.K. Lai, Y.H. Liu, C. Wallraven. Use of nonphotorealistic rendering and photometric stereo in making basreliefs from photographs, Graphical Models, vol. 76(4), pp. 202213, 2014.
 G. Tam, R. R. Martin, P. L. Rosin, Y.K. Lai. An Efficient Approach to Correspondences between Multiple NonRigid Parts, Computer Graphics Forum vol. 33(5), pp. 137146, 2014.
 D. Mills, A. Curtis, G. Davis, P. Rosin, Y.K. Lai. Apocalypto: revealing the Bressingham roll, Journal of Paper Conservation, vol. 15(3), pp. 1419, 2014.
2013
A DataDriven Approach to Realistic Shape Morphing
Computer Graphics Forum, vol. 32(2),
449457, 2013 (Eurographics 2013).
Lin Gao, YuKun Lai, Qixing Huang and ShiMin Hu
Morphing between 3D objects is a fundamental technique in computer graphics.
Traditional methods of shape morphing focus on establishing meaningful
correspondences and finding smooth interpolation between shapes. Such methods
however only take geometric information as input and thus cannot in general
avoid producing unnatural interpolation, in particular for largescale
deformations. This paper proposes a novel datadriven approach for shape
morphing. Given a database with various models belonging to the same category,
we treat them as data samples in the plausible deformation space. These models
are then clustered to form local shape spaces of plausible deformations. We use
a simple metric to reasonably represent the closeness between pairs of models.
Given source and target models, the morphing problem is casted as a global
optimization problem of finding a minimal distance path within the local shape
spaces connecting these models. Under the guidance of intermediate models in the
path, an extended asrigidaspossible interpolation is used to produce the
final morphing. By exploiting the knowledge of plausible models, our approach
produces realistic morphing for challenging cases as demonstrated by various
examples in the paper.
Generalized Anisotropic Stratified Surface Sampling
IEEE Transactions on Visualization and Computer Graphics, vol. 19(7),
11431157, 2013.
Jon Quinn, Frank Langbein, YuKun Lai and Ralph Martin
We introduce a novel stratified sampling technique for mesh surfaces that gives the user control over sampling density and anisotropy via a tensor field. Our approach is based on sampling spacefilling curves mapped onto mesh segments via parametrizations aligned with the tensor field. After a short preprocessing step, samples can be generated in realtime. Along with visual examples, we provide rigorous spectral analysis and differential domain analysis of our sampling. The sample distributions are of high quality: they fulfil the blue noise criterion, so have minimal artifacts due to regularity of sampling patterns, and they accurately represent isotropic and anisotropic densities on the plane and on mesh surfaces. They also have low discrepancy, ensuring that the surface is evenly covered.
Registration of 3D Point Clouds and Meshes: A Survey from Rigid to NonRigid
IEEE Transactions on Visualization and Computer Graphics, vol. 19(7),
11991217, 2013.
Gary Tam, ZhiQuan Cheng, YuKun Lai, Frank Langbein, Yonghuai Liu, David Marshall, Ralph Martin, Xianfang Sun and Paul Rosin
3D surface registration transforms multiple 3D datasets into the same coordinate system so as to align overlapping components of these sets. Recent surveys have covered different aspects of either rigid or nonrigid registration, but seldom discuss them as a whole. Our study serves two purposes: (i) to give a comprehensive survey of both types of registration, focusing on 3D point clouds and meshes, and (ii) to provide a better understanding of registration from the perspective of data ﬁtting. Registration is closely related to data ﬁtting in that it comprises three core interwoven components: model selection, correspondences & constraints and optimization. Study of these components (i) provides a basis for comparison of the novelties of different techniques, (ii) reveals the similarity of rigid and nonrigid registration in terms of problem representations, and (iii) shows how overﬁtting arises in nonrigid registration and the reasons for increasing interest in intrinsic techniques. We further summarise some practical issues of registration which include initializations and evaluations, and discuss some of our own observations, insights and foreseeable research trends.
Efficient Synthesis of Gradient Solid Textures
Graphical Models, vol. 75(3), 104117, 2013.
GuoXin Zhang, YuKun Lai and ShiMin Hu
Preliminary version appears in Proc. Computational Visual Media 2012.
Solid textures require large storage and are computationally expensive to synthesize. In this paper, we propose a novel solid representation called gradient solids to compactly represent solid textures, including a tricubic interpolation scheme of colors and gradients for smooth variation and a regionbased approach for representing sharp boundaries. We further propose a novel approach to directly synthesize gradient solid textures from exemplars. Compared to existing methods, our approach avoids the expensive step of synthesizing the complete solid textures at voxel level and produces optimized solid textures using our representation. This avoids signiﬁcant amount of unnecessary computation and storage involved in the voxellevel synthesis while producing solid textures with comparable quality to the state of the art. The algorithm is much faster than existing approaches for solid texture synthesis and makes it feasible to synthesize highresolution solid textures in full. We also propose a novel application — instant editing propagation on full solids.
Examplebased Color Transfer for Gradient Meshes
IEEE Transactions on Multimedia, vol. 15(3), pp. 549560, 2013.
Yi Xiao, Liang Wan, ChiSing Leung, YuKun Lai and TienTsin Wong
Editing a photorealistic gradient mesh is a tough
task. Even only editing the colors of an existing gradient
mesh can be exhaustive and timeconsuming. To facilitate
userfriendly color editing, we develop an examplebased color
transfer method for gradient meshes, which borrows the color
characteristics of an example image to a gradient mesh. We
start by exploiting the constraints of the gradient mesh, and
accordingly propose a linearoperatorbased color transfer
framework. Our framework operates only on colors and color
gradients of the mesh points and preserves the topological
structure of the gradient mesh. Bearing the framework in
mind, we build our approach on PCAbased color transfer.
After relieving the color range problem, we incorporate a
fusionbased optimization scheme to improve color similarity
between the reference image and the recolored gradient mesh.
Finally, a multiswatch transfer scheme is provided to enable
more user control. Our approach is simple, effective, and
much faster than color transferring the rastered gradient
mesh directly. The experimental results also show that our
method can generate pleasing recolored gradient meshes.
Other Publications:
 P. L. Rosin, Y.K. Lai. Artistic minimal rendering with lines and blocks, Graphical Models, vol. 75(4), pp. 208229, 2013
 Y. Chen, Z.Q. Cheng, R. R. Martin, Y.K. Lai, A. Wang. SuperMatching: feature matching using supersymmetric geometric constraints, IEEE Transactions on Visualization and Computer Graphics, vol. 19(11), pp. 18851894, 2013.
 J. Wu, R. R. Martin, P. L. Rosin, X. Sun, F. C. Langbein, Y.K. Lai, D. Marshall, Y. Liu, Making basreliefs from photographs of human faces, ComputerAided Design, vol. 45(3), pp. 671682, 2013.
 F. M. Anuar, R. Setchi, Y.K. Lai, Trademark image retrieval using an integrated shape descriptor, Expert Systems with Applications, vol. 40(1), pp. 105121, 2013.
 P. L. Rosin, Y.K. Lai, Nonphotorealistic rendering with spot colour. In: Proceedings of Computational Aesthetics, pp. 6776, 2013.
 Y.K. Lai, P. L. Rosin, Nonphotorealistic rendering with reduced colour palettes. In: Image and Videobased Artistic Stylisation, Computational Imaging and Vision series, vol. 42(2), pp. 211236, Springer, 2013.
2012
Improved Initialisation for Centroidal Voronoi Tessellation and Optimal Delaunay
Triangulation
ComputerAided Design, vol. 44(11), pp. 10621071, 2012.
Jonathan A. Quinn, Feng Sun, Frank C. Langbein, YuKun Lai, Wenping Wang and Ralph R. Martin
Centroidal Voronoi tessellations and optimal Delaunay triangulations can be approximated efficiently by nonlinear optimisation
algorithms. This paper demonstrates that the point distribution used to initialise the optimisation algorithms is important. Compared
to conventional random initialisation, certain lowdiscrepancy point distributions help convergence towards more spatially regular
results and require fewer iterations for planar and volumetric tessellations.
Vertex Location Optimisation for Improved Remeshing
Graphical Models, vol. 74(4), pp. 233243, 2012.
YuKun Lai and Ralph R. Martin
Remeshing aims to produce a more regular mesh from a given
input mesh, while representing the original geometry as accurately
as possible. Many existing remeshing methods focus on
where to place new mesh vertices; these samples are placed
exactly on the input mesh. However, considering the output
mesh as a piecewise linear approximation of some geometry,
this simple scheme leads to significant systematic error in nonplanar
regions. Here, we use parameterised meshes and the
recent mathematical development of orthogonal approximation
using Sobolevtype inner products to develop a novel sampling
scheme which allows vertices to lie in space near the input surface,
rather than exactly on it. The algorithm requires little
extra computational effort and can be readily incorporated into
many remeshing approaches. Experimental results show that
on average, approximation error can be reduced by 40% with
the same number of vertices. A similar technique can also be
applied to surface normals to provide more accurate rendering
results with the same number of vertices.
Lp Shape Deformation
Science China Information Sciences, vol. 55(5), pp. 983993, 2012.
Lin Gao, GuoXin Zhang and YuKun Lai
Shape deformation is a fundamental tool in geometric modeling. Existing methods consider preserving
local details by minimizing some energy functional measuring local distortions in the L2 norm. This
strategy distributes distortions quite uniformly to all the vertices and penalizes outliers. However, there is no
unique answer for a natural deformation as it depends on the nature of the objects. Inspired by recent sparse
signal reconstruction work with non L2 norm, we introduce general Lp norms to shape deformation; the positive
parameter p provides the user with a flexible control over the distribution of unavoidable distortions. Compared
with the traditional L2 norm, using smaller p, distortions tend to be distributed to a sparse set of vertices,
typically in feature regions, thus making most areas less distorted and structures better preserved. On the
other hand, using larger p tends to distribute distortions more evenly across the whole model. This flexibility is
often desirable as it mimics objects made up with different materials. By specifying varying p over the shape,
more flexible control can be achieved. We demonstrate the effectiveness of the proposed algorithm with various
examples.
2011
Sketch Guided Solid Texturing
Graphical Models, vol. 73(3), pp. 5973, 2011.
GuoXin Zhang, SongPei Du, YuKun Lai, Tianyun Ni and ShiMin Hu
Compared to 2D textures, solid textures offer the advantage of consistently representing not only the bounding surfaces of objects, but also their interiors. Existing solid texture synthesis methods pay little attention to the generation of conforming textures that capture essential geometric structures or accurately reflect the artists&apos design intentions. In this paper, we propose a novel approach to synthesizing solid textures using 2D exemplar texture images. The generated textures locally agree with a tensor field derived from a few user sketching curves. We use a deterministic approach such that only a small portion of the voxels needs to be synthesized on demand. Correction is the fundamental step in deterministic texture synthesis to update each voxel according to its local neighborhood. We propose a novel history windows representation, which is general enough to represent various previous correction schemes in a unified manner, and a novel dual grid correction scheme based on the representation to significantly reduce the dependent voxels while still producing high quality results. Experimental results demonstrate that our method produces significantly improved solid textures with a very small amount of user interaction.
2010
Metric Driven RoSy Field Design and Remeshing
IEEE Transactions on Visualization and Computer Graphics, vol. 16(1), pp. 95108, 2010.
YuKun Lai, Miao Jin, Xuexiang Xie, Ying He, Jonathan Palacios, Eugene Zhang, ShiMin Hu and Xianfeng David Gu
Designing rotational symmetries on surfaces is an important task for a wide range of graphics applications. This work introduces a rigorous and practical algorithm for automatic NRoSy design on arbitrary surfaces with user defined field topologies. The user has full control of the number, positions and indices of the singularities, the turning numbers of the loops, and is able to edit the field interactively.
Feature Aligned Quad Dominant Remeshing using Iterative Local Updates
ComputerAided Design, vol. 42(2), pp. 109117, 2010.
YuKun Lai, Leif Kobbelt and ShiMin Hu
Preliminary version appears in Proc. ACM Solid and Physical Modeling 2008.
In this paper we present a new algorithm which turns an unstructured triangle mesh
into a quaddominant mesh with edges well aligned to the principal directions of
the underlying surface. Instead of computing a globally smooth parameterization
or integrating curvature lines along a tangent vector field, we simply apply an iterative relaxation scheme which incrementally aligns the mesh edges to the principal
directions. We further obtain the quaddominant mesh by dropping the notaligned
diagonal edges from the triangle mesh. A postprocessing stage is introduced to
further improve the results. The major advantage of our algorithm is its conceptual simplicity since it is merely based on elementary mesh operations such as edge
collapse, flip, and split. The resulting meshes exhibit a very good alignment to surface features and rather uniform distribution of mesh vertices. This makes them
wellsuited, e.g., as CatmullClark Subdivision control meshes.
Towards Artistic Minimal Rendering
ACM Symposium on Non Photorealistic Rendering, pp. 119127, 2010. Try Online Demo
Paul L. Rosin and YuKun Lai
Many nonphotorealistic rendering techniques exist to produce artistic effects from given images. Inspired by various artistic work such as Warhol's, interesting artistic effects can be produced by using a minimal rendering, where the minimum refers to the number of tones as well as the number and complexity of the primitives used for rendering. To achieve this goal, based on various computer vision techniques, our method uses a combination of refined lines and blocks, as well as a small number of tones, to produce abstracted artistic rendering with sufficient elements from the original image. There is always a tradeoff between reducing the amount of information and the ability to represent the shape and details of the original images. Judging the level of abstraction is semanticbased, so we believe that giving users this flexibility is probably a good choice. By changing some intuitive parameters, a wide range of visually pleasing results can be produced. Our method is usually fully automatic, but a small amount of user interaction can optionally be incorporated to obtain selective abstraction.
Harmonic Field Based Volume Model Construction from Triangle Soup
Journal of Computer Science and Technology, vol. 25(3), pp. 562571, 2010.
ChaoHui Shen, GuoXin Zhang, YuKun Lai, ShiMin Hu and R. R. Martin
Surface triangle meshes and volume data are two commonly used representations of digital geometry. Converting from triangle meshes to volume data is challenging, since triangle meshes often contain defects such as small holes, internal structures, or selfintersections. In the extreme case, we may be simply presented with a set of arbitrarily connected triangles, a "triangle soup". This paper presents a novel method to generate volume data represented as an octree from a general 3D triangle soup. Our motivation is the Faraday cage from electrostatics. We consider the input triangles as forming an approximately closed Faraday cage, and set its potential to zero. We then introduce a second conductor surrounding it, and give it a higher constant potential. Due to the electrostatic shielding e®ect, the resulting electric field approximately lies in that part of space outside the shape implicitly determined by the triangle soup. Unlike previous approaches, our method is insensitive to small holes and internal structures, and is observed to generate volumes with low topological complexity. While our approach is somewhat limited in accuracy by the requirement of filling holes, it is still useful, for example, as a preprocessing step for applications such as mesh repair and skeleton extraction.
2009
Automatic and Topology Preserving Gradient Mesh Generation for Image Vectorization
ACM SIGGRAPH 2009, ACM Transactions on Graphics 28(3), Article No. 85.
YuKun Lai, ShiMin Hu and Ralph R. Martin
Gradient mesh vector graphics representation, used in commercial
software, is a regular grid with specified position and color,
and their gradients, at each grid point. Gradient meshes can compactly
represent smoothly changing data, and are typically used for
single objects. This paper advances the state of the art for gradient
meshes in several significant ways. Firstly, we introduce a
topologypreserving gradient mesh representation which allows an
arbitrary number of holes. This is important, as objects in images
often have holes, either due to occlusion, or their 3D structure. Secondly,
our algorithm uses the concept of image manifolds, adapting
surface parameterization and fitting techniques to generate the gradient
mesh in a fully automatic manner. Existing gradientmesh
algorithms require manual interaction to guide grid construction,
and to cut objects with holes into disklike regions. Our new algorithm
is empirically at least 10 times faster than previous approaches.
Furthermore, image segmentation can be used with our
new algorithm to provide automatic gradient mesh generation for
a whole image. Finally, fitting errors can be simply controlled to
balance quality with storage.
Rapid and Effective Segmentation of 3D Models using Random Walks
Computer Aided Geometric Design, vol. 26(6), pp. 665679, 2009.
YuKun Lai, ShiMin Hu, Ralph R. Martin and Paul L. Rosin
Preliminary version appears in Proc. ACM Solid and Physical Modeling 2008.
3D models are now widely available for use in various applications. The demand for automatic model analysis and understanding is ever increasing. Model segmentation is an important step towards model understanding, and acts as a useful tool for different model processing applications, e.g. reverse engineering and modeling by example. We extend a random walk method used previously for image segmentation to give algorithms for both interactive and automatic model segmentation. This method is extremely efficient, and scales almost linearly with the number of faces, and the number of regions. For models of moderate size, interactive performance is achieved with commodity PCs. We demonstrate that this method can be applied to both triangle meshes and point cloud data. It is easytoimplement, robust to noise in the model, and yields results suitable for downstream applications for both graphical and engineering models.
Stripification of FreeForm Surfaces with Global Error Bounds for Developable Approximation
IEEE Transactions on Automation Science and Engineering, vol. 6(4), pp. 700709, 2009.
YonJin Liu, YuKun Lai and ShiMin Hu
Developable surfaces have many desired properties in manufacturing process. Since most existing CAD systems utilize tensorproduct parametric surfaces including Bsplines as design primitives, there is a great demand in industry to convert a general freeform parametric surface within a prescribed
global error bound into developable patches. In this work we propose a practical and efficient solution to approximate a rectangular parametric surface with a small set of C^0joint developable strips. The key contribution of the proposed algorithm is that, several optimization problems are elegantly
solved in a sequence that offers a controllable global error bound on the developable surface approximation. Experimental results are presented to demonstrate the effectiveness and stability of the proposed algorithm.
Robust Principal Curvatures using Feature Adapted Integral Invariants
SIAM/ACM Joint Conference on Geometric and Physical Modeling, pp. 325330, 2009.
YuKun Lai, ShiMin Hu and Fang Tong
3D models are now widely available for use in various applications. The demand for automatic model analysis and understanding is ever increasing. Model segmentation is an important step towards model understanding, and acts as a useful tool for different model processing applications, e.g. reverse engineering and modeling by example. We extend a random walk method used previously for image segmentation to give algorithms for both interactive and automatic model segmentation. This method is extremely efficient, and scales almost linearly with the number of faces, and the number of regions. For models of moderate size, interactive performance is achieved with commodity PCs. We demonstrate that this method can be applied to both triangle meshes and point cloud data. It is easytoimplement, robust to noise in the model, and yields results suitable for downstream applications for both graphical and engineering models.
2008
Fairing Wireframes in Industrial Surface Design
IEEE International Conference on Shape Modeling and Applications, pp. 2935, 2008.
YuKun Lai, YongJin Liu, Yu Zang and ShiMin Hu
Wireframe is a modeling tool widely used in industrial geometric design. The term wireframe refers to two sets of curves, with the property that each curve from one set intersects with each curve from the other set. Akin to the u, visocurves in a tensorproduct surface, the two sets of curves in a wireframe span an underlying surface. In many industrial design activities, wireframes are usually set up and adjusted by the designers before the whole surfaces are reconstructed. For adjustment, the fairness of wireframe has a direct influence on the quality of the underlying surface. Wireframe fairing is significantly different from fairing individual curves in that intersections should be preserved and kept in the same order. In this paper, we first present a technique for wireframe fairing by fixing the parameters during fairing. The limitation of fixed parameters is further released by an iterative gradient descent optimization method with stepsize control. Experimental results show that our solution is efficient, and produces reasonably fairing results of the wireframes.
Note on Industrial Applications of Hu's Surface Extension Algorithm
Geometric Modeling Processing, pp. 304314, 2008.
Zang Yu, YongJin and YuKun Lai
An important surface modeling problem in CAD is to connect two disjoint Bspline patches with the secondorder geometric continuity. In this paper we present a study to solve this problem based on the surface extension algorithm [ComputerAided Design 2002; 34:415419]. Nice properties of this extension algorithm are exploited in depth and thus make our solution very simple and efficient. Various practical examples are presented to demonstrate the usefulness and efficiency of our presented solution.
2007
Robust Feature Classification and Editing
IEEE Transactions on Visualization and Computer Graphics, vol. 13, Jan/Feb, pp. 3445, 2007.
YuKun Lai, QianYi Zhou, ShiMin Hu, Johannes Wallner and Helmut Pottmann
Sharp edges, ridges, valleys and prongs are critical for the appearance and an accurate representation of a 3D model. In this paper, we propose a novel approach that deals with the global shape of features in a robust way. Based on a remeshing algorithm which delivers an isotropic mesh in a feature sensitive metric, features are recognized on multiple scales via integral invariants of local neighborhoods. Morphological and smoothing operations are then used for feature region extraction and classification into basic types such as ridges, valleys and prongs. The resulting representation of feature regions is further used for featurespecific editing operations.
Developable Strip Approximation of Parametric Surfaces with Global Error Bounds
Pacific Graphics, pp. 441444, 2007(poster).
YongJin Liu, YuKun Lai and ShiMin Hu
Developable surfaces have many desired properties in manufacturing process. Since most existing CAD systems utilize parametric surfaces as the design primitive, there is a great demand in industry to convert a parametric surface within a prescribed global error bound into developable
patches. In this work we propose a simple and efficient solution to approximate a general parametric surface with a minimum set of $C^0$joint developable strips. The key contribution of the proposed algorithm is that, several global optimization problems are elegantly solved in a sequence
that offers a controllable global error bound on the developable surface approximation. Experimental results are presented to demonstrate the effectiveness and stability of the proposed algorithm.
Principal curvatures from the integral invariant viewpoint
Computer Aided Geometric Design, vol. 24, pp. 428442, 2007.
Helmut Pottmann, Johannes Wallner, YongLiang Yang, YuKun Lai and ShiMin Hu
The extraction of curvature information for surfaces is a basic problem of Geometry Processing. Recently an integral invariant solution of this problem was presented, which is based on principal component analysis of local neighbourhoods defined by kernel balls of various sizes. It is not only robust to noise, but also adjusts to the level of detail required. In the present paper we show an asymptotic analysis of the moments of inertia and the principal directions which are used in this approach. We also address implementation and, briefly, robustness issues and applications.
2006
Surface Fitting Based on a Feature Sensitive Parameterization
ComputerAided Design, Vol. 38, No. 7, pp. 800807, 2006.
YuKun Lai, ShiMin Hu and Helmut Pottmann
Most approaches to least squares fitting of a Bspline surface to measurement data require a parametrization of the data point set and the choice of suitable knot vectors. We propose to use uniform knots in connection with a feature sensitive parametrization. This parametrization allocates more parameter space to highly curved feature regions and thus automatically provides more control points where they are needed.
Surface Mosaics
The Visual Computer, vol. 22, no. 911, pp. 604611, 2006 (Special issues of Pacific Graphics).
YuKun Lai, ShiMin Hu and Ralph R. Martin
This paper considers the problem of placing mosaic tiles on a surface to produce a surface mosaic. We assume that the user specifies a mesh model, the size of the tiles and the amount of grout, and optionally, a few control vectors at key locations on the surface indicating the preferred tile orientation at these points. From these inputs, we place equalsized rectangular tiles over the mesh such as to almost cover it, with controlled orientation. The alignment of the tiles follows a vector field which is interpolated over the surface from the control vectors, and also forced into alignment with any sharp creases, open boundaries, and boundaries between regions of different colors. Our method efficiently solves the problem by posing it as one of globally optimizing a springlike energy in the Manhattan metric, using overlapping local parameterizations.We demonstrate the effectiveness of our algorithm with various examples.
Feature Sensitive Mesh Segmentation
ACM Symposium on Solid and Physical Modeling, pp. 716, 2006.
YuKun Lai, ShiMin Hu and Ralph R. Martin
This paper considers the problem of placing mosaic tiles on a surface to produce a surface mosaic. We assume that the user specifies a mesh model, the size of the tiles and the amount of grout, and optionally, a few control vectors at key locations on the surface indicating the preferred tile orientation at these points. From these inputs, we place equalsized rectangular tiles over the mesh such as to almost cover it, with controlled orientation. The alignment of the tiles follows a vector field which is interpolated over the surface from the control vectors, and also forced into alignment with any sharp creases, open boundaries, and boundaries between regions of different colors. Our method efficiently solves the problem by posing it as one of globally optimizing a springlike energy in the Manhattan metric, using overlapping local parameterizations.We demonstrate the effectiveness of our algorithm with various examples.
Robust Principal Curvatures on Multiple Scales
Eurographics Symposium on Geometry Processing, pp. 223226, 2006.
YongLiang Yang, YuKun Lai, ShiMin Hu and Helmut Pottmann
Geometry processing algorithms often require the robust extraction of curvature information. We propose to achieve this with principal component analysis (PCA) of local neighborhoods, defined via spherical kernels centered on the given surface F. Intersection of a kernel ball Br or its boundary sphere Sr with the volume bounded by F leads to the socalled ball and sphere neighborhoods. Information obtained by PCA of these neighborhoods turns out to be more robust than PCA of the patch neighborhood Br \F previously used. The relation of the quantities computed by PCA with the principal curvatures of F is revealed by an asymptotic analysis as the kernel radius r tends to zero. This also allows us to define principal curvatures “at scale r” in a way which is consistent with the classical setting. The advantages of the new approach are discussed in a comparison with results obtained by normal cycles and local fitting; whereas the former method somewhat lacks in robustness, the latter does not achieve a consistent behavior at features on coarse scales. As to applications, we address computing principal curves and feature extraction on multiple scales.
2005
Geometric texture synthesis and transfer via geometry images
ACM Symposium on Solid and Physical Modeling, pp. 1526, 2005.
YuKun Lai, ShiMin Hu, Xianfeng Gu and Ralph R. Martin
In this paper, we present an automatic method which can transfer geometric textures from one object to another, and can apply a manually designed geometric texture to a model. Our method is based on geometry images as introduced by Gu et al. The key ideas in this method involve geometric texture extraction, boundary consistent texture synthesis, discretized orientation and scaling, and reconstruction of synthesized geometry. Compared to other methods, our approach is efficient and easytoimplement, and produces results of high quality.
