ACM SIGGRAPH
or TOG 



S.Xiong, J.Zhang, J. Zheng, J.Cai, L.Liu (2014)
"Robust
surface reconstruction via dictionary learning"
ACM Transactions on Graphics
(SIGGRAPH Asia 2014),
Vol.33, No.6, 2014.
Surface reconstruction from point cloud is of great practical
importance in computer graphics. Existing methods often realize reconstruction
via a few phases with respective goals, whose integration may not give an
optimal solution. In this paper, to avoid the inherent limitations of
multiphase processing in the prior art, we propose a unified framework that
treats geometry and connectivity construction as one joint optimization problem.
The framework is based on dictionary learning in which the dictionary consists
of the vertices of the reconstructed triangular mesh and the sparse coding
matrix encodes the connectivity of the mesh. The dictionary learning is
formulated as a constrained L_{2,q}optimization (0 < q < 1), aiming to find the
vertex position and triangulation that minimize an energy function composed of
pointtomesh metric and regularization. Our formulation takes many factors into
account within the same framework, including distance metric, noise/outlier
resilience, sharp feature preservation, no need to estimate normal, etc., thus
providing a global and robust algorithm that is able to efficiently recover a
piecewise smooth surface from dense data points with imperfections.


P.Song, C.W.Fu, P.Goswami, J. Zheng, N.Mitra, D.CohenOr (2013)
"Reciprocal
frame structures made easy"
ACM Transactions on Graphics
(SIGGRAPH 2013),
Vol.32, No.4, 2013.
A reciprocal frame (RF) is a selfsupported 3D
structure made up of three or more sloping rods, which form a closed circuit.
Large RFstructures built as complex grillages of one or a few similar circuits
have an intrinsic beauty derived from their inherent selfsimilar and highly
symmetric patterns. This paper presents an interactive computational tool for
designing large RFstructures over a 3D guiding surface. Users can sketch
designs with a wide variety of RF patterns and interactively modify the
appearance and parameters with preview, and the tool ensures the design's
structure connectivity and coherence. The work contains three key technical
components: (1) we draw an analogy between RFstructures and plane tiling with
regular polygons, and develop a computational scheme to generate coherent RFtessellations
from simple grammar rules; (2) we employ a conformal mapping to lift the 2D
tessellation over a 3D guiding surface, allowing a realtime preview and
efficient exploration of wide ranges of RF design parameters; and (3) we devise
an optimization method to guarantee the collinearity of contact joints along
each rod, while preserving the geometric properties of the RFstructure.


J. Zhang, J. Zheng, C. Wu, J. Cai (2012)
"Variational
mesh decomposition"
ACM Transactions on Graphics
(presented at SIGGRAPH 2012),
Vol.31, No.3, 2012.
This paper presents a variational mesh decomposition algorithm
that can efficiently partition a mesh into a prescribed number of segments. The
algorithm extends the MumfordShah model to 3D meshes, which simultaneously
handles segmentation and boundary smoothing. The efficiency is achieved by
solving the MumfordShah model through a saddlepoint problem that is solved by
a fast primaldual method. A preprocess step is also proposed to determine the
number of segments that the mesh should be decomposed into. By incorporating
this preprocessing step, the proposed algorithm can automatically segment a
mesh into meaningful parts. Furthermore, user interaction is allowed by
incorporating user's inputs into the variational model to reflect user's special
intention.


T. Sederberg, D.Cardon, G.Finnigan, N.North, J. Zheng, T.
Lyche (2004)
"Tspline
simplification and local refinement"
ACM Transactions on Graphics
(SIGGRAPH 2004),
Vol.23, No.3, 2004.
A
typical NURBS surface model has a large percentage of superfluous control
points that significantly interfere with the design process. This paper presents
an algorithm for eliminating such superfluous control points, producing a Tspline. The paper also presents a new
Tspline
local refinement algorithm and answers two fundamental open questions on Tspline
theory.


T. Sederberg, J. Zheng, A. Bakenov, A. Nasri (2003)
"Tsplines
and TNURCCs"
ACM Transactions on Graphics
(SIGGRAPH 2003),
Vol.22, No.3, pp 477484,
2003.
This paper presents a generalization
of nonuniform Bspline surfaces called Tsplines. Tsplines permit Tjunctions
in their control grid, and thus support many valuable operations. TNURCCs (NonUniform
Rational CatmullClark Surfaces with Tjunctions) are a superset of both Tsplines
and Catmull Clark surfaces. Thus, a modeling program for TNURCCs can handle any
NURBS or CatmullClark model as special cases.


J. Zheng, T. Sederberg (2000)
"Estimating tessellation parameter
intervals for rational curves and surfaces"
ACM Transactions on Graphics,
Vol.19, No.1, pp 5677, 2000.
This paper presents a method for determining
a priori
a constant parameter interval for tessellating a rational curve or surface such
that the deviation of the curve or surface from its piecewise linear
approximation is within a specified tolerance. The parameter interval is
estimated based on information about secondorder derivatives in the homogeneous
coordinates, instead of using affine coordinates directly.


T. Sederberg, J. Zheng, D. Sewell, M. Sabin (1998)
"Nonuniform recursive subdivision
surfaces"
ACM SIGGRAPH 1998 Proceedings,
pp 387394, 1998.
This paper
develops rules for nonuniform DooSabin and CatmullClark surfaces
that generalize nonuniform tensor product Bspline surfaces to arbitrary
topologies. This added flexibility allows, among other things, the
natural introduction of features such as cusps, creases, and darts,
while else where maintaining the same order of continuity as their uniform
counterparts.



IEEE Transactions 



Y.Ma, J. Zheng,
J.Xie
(2014)
"Foldoverfree mesh warping for constrained texture
mapping"
IEEE Transactions on Visualization
and Computer Graphics, 2014.
Mapping texture
onto 3D meshes with positional constraints is a popular technique that can
effectively enhance the visual realism of geometric models. Such a process
usually requires constructing a valid mesh embedding satisfying a set of
positional constraints, which is known to be a challenging problem. This
paper presents a novel algorithm for computing a foldoverfree piecewise
linear mapping with exact positional constraints. The algorithm begins with
an unconstrained planar embedding, followed by iterative constrained mesh
transformations. At the heart of the algorithm are radial basis function (RBF)based
warping and the longest edge bisection (LEB)based refinement. A delicate
integration of the RBFbased warping and the LEBbased refinement provides a
provably foldoverfree, smooth constrained mesh warping, which can handle a
large number of constraints and output a visually pleasing mapping result
without extra smoothing optimization. The experiments demonstrate the
effectiveness of the proposed algorithm. 

H.Zhou, J. Zheng,
L.Wei
(2014)
"Representing images using curvilinear feature driven subdivision surfaces"
IEEE Transactions on
Image Processing, Vol.23, No.8, 2014.
This paper
presents a subdivisionbased vector graphics for image representation and
creation. The graphics representation is a subdivision surface defined by a
triangular mesh augmented with color attribute at vertices and feature
attribute at edges. Special cubic Bsplines are proposed to describe
curvilinear features of an image. New subdivision rules are then designed
accordingly, which are applied to the mesh and the color attribute to define
the spatial distribution and piecewisesmoothly varying colors of the image.
A sharpness factor is introduced to control the color transition across the
curvilinear edges. In addition, an automatic algorithm is developed to
convert a raster image into such a vector graphics representation. The
algorithm first detects the curvilinear features of the image, then
constructs a triangulation based on the curvilinear edges and feature
attributes, and finally iteratively optimizes the vertex color attributes
and updates the triangulation. Compared with existing vectorbased image
representations, the proposed representation and algorithm have the
following advantages in addition to the common merits (such as editability
and scalability): 1) they allow flexible mesh topology and handle images or
objects with complicated boundaries or features effectively; 2) they are
able to faithfully reconstruct curvilinear features, especially in modeling
subtle shading effects around feature curves; and 3) they offer a simple way
for the user to create images in a freehand style.


H.Zhu, J. Zheng,
J.Cai, N.Thalmann
(2013)
"Objectlevel image segmentation using low level cues"
IEEE Transactions on
Image Processing, Vol.22, 2013.
This paper
considers the problem of automatically segmenting an image into a small
number of regions that correspond to objects conveying semantics or
highlevel structure. While such objectlevel
segmentation usually requires additional highlevel knowledge or
learning process, we explore what low level cues can produce for
this purpose. Our idea is to construct a feature vector for each pixel,
which elaborately integrates spectral attributes, color Gaussian Mixture
Models and geodesic distance, such that it encodes global color and spatial
cues as well as global structure information. Then we formulate the Potts
variational model in terms of the feature vectors to provide a variational
image
segmentation algorithm that is performed in the feature space. We
also propose a heuristic approach to automatically select the number of
segments. The use of feature attributes enables the Potts model to produce
regions that are coherent in color and position, comply with global
structures corresponding to objects or parts of objects and meanwhile
maintain a smooth and accurate boundary.


Y.Cai, N.Chia, D.Thalmann, N.Kee, J. Zheng,
N.Thalmann
(2013)
"Design
and development of a virtual dolphinarium for children with autism"
IEEE Transactions on Neural
System and Rehabilitation Engineering, Vol.21, No.2, pp 208217.
The recent
proliferation of virtual reality technology applications in the autism
therapy to promote learning and positive behavior among such children has
produced optimistic results in developing a variety of skills and abilities
in them. Dolphinassisted therapy has also become a topic of public and
research interest for autism intervention and treatment. This paper presents
an innovative design and development of a virtual dolphinarium for potential
autism intervention. Instead of emulating the swimming with dolphins, our
virtual dolphin interaction program allows children with autism to act as
dolphin trainers at the poolside and to learn (nonverbal) communication
through hand gestures with the virtual dolphins. Immersive visualisation and
gesturebased interaction are implemented to engage children with autism
within an immersive room equipped with a curved screen spanning a 320 degree
and a highend 5panel projection system. The paper also reports a pilot
study to establish trial protocol of autism screening to explore the
participants' readiness for the virtual dolphin interaction.


T.Nguyen, J.Cai, J. Zhang, J. Zheng
(2012)
"Robust
interactive image segmentation using convex active contour"
IEEE Transactions on Image
Processing, Vol.21. No.8, pp 37343743.
The
stateoftheart interactive image segmentation algorithms are sensitive to
the user inputs and often unable to produce an accurate boundary with a
small amount of user interaction. They frequently rely on laborious user
editing to refine the segmentation boundary. In this paper, we propose a
robust and accurate interactive method based on the recently developed
continuousdomain convex active contour model. The proposed method exhibits
many desirable properties of an effective interactive image segmentation
algorithm, including robustness to user inputs and different
initializations, the ability to produce a smooth and accurate boundary
contour, and the ability to handle topology changes. Experimental results on
a benchmark data set show that the proposed tool is highly effective and
outperforms the stateoftheart interactive image segmentation algorithms.


J. Zhang, J. Zheng,
J.Cai
(2011)
"Interactive mesh cutting using constrained random walks"
IEEE Transactions on Visualization
and Computer Graphics, Vol.17, No.3, pp 357367.
This paper
considers the problem of interactively finding
the cutting contour to extract components from an existing mesh. First, we
propose a constrained random walks algorithm that can add constraints to the
random walks procedure and thus allows for a variety of intuitive user
inputs. Second, we design an optimization process that uses the shortest
graph path to derive a nice cut contour. Then a new mesh cutting algorithm
is developed based on the constrained random walks plus the optimization
process. Within the same computational framework, the new algorithm provides
a novel user interface for interactive mesh cutting that supports three
typical user inputs and also their combinations: 1) foreground/background
seed inputs: the user draws strokes specifying seeds for “foreground” (i.e.,
the part to be cut out) and “background” (i.e., the rest); 2) soft
constraint inputs: the user draws strokes on the mesh indicating the region
which the cuts should be made nearby; and 3) hard constraint inputs: the
marks which the cutting contour must pass. The algorithm uses feature
sensitive metrics that are based on surface geometric properties and
cognitive theory. The integration of the constrained random walks algorithm,
the optimization process, the feature sensitive metrics and the varieties of
user inputs makes the algorithm intuitive, flexible, and effective as well.
The experimental examples show that the proposed cutting method is fast,
reliable, and capable of producing good results reflecting user intention
and geometric attributes. 

W.Yang, J.Cai, J. Zheng,
J. Luo
(2010)
"Userfriendly interactive image segmentation through unified combinatorial
user inputs"
IEEE Transactions on
Image Processing, Vol.19, No.9, pp 24702479.
One weakness in the existing interactive image
segmentation algorithms is the lack of more intelligent ways to understand
the intention of user inputs. In this paper, we advocate the use of multiple
intuitive user inputs to better reflect a user's intention. In particular,
we propose a constrained random walks algorithm that facilitates the use of
three types of user inputs: (1) foreground and background seed input, (2)
soft constraint input, and (3) hard constraint input, as well as their
combinations. The foreground and background seed input allows a user to draw
strokes to specify foreground and background seeds. The soft constraint
input allows a user to draw strokes to indicate the region that the boundary
should pass through. The hard constraint input allows a user to specify the
pixels that the boundary must align with. Our proposed method supports all
three types of user inputs in one coherent computational framework
consisting of a constrained random walks and a local editing algorithm,
which allows more precise contour refinement. Experimental results on two
benchmark data sets show that the proposed framework is highly effective and
can quickly and accurately segment a wide variety of natural images with
ease.


W. Guan, J.Cai, J.Zhang, J. Zheng
(2010)
"Progressive
coding and illumination and view dependent transmission of 3D meshes using
RD optimization"
IEEE Transactions on Circuits
and Systems for Video Technology, Vol.20, No.4, pp 575586.
For transmitting
complex 3D models over bandwidthlimited networks, efficient mesh coding and
transmission are indispensable. The stateoftheart 3D mesh transmission
system employs waveletbased progressive mesh coder, which converts an
irregular mesh into a semiregular mesh and directly applies the zerotreelike
image coders to compress the wavelet vectors, and viewdependent
transmission, which saves the transmission bandwidth through only delivering
the visible portions of a mesh model. We propose methods to improve both
progressive mesh coding and transmission based on thorough ratedistortion
(RD) analysis. In particular, by noticing that the dependency among the
wavelet coefficients generated in remeshing is not being considered in the
existing approaches, we propose to introduce a preprocessing step to scale
up the wavelets so that the inherent dependency of wavelets can be truly
understood by the zerotreelike image compression algorithms. The weights
used in the scaling process are carefully designed through thoroughly
analyzing the distortions of wavelets at different refinement levels. For
the transmission part, we propose to incorporate the illumination effects
into the existing viewdepend progressive mesh transmission system to
further improve the performance. We develop a novel distortion model that
considers both illumination distortion and geometry distortion. Based on our
proposed distortion model, given the viewing and lighting parameters, we are
able to optimally allocate bits among different segments in real time.
Simulation results show significant improvements in both progressive
compression and transmission. 

W.Yang, J. Zheng,
J.Cai, S.Rahardja, C.Chen
(2009)
"Natural
and seamless image composition with color control"
IEEE Transactions on
Image Processing, Vol.18. No.11, pp 25842592.
While the
stateoftheart image composition algorithms subtly handle the object
boundary to achieve seamless image copyandpaste, it is observed that they
are unable to preserve the color fidelity of the source object, often
require quite an amount of user interactions, and often fail to achieve
realism when there exists salient discrepancy between the background
textures in the source and destination images. These observations motivate
our research towards color controlled natural and seamless image composition
with least user interactions. In particular, based on the Poisson image
editing framework, we first propose a variational model that considers both
the gradient constraint and the color fidelity. The proposed model allows
users to control the coloring effect caused by gradient domain fusion.
Second, to have less user interactions, we propose a distanceenhanced
random walks algorithm, through which we avoid the necessity of accurate
image segmentation while still able to highlight the foreground object.
Third, we propose a multiresolution framework to perform image compositions
at different subbands so as to separate the texture and color components to
simultaneously achieve smooth texture transition and desired color control.
The experimental results demonstrate that our proposed framework achieves
better and more realistic results for images with salient background color
or texture differences, while providing comparable results as the
stateoftheart algorithms for images without the need of preserving the
object color fidelity and without significant background texture
discrepancy.


W. Guan, J. Cai, J. Zheng,
C.W.Chen
(2008)
"Segmentationbased
viewdependent 3D graphics model transmission"
IEEE Transactions on
Multimedia, Vol.10. No.5, pp 724734.
For wireless
network based graphics applications, a key challenge is how to efficiently
transmit complex 3D models over bandwidthlimited wireless channels. Most
existing 3D mesh transmission systems do not consider such a viewdependent
delivery issue, and thus transmit unnecessary portions of 3D mesh models,
which leads to the waste in precious wireless network bandwidth. In this
paper, we propose a novel viewdependent 3D model transmission scheme,
where a 3D model is partitioned into a number of segments, each segment is
then independently coded using the MPEG4 3DMC coding algorithm, and finally
only the visible segments are selected and delivered to the client.
Moreover, we also propose analytical models to find the optimal number of
segments so as to minimize the average transmission size. Simulation results
show that such a viewbased 3D model transmission is able to substantially
save the transmission bandwidth and therefore has a significant impact on
wireless graphics applications.


J. Zheng, Y.Y. Cai (2006)
"Interpolation
over arbitrary topology meshes using a twophase subdivision scheme"
IEEE Transactions on Visualization
and Computer Graphics, Vol.12. No.3, pp 301310.
This paper presents a twophase process, based on a topological modification of the control mesh and a subsequent
CatmullClark subdivision, to construct a smooth surface that interpolates some or all of the vertices of a mesh with arbitrary topology. It is also possible to constrain the surface to have specified tangent planes at an arbitrary subset of the vertices to be
interpolated. The method has following features: (1) it is guaranteed to always work and the computation is numerically stable; (2) there is no need to solve a system of linear equations and the whole
computation complexity is O(K) where K is the number of the vertices; and (3) each vertex can be associated with a scalar shape handle for local shape control. These features make interpolation using
CatmullClark surfaces simple and thus make the new method itself suitable for interactive freeform shape design.



CAGD/CAD 



T.Sederberg, J.Zheng (2015)
"Birational
quadrilateral maps"
Computer Aided Geometric Design, Vol. 32, No.1, pp 14.
A generic planar
quadrilateral defines a 2:1 bilinear map. We show that by assigning an
appropriate weight to one vertex of any planar quadrilateral, we can create a
map whose inverse is rational linear.


X. Yang, J. Zheng (2013)
"Curvature tensor computation by piecewise surface interpolation"
ComputerAided Design,
Vol.45, No.12, pp 16391650.
Estimating
principal curvatures and principal directions of a subjacent, unknown, smooth
surface represented by a triangular mesh is an important step in computer aided
design and graphics applications. This paper presents a new method for curvature
tensor estimation on a triangular mesh by replacing flat triangles with
triangular parametric patches and computing Taubin integrala 3x3 symmetric
matrix in integral formulationbased on the parametric patches. Principal
curvatures and principal directions are then computed from Taubin integral. The
method has two novel technical ingredients: (1) a closed form expression of
Taubin integral is derived; and (2) an explicit scheme is developed for
constructing a cubic triangular Bezier patch from a triangle with three corner
normals, which interpolates the three corner positions and normals with its
boundary curves having local cylindrical precision at their two endpoints. All
the computations in the new method are direct in closed form, and except for the
approximation of the subjacent surface by piecewise interpolating patches, all
other calculations are exact. These features make the new method accurate,
efficient and robust.


Y. Wang, J. Zheng (2013)
"Curvatureguided adaptive Tspline surface fitting"
ComputerAided Design,
Vol.45, No.89, pp 10951107.
The problem of
fitting spline surfaces to triangular mesh models is of importance in
computeraided design. Many fitting algorithms have been developed. This paper
proposes several novel plugandplay components or strategies:
the use of
Tsplines
for fitting, a curvatureguided strategy, faithful reparameterization and
initial spline knot replacement, which can
be used to enhance fitting algorithms. An adaptive
Tspline
fitting algorithm integrating these components and strategies is also presented.
The fitting algorithm can generate spline surfaces that well respect the
geometrical features of input mesh models and have a more compact
representation..


J. Pan, J. Zheng, G.Zhao (2013)
"Blind watermarking of NURBS curves and surfaces"
ComputerAided Design,
Vol.45, No.2, pp 144153.
This paper presents
two watermarking methods for NURBS curves and surfaces. Both methods are blind,
shapepreserving and data amountpreserving. These features are often required
in watermarking of CAD models. The first method is based on the replacement of
exterior knots of NURBS. Watermarks are embedded into the crossratio of four
knots in the knot vector(s) and the method is robust to affine transformation,
Möbius reparameterization, and interior knot insertion and removal operations.
The second method is based on reparameterization using Möbius transformation.
Watermarks are embedded into the ratio of two knot intervals selected from the
knot vector(s) and the method is robust to affine transformation and linear
reparameterization. The capacity of the first method is
m−1
for a degree
m
NURBS curve and
m+n−2
for a degree
m×n
NURBS surface, and the capacity of the second method is 1 for a curve and 2 for
a surface. Experiments have been conducted to demonstrate the shapepreserving,
data amountpreserving properties and robustness.


X. Yang, J. Zheng (2012)
"Approximate Tspline surface skinning"
ComputerAided Design,
Vol.44, No.12, pp 12691276.
This paper
considers the problem of constructing a smooth surface to fit rows of data
points. A special class of
Tspline
surfaces is examined, which is characterized to have a global knot vector in one
parameter direction and individual knot vectors from row to row in the other
parameter direction. These
Tspline
surfaces are suitable for lofted surface interpolation or approximation. A
skinning algorithm using these
Tspline
surfaces is proposed, which does not require the knot compatibility of sectional
curves. The algorithm consists of three main steps: generating sectional curves
by interpolating data points of each row by a
Bspline
curve; computing the control curves of a skinning surface that interpolates the
sectional curves; and approximating each control curve by a
Bspline
curve with fewer knots, which results in a
Tspline
surface. Compared with conventional
Bspline
surface skinning, the proposed
Tspline
surface skinning has two advantages. First, the sectional curves and the control
curves of a
Tspline
surface can be constructed independently. Second, the generated
Tspline
skinning surface usually has much fewer control points than a lofted
Bspline
surface that fits the data points with the same error bound. Experimental
examples have demonstrated the effectiveness of the proposed algorithm.


X. Li, J. Zheng (2012)
"An alternative method
for constructing interpolatory subdivision from approximating subdivision"
Computer Aided Geometric Design,
Vol.29, pp 474484.
This paper presents
a new perspective for constructing interpolatory subdivision from primal
approximating subdivision. The basic idea is constructing the subdivision rule
for new inserted vertices of a new interpolatory subdivision scheme based on an
approximating subdivision algorithm applied to a local configuration of the mesh
with one vertex updated for interpolation of the vertex. This idea is
demonstrated by presenting two new interpolatory subdivision schemes based on
Catmull–Clark subdivision for an arbitrary polygonal mesh and Loop subdivision
for a triangular mesh, respectively. These algorithms are simple and have a
small stencil for computing new points. The new perspective also shows a link
between those classic approximating and interpolatory subdivision algorithms
such as cubic Bspline curve subdivision and the fourpoint interpolatory
subdivision, Catmull–Clark subdivision and Kobbelt's interpolatory scheme, and
Loop subdivision and the butterfly algorithm.


X. Li, J. Zheng, T. Sederberg,
T.Hughes, M.Scott (2012)
"On
linear independence of Tspline blending functions"
Computer Aided Geometric Design,
Vol.29, No.1, pp 6376.
This paper shows
that, for any given Tspline, the linear independence of its blending functions
can be determined by computing the nullity of the TsplinetoNURBS transform
matrix. The paper analyzes the class of Tsplines for which no perpendicular
Tnode extensions intersect, and shows that the blending functions for any such
Tspline are linearly independent. 

P. Chiang, J. Zheng, K. Mak,
N.Thalmann, Y.Cai (2012)
"Progressive
surface reconstruction for heart mapping procedure"
ComputerAided Design,
Vol.44, No.4, pp 289299.
The composite
imaging of measured cardiac properties on a reconstructed endocardial surface
allows for the diagnosis of cardiac arrhythmia and myocardial infarct. This
paper presents a new method for the progressive reconstruction of an endocardial
surface during a heart mapping procedure. A generic mesh is first aligned with a
set of anchor points to obtain a first approximation of the surface. Subsequent
deformations are constrained by the preservation of local surface
characteristics and the fidelity of new contract points. The mesh is refined by
local subdivision and its geometrical shape is further improved by edge
swapping. Compared to prior art, the new method can reconstruct a realistic
surface from a set of sparse and random data. It can advantageously provide a
smooth reconstruction at initial acquisition and ensure a geometrical
consistency between consecutive reconstructions. The accurate reconstruction of
a heart chamber provides important visual cues for an interventionalist to
decide on the next mapping site, thus constructively influencing the final
diagnosis. 

W. Chen, J. Zheng,
Y.Cai
(2010)
"Kernel modeling for molecular surfaces using a uniform solution"
ComputerAided Design,
Vol 42, No.4, pp 267278.
This paper
proposes to use rational Bézier surfaces as a uniform approach to model all
three types of molecular surfaces: van der Waals surface, solvent accessible
surface and solvent excluded surface. The solution consists of three steps:
topology modeling, boundary modeling and surface modeling. First, using
weighted
αshape, topology modeling creates two networks to describe the
neighboring relationship of the molecular atoms. Second, boundary modeling
derives all boundary arcs from the networks. Third, surface modeling
constructs all three types of molecular surfaces patchbypatch based on the
networks and the boundary arcs. For SES, the singularity is specially
treated to avoid selfintersections. Instead of approximation, the proposed
solution can produce precise shapes of molecular surfaces. Since rational
Bézier representation is much simpler than trimmed NURBS, computational load
can be significantly saved when dealing with molecular surface modeling.
This research shows that the rational Bézier representations, more
specifically, bicubic or 2×4 rational Bézier surfaces, are sufficient for
kernel modeling of molecular surfaces and related applications. 

J. Zheng (2005)
"Minimizing
the maximal ratio of weights of a rational Bezier curve"
Computer Aided Geometric Design, Vol.
22, No. 3, pp 275280
This paper presents
a solution to the problem of reparameterizing a rational curve by a Moebius
transformation such that the maximal ratio of weights in the reparameterized
representation is minimized. The problem is reduced to solving a linear
programming problem, which can be solved directly and simply. The result can be
used to reparameterize rational curves so as to yield tight bounds on
derivatives.


W.Li, S.Xu, J.Zheng, G.Zhao
(2004)
"Target
curvature driven fairing algorithm for planar cubic Bspline curves"
Computer Aided Geometric Design, Vol. 21., No.5., pp.499513.
This paper proposes
to use target curvature plots to identify bad points or bad curve segments of a
given Bspline curve. Then the control points of the curve are modified by a
local constrained optimization, which involves the shape fairness and the
coherence to the original design. The target curvature plots are prescribed by
designers according to their design intention.


X.Song, T.Sederberg, J.Zheng, R.Farouki, J.Hass
(2004)
"Linear
perturbation methods for topologically consistent representations of freeform
surface intersection"
Computer Aided Geometric Design, Vol. 21, No.3.
By applying
displacement maps to slightly perturb two freeform surfaces, one can ensure exact
agreement between the images in R^3
of parameterdomain approximations to their curve of intersection. Thus, at the
expense of slightly altering the surfaces in the vicinity of their intersection,
a perfect matching of the surface trimming curves is guaranteed. This exact
agreement of contiguous trimmed surfaces is essential to achieving topologically
consistent solid model constructions through Boolean operations, and has a
profound impact on the efficiency and reliability of applications such as
meshing, rendering, and computing volumetric properties.


T. Sederberg, J. Zheng, Song
X. (2004)
"A conjecture on tangent
intersections of surface patches"
Computer Aided Geometric Design,
Vol.21, No.1
This paper provides
some evidences to show that if two surface patches intersect with G^{1}
continuity along an entire curve, the probability is one that the curve is
rational. This idea has significance for surface intersection algorithms. 

J. Zheng, T. Sederberg (2003)
"Gaussian and mean curvatures of rational Bezier patches"
Computer Aided Geometric Design, Vol. 20, No. 6, pp 297301
This paper derives
formulae for Gaussian and mean curvatures for rational Bézier surface patches.
The formulae are expressed in terms of simple geometric quantities (lengths and
areas) obtained from the control mesh. These formulae provide more geometric
intuition and are easier to compute than the generic formulae from differential
geometry. Both the tensor product and triangular patch cases are addressed. 

T. Sederberg, J. Zheng, Song
X. (2003)
"Knot intervals and multidegree
splines"
Computer Aided Geometric Design,
Vol.20, No.7, pp 455468.
This paper studies the merits of using knot interval notation for Bspline
curves. Using knot interval notation, the paper introduces MDsplines, which are
Bsplinelike curves that are comprised of polynomial segments of various
degrees (MD stands for "multidegree"). The paper focuses on MDsplines
of degree 1, 2, and 3, as well as degree 1 and n.


Chen F., J. Zheng, T. Sederberg (2001)
"The
mubasis of a rational ruled
surface"
Computer Aided Geometric Design,
Vol.18, No.1, pp 6172.
This
paper presents a simple
algorithm for computing the mubasis for a rational ruled
surface. The mubasis consists of two polynomials p(x,y,z,s)
and q(x,y,z,s) that are linear in x,y,z
and degree mu
and mmu
in s respectively, where m is the degree of the implicit equation.
The implicit equation of the surface is then obtained by merely taking the
resultant of p and q with respect to s. This
implicitization algorithm is faster and/or more robust than previous methods. 

J. Zheng, Wang G.Z., Liang Y. (1995)
"GC^{n} continuity conditions for
adjacent rational parametric surfaces"
Computer Aided Geometric Design,
Vol.12, No.2, pp 111129. This
paper derives the constraints on the homogeneous surface belonging to a certain
rational surface that are both necessary and sufficient to ensure
that the rational surface is nthorder geometric continuous. This gives
up the strong restriction that requires the homogeneous surface to be as smooth
as the rational surface. Further the conditions for the rectangular rational Bézier
patches are developed, and some simple and practical sufficient conditions are
presented which might give a valid means for the construction of GC^{n}
connecting surfaces.


J. Zheng, Wang G.Z., Liang Y. (1992)
"Curvature continuity between
adjacent rational Bezier patches"
Computer Aided Geometric Design,
Vol.9, No.5, pp 321335.
This paper discusses
the curvature continuity between two adjacent rational Bézier surfaces. The necessary and sufficient
conditions are derived, and further, a series of simple sufficient conditions
are developed. With them one can both check the geometric continuity between two
surfaces and construct a rational surface possessing curvature continuity with a
given rational patch along a certain boundary. 


Others




W.Zhang, J. Zheng, N.Magnenat
Thalmann (2015)
"Realtime subspace integration for examplebased elastic material"
Computer Graphics Forum (EUROGRAPHICS
2015), Vol.34, No.2.
Examplebased material allows simulating complex material
behaviors in an artdirected way. This paper presents a method for fast subspace
integration for examplebased elastic material, which is suitable for realtime
simulation in computer graphics. At the core of the method is the formulation of
a new potential using examplebased Green strain tensors. By using this
potential, the deformation can be attracted towards the examplebased
deformation feature space, the example weights can be explicitly obtained and
the internal force can be decomposed into the conventional one and an additional
one induced by the examples. The realtime subspace integration is then
developed with subspace integration costs independent of geometric complexity,
and both the reduced conventional internal force and additional one being cubic
polynomials in reduced coordinates. Experiments demonstrate that our method can
achieve realtime simulation while providing comparable quality with the prior
art.


C. Chen, J.Cai, J. Zheng, T.
Cham, G. Shi (2015)
"Kinect
depth recovery using a colorguided, regionadaptive, and depthselective
framework"
ACM Transactions on Intelligent
Systems and Technology, Vol.6, No.2, 2015.
Considering the existing depth recovery approaches have different limitations
when applying to Kinect depth data, in this paper, we propose to integrate their
effective features including adaptive support region selection, reliable depth
selection and color guidance together under an optimization framework for Kinect
depth recovery. In particular, we formulate our depth recovery as an energy
minimization problem, which solves the depth holefilling and denoising
simultaneously. The energy function consists of a fidelity term and a
regularization term, which are designed according to the Kinect characteristics.
Our framework inherits and improves the idea of guided filtering by
incorporating structure information and prior knowledge of Kinect noise model.
Through analysing the solution to the optimization framework, we also derive a
local filtering version which provides an efficient and effective way of
improving the existing filtering techniques.


Y.Zhang, J. Zheng, N.Magnenat
Thalmann (2014)
"Exampleguided anthropometric human body modeling"
The Visual Computer, 2014.
This paper presents an exampleguided, anthropometrybased
modeling method for creating 3D human body models from users’ input of partial
anthropometric measurements with a given example dataset. Rather than directly
forming a mapping between the partial measurements and the body model, we
first estimate a set of chosen 30 measurements from the input based on the
exampleoriented measurement analysis. We then create an initial 3D model using
the exampleoriented radial basis function model that maps the set of 30
measurements to the body shape space and is established based on the given
examples. We finally refine the 3D model by constrained optimization to create
the target body model. Our method has several advantages: (1) the created model
is guaranteed to match the input measurements and reflects the shape
characteristics of examples; (2) the input requirement is modest, which makes it
useful in practice; and (3) the information of both the measurements and
examples is fully utilized. We demonstrate the effectiveness, accuracy,
flexibility and extensibility of the method by various experimental evaluations
and a Kinectbased body customization application.


Q.Duan, J.Cai, J. Zheng (2014)
"Compressive environment matting"
The Visual Computer, 2014.
The existing highquality environment matting methods usually
require the capturing of a few thousand sample images and spend a few hours in
data acquisition. In this paper, a novel environment matting algorithm is
proposed to capture and extract the environment matte data effectively and
efficiently. First, the recently developed compressive sensing theory is
incorporated to reformulate the environment matting problem and simplify the
data acquisition process. Next, taking into account the special properties of
light refraction and reflection effects of transparent objects, two advanced
priors, group clustering and Gaussian priors, as well as other basic constraints
are introduced during the matte data recovery process to combat with the limited
image samples, suppress the effects of the measurement noise resulted from data
acquisition, and faithfully recover the sparse environment matte data. Compared
with most of the existing environment matting methods, our algorithm
significantly simplifies and accelerates the environment matting extraction
process while still achieving highaccurate composition results.


D.Xu, Q.Duan, J. Zheng,
J.Zhang, J. Cai, T.Cham (2014)
"Recovering
surface details under general unknown illumination using shading and coarse
multiview stereo"
IEEE Conference on Computer Vision
and Pattern Recognition (CVPR) 2014.
Reconstructing
the shape of a 3D object from multiview images under unknown, general
illumination is a fundamental problem in computer vision and high quality
reconstruction is usually challenging especially when high detail is needed.
This paper presents a total variation (TV) based approach for recovering surface
details using shading and multiview stereo (MVS). Behind the approach are our
two important observations: (1) the illumination over the surface of
an object tends to be piecewise smooth and (2) the recovery of surface
orientation is not sufficient for reconstructing geometry, which were previously
overlooked. Thus we introduce TV to regularize the lighting and use visual hull
to constrain partial vertices. The reconstruction is formulated as a constrained
TV minimization problem that treats the shape and lighting as unknowns
simultaneously. An augmented Lagrangian method is proposed to quickly solve the
TVminimization problem. As a result, our approach is robust, stable and is able
to efficiently recover high quality of surface details even starting with a
coarse MVS. These advantages are demonstrated by the experiments with synthetic
and real world examples.


Y.Li, W.Chen, Y.Cai, A.Nasri, J. Zheng (2015)
"Surface
skinning using periodic Tspline in semiNURBS form"
Journal of Computational and
Applied Mathematics, Vol.273. pp.116131, Jan 2015.
NURBS skinning is
a powerful and effective process in Computer Aided Geometric Design. It
constructs a surface by interpolating a set of cross sectional NURBS curves.
These curves however may not be compatible, i.e., they have different knot
vectors. This incompatibility is conventionally solved by knot refinement
bringing all curves to share the same knot vector, which leads to an explosion
in the number of control points defining the skinned surface. Another
disadvantage of NURBS skinning is the difficulty of local modification:
adjusting one cross section may result in a global change of the surface. In
this paper, we present a method for surface skinning using periodic
Tsplines,
which is able to handle closed cross sections, support local modifications and
control smoothness along the cross sectional curves. We provide explicit
formulae for constructing such
Tspline
skinned surfaces, which avoid solving a large system of equations. Experimental
results and theoretical analysis confirm that our approach is better than NURBS
skinning as it generates surfaces with fewer control points.


P.Song, C.W.Fu, P.Goswami, J. Zheng, N.Mitra, D.CohenOr (2014)
"An
interactive computational design tool for large reciprocal frame structures"
Nexus Network Journal,
Vol.16, No.1, pp.109118, 2014.
This paper presents
the detail of our interactive tool for designing reciprocal frame (RF)
structures. In general, our tool addresses the RF design problem with three
major steps: (1) it supports the design of RFtessellation by connecting RF
patterns and plane tiling; (2) it delivers interactive preview and exploration
of RF designs in 3D space through conformal mapping; and (3) it performs a novel
optimization method to arrange the rods in the RFstructures, so that we can
ensure rod collinear contacts in the structures. This paper supplements our
previous work with implementation details, user interface design and operations,
as well as a preliminary study and various new results we devised from the tool.


X.Yang, J. Zheng, D.Wang (2014)
"A
computational approach to joint line detection on triangular meshes"
Engineering with Computers,
Vol.30, No.4, pp.583597.
This paper presents formulae for evaluating
differential quantities at vertices of triangular meshes that may approximate
potential piecewise smooth surfaces with discontinuous normals or discontinuous
curvatures at the joint lines. We also define the C^{1}
and C^{2} discontinuity
measures for surface meshes using changing rates of onesided curvatures or
changing rates of curvatures across mesh edges. The curvatures are computed
discretely as of local interpolating surfaces that lie within a tolerance to the
mesh. Together with proper estimation of local shape parameters, the obtained
discontinuity measures own properties like sensitivity to salient joint lines
and being scale invariant. A simple algorithm is finally developed for detection
of C^{1} or
C^{2} discontinuity
joint lines on triangular meshes with even highly nonuniform triangulations.
Several examples are provided to demonstrate the effectiveness of the proposed
method.


T.Nguyen, J.Cai, J. Zheng,
J.Li (2013)
"Interactive object segmentation from multiview images"
Journal of Visual Communication
and Image Representation, Vol.24, No.4, pp 477485.
This paper
presents a nontrivial solution to the following problem: given a set of
calibrated or uncalibrated multiview images, by interactively cutting 3 to 4
images, can the foreground object of the rest images be quickly cutout
automatically and accurately? Our idea is to integrate 3D segmentation with 2D
segmentation so as to combine their advantages. Our proposed system iteratively
performs 2D and 3D segmentation, where the 3D segmentation results are used to
initialize 2D segmentation and ensure the silhouette consistency among different
views and the 2D segmentation results are used to provide more accurate cues for
the 3D segmentation. The experimental results show that the proposed system is
able to generate highly accurate segmentation results, even for some challenging
realworld multiview image sequences, with a small amount of user input.


H.Zhou, J. Zheng, L.Wei (2013)
"Texture
aware image segmentation using graph cuts and active contours"
Pattern Recognition, Vol.46.
No.6, pp 17191733.
The problem of segmenting a foreground object out
from its complex background is of great interest in image processing and
computer vision. Many interactive segmentation algorithms such as graph cut have
been successfully developed. In this paper, we present four technical components
to improve graph cut based algorithms, which are combining both color and
texture information for graph cut, including structure tensors in the graph cut
model, incorporating active contours into the segmentation process, and using a
"softbrush" tool to impose soft constraints to refine problematic boundaries.
The integration of these components provides an interactive segmentation method
that overcomes the difficulties of previous segmentation algorithms in handling
images containing textures or low contrast boundaries and producing a smooth and
accurate segmentation boundary. Experiments on various images from the Brodatz,
Berkeley and MSRC data sets are conducted and the experimental results
demonstrate the high effectiveness of the proposed method to a wide range of
images.


X.Wu, J. Zheng, C.Wu, Y.Cai (2013)
"Variational structuretexture image decomposition on manifolds "
Signal Processing 93(7):
17731784, 2013.
This paper considers the problem of decomposing an
image defined on a manifold into a structural component and a textural
component. We formulate such decomposition as a variational problem, in which
the total variation energy is used for extracting the structural part and based
on the properties of texture one of three norms, L^{2}, L^{1}
and G, is used in the fidelity term for the textural part. We develop
efficient numerical methods to solve the proposed variational problems using
augmented Lagrangian methods (ALM) when the manifold is represented by a
triangular mesh. The contributions of the paper are twofold: (1) We adapt the
variational structure–texture image decomposition to manifolds, which takes the
intrinsic property of manifolds into account. The nonquadratic fidelity terms
with L^{1} and G norms are extended to 3D triangular
meshes for the first time. (2) We show how to efficiently tackle the variational
problems with nonlinearity/nondifferentiability terms by iteratively solving
some subproblems that either have closed form solutions or are to solve linear
equations.


X.Li, J. Zheng (2013)
"Interproximate curve subdivision"
Journal of Computational and
Applied Mathematics, Vol.244. pp.3648, May 2013.
This paper presents a new curve subdivision
algorithm called interproximate subdivision for generating curves that
interpolate some given vertices and approximate the other vertices. By the
interproximate subdivision, only the vertices specified to be interpolated are
fixed and the other vertices are updated at each refinement step. The refinement
rules are derived to ensure that the eigenvalues of the refinement matrix
satisfy the necessary condition of
C^{2}
continuity. The interproximate subdivision also contains tension parameters
assigned to vertices or edges for shape adjustment. Compared to the 4point
interpolatory subdivision scheme, the interproximate subdivision does not force
the new inserted vertices to be interpolated and is thus expected to have
improved behavior; and compared to the cubic
Bspline
refinement scheme, the interproximate subdivision is able to generate curves
interpolating userspecified vertices. In addition, the paper also presents two
extensions of the interproximate subdivision: one automatically adapts the
tension parameters locally according to the geometry of the control polygon
during the refinement to achieve convexity preservation and the other
automatically relaxes the interpolating property of some vertices to achieve
better shape behavior.


P. Chiang, Y.Cai, K. Mak,
J. Zheng (2013)
"A
Bspline approach to phase unwrapping in tagged cardiac MRI for motion tracking"
Magnetic Resonance in Medicine 69:
12971309, 2013.
A novel BSpline
based approach to phase unwrapping in tagged magnetic resonance images is
proposed for cardiac motion tracking. A bicubic Bspline is used to model the
absolute phase. The phase unwrapping problem is formulated as a mixed integer
optimization problem that minimizes the sum of the difference between the
spatial gradients of absolute and wrapped phases, and the difference between the
rewrapped and wrapped phases. In contrast to the existing techniques for motion
tracking, the proposed approach can overcome the limitation of interframe
halftag displacement and increase the robustness of motion tracking. The paper
further presents a hybrid harmonic phase imagingBspline method to take the
advantage of the harmonic phase imaging method for small motion and the
efficiency of the BSpline approach for large motion. The proposed approach has
been successively applied to a full set of cardiac MRI scans in both long and
short axis slices with superior performance when compared with the harmonic
phase imaging and quality guided pathfollowing methods.


P. Chiang, J. Zheng, Y.Yu, K. Mak,
C.Chui, Y.Cai (2013)
"A VR
simulator for intracardiac intervention"
IEEE Computer Graphics and
Applications,
Vol.33, No.1, pp 4457, 2013.
The process of
learning diagnosis and minimally invasive treatment of heart diseases takes
substantial time due to the complex nature of the diseases and the high skill
set required to manipulate surgical devices, especially in percutanous
intracardiac cases. We are interested to develop a novel simulator to create a
realistic and lowcost training environment for intracardiac intervention. This
paper focuses on the concept, design and implementation of a Virtual Reality (VR)
simulator for intracardiac intervention. Instead of using traditional Finite
Element Method (FEM), a new geometricalbased method is proposed to model the
interaction between an intracardiac catheter and the heart wall. A
boundaryenhanced voxelization technique is developed to accelerate the process
for detecting catheterheart interactions. A tactile interface is designed
incorporating a VR catheter unit to track the catheter movement within the
virtual heart. A progressive approach is implemented to reconstruct the heart
chamber for the application of heart mapping.


X. Yang, J. Zheng (2013)
"Shape
aware normal interpolation for curved surface shading from polyhedral
approximation "
The Visual Computer, Vol. 29
(3): 189201, 2013.
Independent
interpolation of local surface patches and local normal patches is an efficient
way for fast rendering of smooth curved surfaces from rough polyhedral meshes.
In this paper, we present two schemes based on the Gregory normal patch or the
sidevertex interpolating normal for normal interpolation along with cubic
Bezier triangles for rendering curved surfaces from rough triangular meshes.
Compared to the previous quadratic normal interpolation method, the proposed two
methods can generally produce more realistic shading results for rendering rough
triangular meshes.


H.Zhou, J. Zheng, X.Yang (2012)
"Euler arc splines for curve completion"
Computers &
Graphics, Vol.36.
No.6, pp.642650.
This paper introduces a special arc spline called an Euler arc
spline as the basic form for visually pleasing completion curves. It is
considered as an extension of an Euler curve in the sense that the points in the
Euler curve are replaced by arcs. A simple way for specifying it, which is
suitable for shape completion, is presented. It is shown that Euler arc splines
have several properties desired by aesthetics of curves, in addition to
computational simplicity and NURBS representation. An algorithm is proposed for
curve completion using Euler arc splines. The development of the algorithm
involves two optimization processes, which are converted into a single
minimization problem in two variables solved by the LevenbergMarquardt
algorithm. Compared to previous methods, the proposed algorithm always
guarantees the interpolation of two boundary conditions.


A. Nasri, K.Sinno, J. Zheng (2012)
"Local Tspline surface skinning "
The Visual Computer, Vol. 28.,
No.68, pp 787797.
Skinning is a
process of generating a surface from a set of given curves. In the interpolating
approach, the incompatibility of the input NURBS curves are solved by knot
insertion, which often leads to an explosion in the number of control points
defining the skinned surface. In this paper, we present a solution to this
problem using Tsplines. Compared to existing approaches, a Tspline skinned
surface interpolates a set of incompatible curves with a control mesh of fewer
vertices. Moreover, our approach is a local construction.


Q.Duan, J. Zheng, J.Cai (2011)
"Flexible
and accurate transparentobject matting and compositing using refractive vector
field"
Computer
Graphics Forum, Vol.30. No.6, pp 18121824.
In digital image editing, environment matting and compositing are
fundamental and interesting operations that can capture and simulate the
refraction and reflection effects of light from an environment. The
stateoftheart realtime environment matting and compositing method is short
of flexibility, in the sense that it has to repeat the entire complex matte
acquisition process if the distance between the object and the background is
different from that in the acquisition stage, and also lacks accuracy, in the
sense that it can only remove noises but not errors. In this paper, we introduce
the concept of refractive vector and propose to use a refractive vector field as
a new representation for environment matte. Such refractive vector field
provides great flexibility for transparentobject environment matting and
compositing. Particularly, with only one process of the matte acquisition and
the refractive vector field extraction, we are able to composite the transparent
object into an arbitrary background at any distance. Furthermore, we introduce a
piecewise vector field fitting algorithm to simultaneously remove both noises
and errors contained in the extracted matte data. Experimental results show that
our method is less sensitive to artifacts and can generate perceptually good
composition results for more general scenarios.


W.Chen, R.Yu, J. Zheng, Y.Cai,
C.Au (2011)
"Triangular
Bezier subsurfaces on a triangular Bezier surface"
Journal of Computational and
Applied Mathematics, Vol.235. No.17, pp.50015016.
This paper considers the problem of computing the Bezier
representation for a triangular subpatch on a triangular Bezier surface. The
triangular subpatch is defined as a composition of the triangular surface and a
domain surface that is also a triangular Bezier patch. Based on de Casteljau
recursions and shifting operators, previous methods express the control points
of the triangular subpatch as linear combinations of the construction points
that are constructed from the control points of the triangular Bezier surface.
The construction points contain too many redundancies. This paper derives a
simple explicit formula that computes the composite triangular subpatch in
terms of the blossoming points that correspond to distinct construction points
and then an efficient algorithm is presented to calculate the control points of
the subpatch.


P.Chiang, Y.Cai, K.Mak, E.Soe, C.
Chui, J. Zheng (2011)
"A
geometric approach to the modeling of the catheterheart interaction for VR
simulation of intracardiac intervention"
Computers &
Graphics, Vol.35. No.5, pp.10131022.
Cardiac intervention is a minimally invasive diagnostic and
therapeutic procedure used to treat cardiac diseases. The mapping of heart
geometry with minimal visual assistance presents a technical challenge for
interventional cardiologists attempting catheter navigation. This paper presents
a geometric approach to modeling the catheterheart interaction for VR
simulations of catheter navigation within a heart chamber. Three types of
modeling are used to model the interaction between the catheter and the heart
wall: nonslip, pseudoslip and slip modeling. A twostep shape memory process
that minimizes the bending of and strain on the catheter is designed for
catheter deformation for nonslip or pseudoslip contact, and a progressive
group linkage bending process that constrains the catheter curvature and
position within the volume enclosure is designed for catheter deformation for
slip contact. The proposed model is consistent with the observations made during
the experiment. The model is able to deform the catheter in any freestate shape
within the volume enclosure and is independent of local motion increment. Thus,
it presents advantages in terms of complexity and realtime requirements.


J Zhang, J. Zheng, J. Cai (2010)
"A
diffusion approach to seeded image segmentation"
IEEE Conference on Computer Vision
and Pattern Recognition (CVPR) 2010, pp.21252132.
Seeded image
segmentation is a popular type of supervised image segmentation in computer
vision and image processing. Previous methods of seeded image segmentation treat
the image as a weighted graph and minimize an energy function on the graph to
produce a segmentation. In this paper, we propose to conduct the seeded image
segmentation according to the result of a heat diffusion process in which the
seeded pixels are considered to be the heat sources and the heat diffuses on the
image starting from the sources. After the diffusion reaches a stable state, the
image is segmented based on the pixel temperatures. To better control diffusion,
we propose to incorporate the attributes of the image into the diffusion
process, yielding an anisotropic diffusion method for image segmentation.


J. Zheng, Y. Wang (2010)
"Periodic
Tsplines and tubular surface fitting"
Curves and Surfaces 2010, pp.731746.
This paper discusses a special type of Tspline surfaces called
periodic Tsplines that are closed in one parameter direction, and their
application in tubular surface fitting. First, a global representation is
proposed for representing periodic Tsplines. This representation does not
require repeating control points, which facilitates surface fitting process.
Then, an algorithm for adaptively fitting periodic Tsplines to a tubular
triangular mesh that has the same topology as a cylinder is presented. The
resulting periodic Tspline is obtained respecting the geometric distribution of
the input mesh. The use of periodic Tsplines for tubular surface fitting has at
least two advantages: 1) adaptive fitting is easily achieved due to the local
refinement of Tsplines; 2) the algorithm avoids cutting the mesh to make it a
disk topologically for conventional Bspline fitting due to the periodic
representation and this overcomes the drawback of finding a good cutting path,
which is usually difficult.
.


J.Zhang, C.Wu, J.Cai, J. Zheng,
X.Tai
(2010)
"Mesh
snapping: robust interactive mesh cutting using fast geodesic curvature
flow"
Computer Graphics Forum
(Eurographics'2010), Vol.29, No.2, pp 517526.
This paper
considers the problem of interactively finding the cutting contour to
extract components from a given mesh. A geodesic curvature flow based
framework is proposed to solve this problem. Since in many cases the
meaningful cutting contour on a 3D mesh is locally shortest in the sense of
some weighted curve length, the geodesic curvature flow is an ideal tool for
our problem. It evolves the cutting contour to the nearby local minimum. We
should mention that the previous numerical scheme, discretized geodesic
curvature flow (dGCF) is too slow and has not been applied to mesh
segmentation. With a careful observation to dGCF, we devise here a fast
computation scheme called fast geodesic curvature flow (FGCF), which only
needs to solve a smaller and easier problem. The initial cutting contour is
generated by a variant of random walks algorithm, which is very fast and
gives reasonable cutting result with little user input. Experiment results
on the benchmark mesh segmentation data set show that our proposed framework
is robust to user input and capable of producing good results reflecting
geometric features and human shape perception. 

W. Chen, J. Zheng, Y. Cai (2010)
"Monge
mapping using hierarchical NURBS"
The Visual Computer, Vol. 26,
No.68, pp.779789.
In this paper,
Monge mapping technique is developed for detail and local shape modification of
NURBS represented geometry in 3D environment. Based on multiresolution and
refinement schemes, hierarchical NURBS (HNURBS) is investigated to design a
mechanism for the purpose of carrying localized geometric information. Monge
mapping on HNURBS patch can be easily performed via simple cut&paster
operation. Parametric control of the local shapes is developed to facilitate
easier and better 3D local modeling.


M. Hu, J. Feng, J. Zheng (2010)
"An
additional branch free algebraic Bspline curve fitting method"
The Visual Computer, Vol. 26,
No.68, pp.801811.
Algebraic curve fitting based on algebraic distance is simple,
but it has a disadvantage of inclining to a trivial solution. Researchers
therefore introduce some constraints into the objective function in order to
avoid the trivial solution. However, this often causes additional branches.
Fitting based on geometric distance can avoid additional branches, but it does
not offer sufficient fitting precision. In this paper we present a new algebraic
Bspline curve fitting method which combines both geometric distance and
algebraic distance. The method first generates an initial curve by a distance
field fitting that takes geometric distance as the objective function. Then
local topologypreserving calibrations based on algebraic distance are performed
so that each calibration doesn't produce any additional branches. In this way,
we obtain an additional branch free fitting result whose precision is close to
or even better than that produced by purely algebraic distance based methods.


C. Au, Y. Cai, J. Zheng, T.
Woo (2010)
"Orienting a protein model by crossing number to generate the characteristic
views for identification"
Computer Modeling in Engineering &
Sciences, Vol. 68, No.3, pp.221237.
A protein model
(such as a ribbon model) can be created from the atomic coordinates in the
protein data base files. These coordinates are obtained by Xray crystallography
or NMR spectroscopy with the protein arbitrarily oriented. As such, identifying
or comparing a novel structure with a known item using protein model in the
protein data base can be a timely process since a large number of
transformations may be involved. The identification efficiency will be improved
if the protein models are uniformly oriented. This paper presents an approach to
orient a protein model to generate the characteristic views with minimum and
maximum crossings respectively. The projection directions for these
characteristic views are determined by a set of crossing maps (Cmaps).
Reorientating the protein models in the protein data base to two characteristic
views will facilitate the process of identification.


Y.Wang, J. Zheng
(2010)
"Tubular triangular mesh parameterization and applications"
Journal of Visualization and
Computer Animation, Vol 21, No.2, pp 91102.
Triangular
meshes are a popular geometric representation for 3D models used in computer
graphics. Parameterization is a process that establishes a mapping between
the surface of a model and a suitable domain. This paper considers the
problem of parameterizing triangular meshes that have tubular shapes. Unlike
an open mesh that is of plane topological type, a tubular mesh gives rise to
some special issues in parameterization due to its mesh structure. This
paper presents an edgebased parameterization method, in which the edges
rather than the vertices of the mesh are treated as the target for
parameterization. It first parameterizes the edges on the two boundaries of
the tubular mesh, then parameterizes the internal edges based on the mean
value coordinates, and finally computes the parameters of the mesh vertices.
The method does not need cutting of the mesh. It improves conventional
cuttingbased algorithms, which cut the mesh to make it a disk
topologically, and overcomes the problems of cutting paths that are the
zigzag paths leading to suboptimal parameterizations and the difficulty in
finding good cutting paths. Some applications such as surface fitting and
texture mapping are also provided.


J. Zheng
(2009)
"C^{1}
NURBS representation of G^{1}
composite rational Bezier curves"
Computing, Vol.86. No2, pp
257268.
This paper is concerned with the
rerepresentation of a G^{1} composite rational Bezier curve.
Although the rational Bezier curve segments that form the composite curve
are G^1 continuous at their joint points, their homogeneous representations
may not be even C^{0} continuous in the homogeneous space. In this
paper, an algorithm is presented to convert the G^{1} composite
rational Bezier curve into a NURBS curve whose nonrational homogeneous
representation is C^{1} continuous in the homogeneous space. This
rerepresentation process involves reparameterization using Moebius
transformations, smoothing multiplication and parameter scaling
transformations. While the previous methods may fail in some situations, the
method proposed in this paper always works.


W. Chen, Y. Cai, J. Zheng
(2008)
"Constructing triangular meshes of minimal area"
ComputerAided Design and
Applications, Vol.5. No.14, pp.508518.
This paper is
concerned with the problem of constructing an aesthetically pleasing
triangular mesh with a given closed polygonal contour in three dimensional
space as boundary. Triangular meshes of minimal area from all triangular
meshes with the prescribed boundary are suggested as the candidates for this
problem. An iterative algorithm of constructing such a triangular mesh from
a given polygonal boundary is presented. Experimental examples show that the
proposed algorithm is reliable and effective. Some related theoretical
issues, possible extensions and applications are also discussed. 

I. Chandrasekaran, Y. Cai, C.Cao,
B. Lu, J. Zheng
(2007)
"Virtual
reality prototyping of biomolecules"
Virtual and Physical
Prototyping, Vol.2. No.1, pp.3749.
Modelling,
sharing and transmission of 3D graphics data of biomolecules are essential in many bio visualization tasks from
collaborative research and education to molecular simulation and drug
discovery. In the current paper, modelling and representing of biomolecular
structure for virtual and physical rapid prototyping is presented. Our aim
is to devise a uniform solution for visualizing, browsing, interacting and
prototyping of biomolecules in various environments including internet,
immersive virtual reality (VR), and rapid manufacturing. To do so, we use
non uniform rational Bspline surfaces (NURBS) to represent protein
secondary structure and surface structure. NURBS protein structures are then
tessellated to form biomolecular graphics models. Their triangular mesh
representation is next extracted from their scene graph. A geometric
optimization process is followed to make data compatible for their
formatting in compact and consistent VR standard to support protein internet
browsing, protein VR visualization, protein 3D rapid prototyping and crystal
subsurface laser engraving. 

Y.Y.Cai, B.Lu, J. Zheng, L.
Lin (2006)
"Immersive
protein gaming for bio edutainment"
Simulation and Gaming, Vol.37. No.4, pp.466275.
Learning
through playing is one of the natural ways for
knowledge and skill acquisition. Games have long been used as a tool for
education, from concept building to problem solving. Through fun learning,
students may further develop their curiosities and interest in their study. This paper addresses the issue of learning biomolecular
structures by Virtual Reality (VR) gaming. A bio edutainment system is developed
for protein structure learning. It consists of mainly three components: visualization, modeling and interaction, on top of various supporting
technologies such as Graphics and Networking. Via virtual reachin and handson,
students can interact with amino acid sequences, protein ahelices, bsheets and
other protein structural information.


J. Zheng, Y.Y. Cai (2005)
"Making
DooSabin surface interpolation always work over irregular meshes"
The Visual Computer, Vol.21,
No.4., pp 242251
This paper presents
a reliable method for constructing a control mesh whose DooSabin subdivision
surface interpolates the vertices of a given mesh with arbitrary topology. The
method improves on existing techniques in two respects: (1) it is guaranteed to
always work
for meshes of arbitrary topological type; (2) there is no need to solve a system
of linear equations to obtain the control points. Extensions to include normal
vector interpolation and/or shape adjustment are also discussed.


J. Zheng, T. Sederberg, R. Johnson
(2004)
"Least squares methods for solving
differential equations using Bezier control points"
Applied Numerical Mathematics,
Vol. 48, No.2
This paper investigates the use of the control points of the
Bernstein Bezier form for numerically solving differential equations. Two least squares
type schemes based on degree raising and subdivision are proposed. The convergence of the methods applied to twopoint boundary value
problems is analyzed.


J. Zheng, Wang G.Z. (2003)
"Perturbing Bezier coefficients for
best constrained degree reduction in L2norm"
Graphical Models, Vol.65,
No.6., pp 351368
This paper shows how the Bézier coefficients of a given degree n polynomial
are perturbed, based on minimizing a weighted Euclidean norm, so that it can be reduced to a degree m (<n)
polynomial with the constraint that continuity of a prescribed order is
preserved at the two endpoints. Then the paper proves that the problem of finding a best L_{2}approximation
over the interval [0,1] for constrained degree reduction is equivalent to that
of finding a minimum perturbation vector in a certain weighted Euclidean norm.
The relevant weights are derived.


J. Zheng, T. Sederberg,
Chionh E.W., D. Cox (2003)
"Implicitizing rational surfaces
with base points using the method of moving surface"
Topics in Algebraic Geometry and
Geometric Modeling, Contemporary Mathematics Series, Vol. 334, Ron
Goldman and Rimvydas Krasauskas, eds., AMS, pp 151168. ISBN 0821834207.
The method of moving planes and moving quadrics can express the
implicit equation of a parametric surface as the determinant of a matrix M.
The rows of M correspond to moving planes or moving quadrics that follow the
parametric surface. Previous papers on the method of moving surfaces have shown that a simple base point
has the effect of converting one moving quadric to a moving plane. A much more general version of the method of moving surfaces is
presented in this paper that is capable of dealing with multiple base points.
This is a unifying approach whereby tensor product surfaces, pure degree surfaces, and
"cornercut"
surfaces, can all be implicitized under the same framework and do not need to be treated as distinct cases. The central idea in this
approach is that if a surface has a base point of multiplicity k, the moving surface blending functions must have the same base
point, but of multiplicity k1. 

T. Sederberg, J. Zheng (2002)
"Algebraic methods for computer
aided geometric design"
Handbook of Computer Aided Geometric
Design, G. Farin, J. Hoschek, M.S. Kim, eds., Elsevier, NorthHolland,
pp.363387.
ISBN: 0444511040.
The concepts and methods of algebra and algebraic geometry have found
significant applications in many disciplines. This chapter presents a collection of
gleanings from algebra or algebraic geometry that
hold practical value for the field of computer aided geometric design. We focus on the insights, algorithm
enhancements and practical capabilities that algebraic methods have contributed to
CAGD. Specifically, we examine resultants and Gröbner basis, and discuss their
applications in implicitization, inversion, parametrization and intersection algorithms. Other topics of CAGD research work using algebraic methods
are also outlined. 

J. Zheng, T. Sederberg (2001)
"A direct approach to computing
the mubasis of planar rational curves"
Journal of Symbolic Computation,
Vol.31, No.5, pp 619629.
This paper presents
an O(n^{2}) algorithm, based on Gröbner basis techniques,
to compute the
basis of a degree n planar rational curve. The prior method involved
solving a set of linear equations whose complexity by standard numerical methods
was O(n^{3}). 

T. Sederberg, J. Zheng, K.
Klimaszewski,
T. Dokken (1999)
"Approximate implicitization using
monoid curves and surfaces"
Graphical Models and Image
Processing, Vol.61, No.4, pp 177198.
This paper presents an approach to finding an approximate implicit equation and
an approximate inversion map of a rational parametric curve or surface. High accuracy of the approximation is achieved with a
small number of lowdegree curve segments or surface patches. By
using monoid curves and surfaces, the method eliminates the undesirable
singularities and "phantom" branches normally associated with implicit
representation. The monoids are expressed in exact implicit and parametric
equations simultaneously, and upper bounds are derived for the approximate
errors.


Wang G.Z., J. Zheng (1997)
"Bounds on the moving control points
of hybrid curves"
Graphical Models and Image
Processing, Vol.59, No.1, pp 1925. This
paper provides several methods to
estimate the error bounds for the approximation to the moving control point of
the hybrid curves. When the given rational Bézier curves satisfies the
convergent conditions for moving control point of the hybrid curve, the polynomial Bézier curves
that approximate the rational Bézier curve can
be obtained by replacing the moving control point with the special point.





 