CHINESE JOURNAL OF MECHANICAL ENGINEERING
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Vol. 29,aNo. 6,a2016
DOI: 10.3901/CJME.2016.0720.084, available online at www.springerlink.com; www.cjmenet.com
Digital Relief Generation from 3D Models
WANG Meili1, SUN Yu1, ZHANG Hongming1, *, QIAN Kun2, CHANG Jian2, and HE Dongjian3
1 College of Information Engineering, Northwest A & F University, Yangling 712100, China
2 National Center for Computer Animation, Bournemouth University, Poole BH12 5BB UK
3 College of Mechanical and Electronic Engineering, Northwest A & F University,
Yangling 712100, China
Received May 12, 2016; revised July 15, 2016; accepted July 20, 2016
Abstract: It is difficult to extend image-based relief generation to high-relief generation, as the images contain insufficient height
information. To generate reliefs from three-dimensional (3D) models, it is necessary to extract the height fields from the model, but this
can only generate bas-reliefs. To overcome this problem, an efficient method is proposed to generate bas-reliefs and high-reliefs directly
from 3D meshes. To produce relief features that are visually appropriate, the 3D meshes are first scaled. 3D unsharp masking is used to
enhance the visual features in the 3D mesh, and average smoothing and Laplacian smoothing are implemented to achieve better
smoothing results. A nonlinear variable scaling scheme is then employed to generate the final bas-reliefs and high-reliefs. Using the
proposed method, relief models can be generated from arbitrary viewing positions with different gestures and combinations of multiple
3D models. The generated relief models can be printed by 3D printers. The proposed method provides a means of generating both
high-reliefs and bas-reliefs in an efficient and effective way under the appropriate scaling factors.
Keywords: high-relief, bas-relief, mesh enhancement, scaling
1
Introduction
Reliefs are sculptured artworks in which a modeled
shape is raised or lowered and usually attached to a planar
background[1]. There are three main types of relief:
high-reliefs, bas-reliefs, and sunken-reliefs. In a high-relief,
the raised sculpture is over 50% of the scale height of the
image being represented. Bas-reliefs, by comparison, are
much more compressed, and are suitable for scenes with
many figures, landscapes, or architectural backgrounds. In
sunken-reliefs, the figures are actually carved into the
surfaces.
Existing relief models created by artists involve complex
procedures. Once the relief models have been produced,
they are not easy to modify or maintain. Such reliefs also
only represent a single viewing point. However, animators
and artists prefer a digital relief—an object having the
characteristics of a real relief, but with the advantages of
being virtual. There are many 3D models in the public
domain that could be processed into reliefs that are easily
amended and refined. A system to produce digital reliefs
must allow for interactive design and generate standard 3D
* Corresponding author. E-mail: [email protected]
Supported by National Natural Science Foundation of China(Grant Nos.
61402374, 41301283), National Hi-tech Research and Development
Program of China(863 Program, Grant No. 2013AA10230402), and China
Postdoctoral Science Foundation
© Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2016
relief representations.
Previous relief generation research has mainly
considered bas-relief generation, which is very challenging.
For example, generating a bas-relief requires a 3D model to
be compressed into an almost flat plane while preserving
the details of the image and avoiding any distortion of the
shapes.
The general approach is to start with height field data or
a 3D model, and then apply image processing techniques to
produce the relief[2]. In this paper, we propose a method to
simultaneously generate digital high-reliefs and bas-reliefs
by setting different scaling factors. We develop a boosting
algorithm with different smoothing schemes to enhance the
geometrical details, and employ a nonlinear method to
scale the 3D meshes while preserving their features[3].
The remainder of this paper is organized as follows.
Section 2 reviews related work, both for image-based and
model-based techniques. Then a detailed mesh
enhancement and relief generation method is presented in
section 3. The output given by our method and the results
of a parameter test are presented in section 4. We conclude
the paper in section 5 with a discussion of some of the
advantages and limitations of our approach.
2
Related Work
Reliefs can be generated by direct modeling, images, and
3D models. Direct modeling requires special expertise and
CHINESE JOURNAL OF MECHANICAL ENGINEERING
is a labor-intensive process.
2.1 Bas-relief generation from images
A method of generating bas-reliefs from a pair of input
images using an iterative least-squares optimization to
reconstruct the relief surfaces proposed by ALEXA and
MATUSIK[4].
An algorithm for bas-relief generation from 2D images
with gradient operations, such as magnitude attenuation and
image enhancement, greatly improved the quality of the
relief[5]. A novel method for the digital modeling of basreliefs from a composite normal image was presented by JI,
et al[6], who composed several layers of normal images into
a single normal image. An image-based relief generation
method was designed especially for brick and stone reliefs,
providing a two-level approach for estimating the height
map from single images, with a mesh deformation scheme
and normal computation. However, it is difficult to extend
image-based relief generation to high-relief generation, as
the images contain insufficient height information and the
computation time is much greater[7].
2.2 Model-based relief generation
A computer-assisted relief generation system was
developed by CIGNONI, et al[8], who applied a
compression that is inversely proportional to the height
value followed by a linear rescaling to generate 3D basand high-reliefs from 3D models.
Clearly, reliefs generated from 3D objects are considered
to be a promising means of creating bas-reliefs, and also
allow for the reuse of existing 3D models. The final
generated reliefs convey real height information, which
could easily be machined directly into real reliefs.
Furthermore, the generated 3D reliefs can be edited and
modified before real machining. The challenge is to retain
the fine details of a 3D object while greatly compressing its
depths to produce an almost planar result. To achieve the
highest-quality results, it is important that the sharpness,
richness of detail, and accuracy is taken into account.
Existing techniques use different feature-preserving
methods to generate bas-relief models with rich details,
even with high compression ratios[9–12].
An improved relief generation method proposed by
KERBER, et al[13] added a user interface and implemented
the algorithm on graphics hardware. This allowed the
generation of real-time dynamic reliefs given an animated
model.
A series of gradient-based algorithms have been
proposed by ZHANG, et al[14], including height field
deformation, high slope optimization, and fine detail
preservation. These can be used to generate bas-reliefs
interactively. Recently, a unified framework presented by
SCHULLER, et al[15] created bas-reliefs from target shapes,
viewpoints, and space restrictions.
Most of the methods mentioned above first convert 3D
models into height fields, which can only generate
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bas-reliefs. A method proposed by ARPA, et al[16]
synthesized high-reliefs using differential coordinates.
High-relief synthesis is semi-automatic, and can be
controlled by user-defined parameters to adjust the depth
range and the placement of the scene elements with respect
to the relief plane. Our proposed method can generate both
high-reliefs and bas-reliefs from 3D models with high
efficiency, making it computationally feasible to obtain
different viewpoints under different gestures of a single
model, and also to combine models together to generate
more multiple relief models.
3
Mesh Enhancement and Relief Generation
Meshes can be represented in a number of methods using
different data structures to store the vertex, edge, and face
data. Among those methods, the Face-Vertex mesh, which
represents an object as a set of faces and a set of vertices, is
widely used for mesh representation[17]. The method
proposed in this paper is based on a Matlab toolbox
provided by GABRIEL[18]. In this platform, vertexes store
the 3D vertex positions and faces store 3-tuples giving the
number of vertices forming faces as two matrixes.
When a 3D mesh is provided, the algorithm first
enhances the mesh using 3D unsharp masking (USM),
which flattens the mesh while preserving its details.
3D USM is implemented by a simple smoothing scheme.
The smoothed mesh is subtracted from the original mesh to
extract the mesh’s higher-order features. These features can
be enhanced by scaling them and adding them back into the
original mesh[19]. After enhancing the features, a
proportional nonlinear scaling scheme is adopted to
produce the final bas-reliefs and high-reliefs with different
scaling factors.
3.1 Unsharp masking
USM is a feature-enhancement technique in image
processing that splits a signal into low- and high-frequency
components. An input image is convolved with a low-pass
kernel, resulting in a smooth version of the input image.
Subtracting the smooth version from the original image
leads to a high-frequency image containing peaks at a
small-scale level of detail. Adding a multiple of the
high-frequency image back into the smooth image
emphasizes the fine structures in the newly reassembled
image.
3D USM is an extension and derivative of 2D USM. Its
main function is to extract the mesh’s higher-order features.
In the 3D case,
M sharp = M 0 +  ´ ( M 0 - M smooth ),
(1)
where Msharp is the sharpened mesh, M0 is the base mesh,
Msmooth is the smoothing mesh with different smoothing
strategies, and  is the amount of enhancement. The
adjustment of  can be used for artistic control.
Y WANG Meili, et al: Digital Relief Generation from 3D Models
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3.2
Mesh smoothing strategies
3.2.1 Average smoothing
The simplest approach is average smoothing, which is
widely used in image processing. It replaces each vertex
with the average of its one-ring vertices. Average
smoothing is straightforward to implement and has high
computational efficiency, but can cause blurring. It is
expressed as
Pin = Pio +
å
Q,
(2)
QÎ N ( Pio )
where Pin is an updated vertex of Pi, Pio is the original
vertex of Pi, and N(Pio) are the one-ring neighbors of Pio.
3.2.2 Laplacian smoothing
Laplacian smoothing changes the node positions without
modifying the topology of the mesh. It is simple to
implement, because a given vertex only requires
information about its immediate neighbors. For each vertex
in a mesh, a new position is chosen based on local
information, and the vertex is gradually moved there. There
are a number of different approximations for the Laplacian
operator, and each has a particular use[20–21]. The discrete
approximation can be described as
L( xi ) =
1
å wij
å
wij ( x j - xi ),
(3)
jÎ N (i )
where wij is the weight for the edge with end points (xi, xj).
There are several schemes for defining the weights wij:
combinatorial, distance, and conformal weights. The
combinatorial weight is an adjacency matrix, and any
arbitrary edge weight is the Euclidean distance of the two
faces connected by the edges.
The distance weight is the nonlinear operator:
w( pi ) =
E=
q - pi
1
,
å
E qÎ N (i ) q - pi
å
(4)
q - pi ,
jÎ N (i )
where |q - pi| is the distance between vertex q and pi, w(pi)
is the weight matrix between pi and its one-ring neighbors,
and E is the distance sum of pi and its neighbors.
In the conformal weight approach, for a mesh with
triangular faces and vertices vi, vj, vk, the angle between
edge (vk, vi) and edge (vk, vj) can be expressed as angle
(vk - vi, vk - vj), so w(i, j) can be calculated as
w(i, j ) = cot( angle(vk - vi , vk - v j )).
(5)
In Eq. (5), vertexes vk and vj belong to one-ring
neighbors of vertex vi. This weight scheme smooths the
mesh while preserving its shape, minimizing potential
distortion related to angle changes. Laplacian smoothing
can be applied iteratively to obtain the desired mesh
smoothness. In the experiments described in this paper, the
conformal weight approach has been applied.
3.3 Nonlinear scaling scheme
To scale 3D meshes efficiently, a nonlinear scaling
should be used instead of linear scaling, because linear
scaling cannot distinguish the important parts of the mesh.
The objective is to scale the height of the relief proportional
to the height field. To generate a relief, the higher part of
the object should be scaled more than the lower part to
preserve the features. An attenuation function can be used
for this purpose [3]:
é

ê
G ( h) = SF ´ êsgn(h)
h
ê
ë
æ h ö÷ ùú
çç ÷ .
ú
ççè  ÷÷ø ú
û
(6)
The scaling factor SF controls the depth compression
ratio, with larger values signifying less compression. For
bas-relief generation, a small value is chosen to present the
model in a nearly flat plane, whereas for high-relief, a
relatively large value is applied. SF also defines the level of
preservation of details, where a small value would smooth
out small depth changes in the model. The parameter 
determines the degree to which the height has changed.
Larger heights are scaled more (assuming 0< <1).
Choosing  =0.1 and  =0.9 gives the scaling suggested by
FATTAL, et al[3].
4
Results of Relief Generation
4.1 High-reliefs
In high-reliefs, the height is over half of the natural depth
of the surface. Therefore, according to the definition in
section 3.3, SF is greater than 0.5.
We use the Armadillo model as an example to illustrate
the results of the algorithm. For high-relief generation, we
set  =0.2 and examined the output with SF=0.7, SF=0.6,
and SF=0.5. All testing models were taken from Aim
Shape.
It can be seen from Fig. 1 that the higher value of SF(0.7)
preserves more features, although the overall details are
preserved for all SF. The influence of  will be examined
in section 4.4.
4.2 Bas-relief
In bas-reliefs, the height is less than half of the natural
depth. Recent studies have assumed a compression ratio of
0.02. Fig. 2 demonstrates the bas-reliefs of the Armadillo
models generated by the proposed method with  =0.2 and
SF=0.02. The mesh enhancement techniques and nonlinear
scaling scheme effectively preserve the details of the
CHINESE JOURNAL OF MECHANICAL ENGINEERING
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models in bas-relief.
4.3 Multiple views and multiple models
It is straightforward to apply different viewing angles
under different gestures to the original model, because the
proposed method operates directly on 3D meshes. For
example, adjusting the original model to different
viewpoints under different gestures and then applying the
proposed algorithm generates bas-reliefs with different
view angles. An example with the Armadillo model is
shown in Fig. 4.
Fig. 1.
Fig. 2.
High-reliefs with Armadillo model
Armadillo bas-relief generated
by the proposed algorithm
Fig. 4.
Bas-reliefs with different poses
of a single model
An extension of the proposed method is the generation of
complex combined relief models. The use of different
models of a meaningful scene to generate multiple models
is illustrated in Fig. 5 and Fig. 6. The proposed method has
a relatively low computation time, with the combination of
Raptor and Ball requiring about 50 s to get the final relief
models.
Fig. 3 presents examples showing the performance of the
proposed algorithm on Raptor and Ball models. It can be
seen that bas-reliefs are generated in which the details have
been preserved.
Fig. 5. Example of bas-reliefs with multiple models
Fig. 3.
Bas-reliefs with different models
4.4 Smoothing comparison and parameter testing
Fig. 7 compares two smoothing strategies. Fig. 7(a) is the
original model, and Fig. 7(b) shows the effect of average
smoothing. Figs. 7(c)(e) illustrate the effect of Laplacian
smoothing with different weight strategies. Average
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Y WANG Meili, et al: Digital Relief Generation from 3D Models
smoothing is easy to implement, but the smoothing result
cannot be changed and sometimes suffers from blurring
(Fig. 7(b)). Although Laplacian smoothing is relatively
easy to implement compared to bilateral filtering and
cross-bilateral filtering, the smoothing results can be
adjusted iteratively(Fig. 7(c)), allowing some additional
influence on the final relief models.
Fig. 6.
undesired deformation when applied to 3D USM. In a
generic USM, the high-frequency part is linearly scaled by
a specified factor and added back into the original. A
suitable factor, in this case  , must be chosen carefully,
because artifacts are triggered by a larger  in the final
bas-relief generation, as seen in Fig. 8. Aesthetically
pleasing results are produced with  =0.2.
Another example of bas-reliefs with multiple models
Fig. 8.
Different  from 0.2 to 1.0
4.5 3D printing
A Projet 3510 SD was used to print some of our
bas-relief models to validate the effectiveness of our
proposed method. The results are shown in Fig. 9. The 3D
printer mesh volume was 298 mm ´ 185 mm ´ 203 mm,
the resolution was 345 DPI ´ 375 DPI ´ 790 DPI, the
precision was 0.025–0.05mm, and the material was Visi–Jet
M3 X. The size of the 3D bas-reliefs produced by this
method was 100 mm ´ 150 mm ´ 5 mm.
Fig. 7. Two smoothing strategies results
We now find the parameter that most strongly influences
the results and determine its appropriate value. The test
case will be on bas-relief generation of the Skull model.
The results for various enhancement levels  are as
follows.
It can be seen from Fig. 8 that, as  increases, the relief
models are enhanced. However, larger  values result in
Fig. 9.
3D printed models
CHINESE JOURNAL OF MECHANICAL ENGINEERING
5 Conclusions
(1) To preserve the original details in both high-reliefs
and bas-reliefs, USM and a nonlinear scaling scheme are
developed and implemented.
(2) It is relatively easy to implement the proposed
method, because it operates directly on 3D meshes.
Furthermore, it is amenable to relief generation from
multiple viewpoints under different gestures of the original
model, and can also be extended to relief generation by
multiple models.
(3) A physical 3D prototype can be produced by 3D
scanners to satisfy artistic necessities.
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Biographical notes
WANG Meili, born in 1982, is currently an associate professor at
College of Information Engineering, Northwest A & F University,
China. She received her PhD degree from Bournemouth
University, UK, in 2011. Her research interests include
computer-aided design, image processing, and 3D modeling.
Tel: +86-29-87091249; E-mail: [email protected]
SUN Yu, born in 1994, is currently a graduate candidate at
Clemson University, United States. He received his bachelor’s
degree from Northwest A & F University, China in 2016. His
research interests include computer animation, games, and 3D
modeling. Tel: +86-150-2903-0583; E-mail: [email protected]
ZHANG Hongming, born in 1979, is currently an associate
professor at College of Information Engineering, Northwest A & F
University, China. He received his PhD degree from Northwest A
& F University, China in 2012. His research interests include
spatial big data analysis, soil erosion mapping, and digital terrain
analysis.
Tel: +86-29-87091249; E-mail: [email protected]
QIAN Kun, born in 1986, is currently a PhD candidate at National
Center for Computer Animation, Bournemouth University. He
received his master’s degree in computer science from University
of Electronic Science and Technology of China. His research
mainly focuses on physics-based animation, deformation
simulation, collision detection, haptic rendering, and virtual
surgery.
Tel: +44-01202962249; E-mail: [email protected]
CHANG Jian, born in 1977, is currently an associate professor at
National Centre for Computer Animation, Bournemouth
University, UK. He received his PhD degree in computer graphics
in 2007 from the National Centre for Computer Animation,
Bournemouth University. His research focuses on a number of
topics related to geometric modeling, algorithmic art, character
rigging and skinning, motion synthesis, deformation and
physical-based animation, and novel human computer interaction.
He also has a strong interest in applications in medical
visualization and simulation.
Tel: +44-0781-4891106; E-mail: [email protected]
HE Dongjian, born in 1957, is currently a professor at the College
of Mechanical and Electronic Engineering, Northwest A & F
University, China. He received his PhD degree from Northwest A
& F University, China in 1998. His research interests include
image analysis and recognition, intelligent detection and control,
multimedia networks, and virtual reality.
Tel: +86-153-3249-1226; E-mail:[email protected]