Style-Content Separation by Anisotropic Part Scales

Style-Content Separation by Anisotropic Part Scales
Style-Content Separation by Anisotropic Part Scales
Kai Xu∗†
∗
Honghua Li∗†
Simon Fraser University
Hao Zhang∗
†
Daniel Cohen-Or‡
Yueshan Xiong†
National University of Defense Technology
‡
Zhi-Quan Cheng†
Tel-Aviv University
Abstract
We perform co-analysis of a set of man-made 3D objects to allow
the creation of novel instances derived from the set. We analyze
the objects at the part level and treat the anisotropic part scales as a
shape style. The co-analysis then allows style transfer to synthesize
new objects. The key to co-analysis is part correspondence, where a
major challenge is the handling of large style variations and diverse
geometric content in the shape set. We propose style-content separation as a means to address this challenge. Specifically, we define
a correspondence-free style signature for style clustering. We show
that confining analysis to within a style cluster facilitates tasks such
as co-segmentation, content classification, and deformation-driven
part correspondence. With part correspondence between each pair
of shapes in the set, style transfer can be easily performed. We
demonstrate our analysis and synthesis results on several sets of
man-made objects with style and content variations.
Keywords: co-analysis, style-content separation, shape analysis,
part correspondence, segmentation
1
Introduction
One of the main goals of computer graphics research is to provide
effective means for artists and non-experts in geometry modeling
to easily create useful digital 3D models. In this paper, we are interested in the creation of novel 3D models of man-made objects
which retain the characteristics of a given example set belonging to
a certain class; see Figure 1. This problem is particularly challenging when the synthesis process is unsupervised, that is, the given
set of objects are not manually tagged with semantic labels and the
correspondence among them is unspecified and difficult to compute
due to the significant shape variations in the set. Such shape variations are quite typical of many classes of man-made objects.
The set of chairs in Figure 1 (more in Figure 7) clearly contain subclasses such as swivel office chairs, armchairs, folding chairs, and
bar stools, as reflected by the geometric “content” of the chairs’
functional parts. At the same time, one can also classify the whole
set into clusters based on some notion of “style”, e.g., high vs. low
back, long vs. short legs. It seems obvious that the shape parts play
a fundamental role in analyzing the set or as we call it in this paper, co-analysis. Specifically, the shape parts are the representative
entities and not feature points, e.g., there is no obvious feature correspondence between the four legs of a bar stool and a swivel base
with five wheels, however they both function as the “leg part”. It
is evident that both part identification and making a distinction between the styles and contents associated with the parts represent an
essential understanding of the semantics of the set of shapes.
Style-content separation is indeed fundamental to human perception and this ability is reflected in routine tasks such as understanding words (the content) spoken in different accents (the style)
and recognizing letters in different fonts [Tanenbaum and Freeman
2000]. An important ability enabled by the separation is the meaningful extrapolation of new data from existing observations, a process of creation which interests us. However, while natural and
easy to do by humans, style-content separation is known to be very
difficult for machines [Hofstadter 1985]. In this paper, we are interested in developing effective means of style-content separation for
Figure 1: Style-content separation by anisotropic part scales facilitates part correspondence among a diverse set of chairs (top).
The separation is shown by the table with rows representing identified styles. The correspondences allow automatic synthesis of novel
shapes (shaded in gold) from the example set via style transfer.
co-analysis of a set of 3D models and demonstrate the crucial role
such a separation plays during this process and in shape creation.
Works on style-content classification using machine learning techniques have focused on presumed parameterized models [Tanenbaum and Freeman 2000; Wang et al. 2007] or statistical modeling
using PCA [Blanz and Vetter 1999; Brand and Hertzmann 2000].
Styles and contents are learned from training data or derived by
model fitting and as such, they are generic and data-dependent. In
all of these works, a prerequisite is data correspondence and this
has been dealt with independently from style-content analysis, e.g.,
using crude image alignment or designated markers for correspondence. In contrast, we argue that the correspondence problem itself
can be the main challenge, particularly for a diverse set of objects
such as the one in Figure 1 and others shown in this paper. As a
result, style-content separation should be applied at this stage.
Given a set of 3D mesh models, we co-analyze them
at the part level. This is motivated by the reduced representative
power of feature points for man-made shapes. As the shape style,
we consider the individual and relative anisotropic scales of the
shape parts. Although the anisotropic scale of an individual shape
part is an admittedly primitive geometric attribute, when the part
scalings in the whole shape are non-homogeneous, as exhibited by
the chair set in Figure 1, they are already challenging any existing
method for shape alignment or correspondence. In our analysis, we
use tight oriented bounding boxes (OBBs) of the shape parts as a
coarse representation and define a set of OBB graphs to capture the
various part compositions of a given shape.
Overview.
Our style-content separation algorithm proceeds in four steps as illustrated in Figure 2. We elaborate on each step in Section 3.
Figure 2: An overview of the co-analysis pipeline.
1. Style separation: A style signature called anisotropic part
scale (APS) can be defined for each part composition of a
given shape. Given a part composition, its APS characterizes the individual anisotropic part scales and their differences, which are encoded into the corresponding OBB graph.
The signature is given by Laplacian graph spectra, which
are permutation-independent, allowing their comparison to be
correspondence-free. Style separation is achieved by unsupervised learning of the APS signatures via spectral clustering.
2. Co-segmentation: This is performed in each resulting style
cluster to obtain intra-style part correspondence. The approach we take follows the consistent mesh segmentation algorithm of [Golovinskiy and Funkhouser 2009]. Since this
method relies on a global rigid alignment, its performance can
be greatly improved by style separation which serves to factor
out the effect of non-homogeneous part scaling.
3. Inter-style part correspondence: This is computed between
styles, specifically the co-segmentations derived for the styles,
using a novel “deform-to-fit” procedure. The deformationdriven approach allows for partial matching and seeks the best
fitting of OBBs through scaling, rotation, and sliding operations. This step is facilitated by co-segmentation since it represents a unified representation for each style, thus reducing
the search space for partial matching between styles.
4. Content classification: With part correspondence between
each pair of shapes in the set, content classification can be performed on corresponding parts using existing shape descriptors, such as the light field descriptor [Chen et al. 2003]. The
part-level approach leads to more refined classification results
than those obtained by global comparison.
The result of style-content separation is a table where styles are arranged into the rows and contents into the columns. Shape synthesis via style transfer is accomplished by transferring an APS
style i (from the i-th style cluster) to any example shape (the source
model) in the set, that is, by re-scaling the parts of the source model,
through OBB scaling and space deformation, according to style i.
The style transfer is rather straightforward as long as there is a part
correspondence between the source model and the co-segmentation
of the i-th style cluster. Such correspondences are already available
after deform-to-fit (step 3 in the pipeline).
Contributions.
The main contributions of the paper include:
• A new framework for co-analysis of a 3D set via style-content
separation by anisotropic part scales, allowing for effective
part correspondence and shape creation via style transfer.
• A novel unsupervised algorithm for style-content separation
that is correspondence-free.
• A deformation-driven part correspondence scheme suitable
for man-made shapes via “deform-to-fit” of part OBBs.
• Style separation by anisotropic part scales effectively removes
non-homogeneous part scaling from the co-analysis equation,
facilitating analysis tasks such as co-segmentation, part correspondence, and content classification.
2
Related work
Most works on automatic shape synthesis have focused on organic
shapes, such as faces [Blanz and Vetter 1999], the body shapes of
humans [Allen et al. 2003; Anguelov et al. 2005] or other creatures [Praun et al. 2001; Kilian et al. 2007]. The typical approach
first establishes correspondences between a set of example shapes
and then computes variations among the corresponding entities.
The common shape representation is a polygon mesh and the corresponding entities are given by the mesh vertices. A statistical
model of the variations then allows one to generate a new shape
via a blending process. A similar paradigm can be applied to the
synthesis of motion [Brand and Hertzmann 2000; Wang et al. 2007;
Lau et al. 2009] or images [Drori et al. 2003].
Perhaps the best known part-based shape synthesis is the work on
modeling by examples [Funkhouser et al. 2004]. The conceptual
design task is controlled by the user while content-driven search
of whole shapes or shape parts allows geometry variations to be
added via part substitution. Our synthesis approach is different and
it seeks to automatically generate “more of the same” from an example set of shapes belonging to a certain class. We specifically
learn the part scale styles from the set and synthesize by analogy.
To enable style transfer, the key is to obtain part correspondence
through co-analysis. Shape correspondence is a well-studied problem [van Kaick et al. 2010]. Most methods, particularly those for
registration or statistical modeling, assume that the shapes to be
matched during correspondence do not differ significantly. A few
more recent papers [Zhang et al. 2008; Lipman and Funkhouser
2009] attempt to handle large shape deformations, but like most
previous works, they focus on organic shapes and rely on extracted
surface feature points to define a meaningful correspondence. Recent work of Au et al. [2010] also deals with organic shapes but
it matches skeletal features which can be seen to represent shape
parts. However, their algorithm, like others, is sensitive to topological changes and non-homogeneous part scalings.
There seems to be a recent trend towards the analysis and processing of man-made objects [Fu et al. 2008; Pauly et al. 2008; Xu
et al. 2009]. Of relevance is the work of Gal et al. [2009] on iWires,
an interactive editing system for man-made shapes based on shape
analysis. Bokeloh et al. [2010] derives procedural models from a
single input example via symmetry analysis. The analysis results
in a decomposition of the example shape so that new instances can
be generated automatically using the procedural rules. Our synthesis is also automatic, however instead of using procedural models
computed from a single input example, we seek to generate “more
of the same” shapes from a set of examples via style transfer.
Corresponding man-made shapes is difficult due to the oftentimes
large intra-class shape variations including non-homogeneous part
scaling and even topological changes. The reduced usefulness of
feature points is also an issue, preventing the use of many classical
correspondence schemes [van Kaick et al. 2010]. Last but not least,
meaningful deformation of man-made shapes, e.g., for editing [Gal
et al. 2009; Xu et al. 2009], is challenging since such deformation
cannot be free-form [Botsch and Sorkine 2008] and a strong emphasis on shape semantics is necessary.
Much work has been done on mesh segmentation but mostly on individual models [Katz and Tal 2003; Shamir 2008]. Existing works
on co-analysis of a set include those on consistent mesh segmentation, which can possibly imply a group correspondence. Shapira
et al. [2008] rely on the shape diameter function and Kraevoy et
al. [2007] on convexity and compactness to consistently segment
organic shapes including humans and animals. Golovinskiy and
Funkhouser [2009] resort to global alignment to initialize a clustering scheme to compute consistent mesh segmentation. Global
alignment to remove anisotropic scales has been proposed by Kazhdan et al. [2004] to improve shape alignment and retrieval. The key
difference between our approach and the last two methods is that
our scaling or alignment is part-aware and in particular, it is able to
successfully handle non-homogeneous part scaling, which is common to man-made shapes [Kraevoy et al. 2008].
Finally, we mention the recent work of Kalogerakis et al. [2010]
on learning mesh segmentation and labeling. Assigning semantic
labels to a set of consistently segmented shapes does imply a part
correspondence. However, they use supervised learning, while our
co-analysis is entirely unsupervised.
3
Style-content separation and style transfer
The input to our co-analysis (Figure 2) is a set of shapes given by
polygonal meshes. The mesh models need not be closed manifolds
but we assume that each consists of one or more piecewise smooth
surface patches. The models used in this paper are man-made
shapes from the iWires dataset [Gal et al. 2009] and the Princeton Shape Benchmark [Shilane et al. 2004]; these models all share
the geometric characteristics described above. The output of the
co-analysis is a table such as the one in Figure 1, the result of stylecontent separation. In this section, we detail the steps of the coanalysis pipeline. First, we define the OBB graph, which provides a
coarse representation of a given part composition of an input shape.
The oriented bounding box (OBB) of a shape part
captures the scales of the part along three major directions. These
scale attributes define the APS signature used during style clustering. The OBBs also serve as the primitives for the deform-to-fit step
which computes inter-style part correspondence. Now we describe
how an OBB graph is constructed for a given input mesh.
OBB graph.
We first segment the mesh into parts, where many choices of existing mesh segmentation algorithms [Shamir 2008] may be employed. We have chosen the normalized cut approach based on
surface concavity, one of the algorithms considered in the random
cuts approach to mesh segmentation [Golovinskiy and Funkhouser
2008]. Obviously, determining the appropriate number of segments
is not an easy problem. Hence, we simply over-segment each shape
and rely on subsequent steps to arrive at the right part count. In our
experiments, we over-segment up to Smax = 15 parts.
We compute the OBB for each part using PCA. The initial OBB
graph is then built whose nodes are the OBBs of the mesh parts and
edges encode adjacency between parts. Adjacency is detected simply by performing intersection tests among the mesh parts. During
subsequent processing, adjacent parts can be merged resulting in
a new OBB for the two parts and a new part composition for the
shape. This can be modeled naturally via recursive contraction of
the OBB graph. Hence, each derivable part composition through
pairwise part merging has an associated OBB graph.
We learn the APS (anisotropic part scale) styles
of the input set by clustering and to that end, we need to define
an appropriate distance measure between the styles of two shapes.
To truly capture how the anisotropic part scales differ between two
shapes, a meaningful part correspondence is required. However,
our goal is to accomplish this in a correspondence-free manner and
allow style-based clustering to facilitate part correspondence.
Style clustering.
Clearly, if two shapes have similar anisotropic part scales, then
there must be a number n∗ such that two size-n∗ part compositions
(compositions with n∗ parts) of the two shapes have the closest
match in their corresponding part scales. Thus we need to search
through n, the part counts, to find that optimal value. For a particular fixed n, we need to consider all possible part compositions
having size n. However, instead of establishing correspondence between the parts, we define a permutation-independent signature so
that their comparison is correspondence-free. We design such a signature, which we call the APS signature. The signature is a function
of the part composition and we describe it later.
Given two input shapes p and q, for each n within a prescribed
range IAP S , we search through all part compositions of size n for
the two shapes and find the smallest distance between the APS signatures for the part compositions. The APS style distance D between the two shapes is the smallest such distance for all n:
√
D(p, q) =
min
||AP S(cp ) − AP S(cq )||/ α n,
n∈IAP S ,|cp |=|cq |=n
where cp and cq are part compositions of shapes p and q, respectively, and | · | denotes the size of a part composition. Note that the
distance is weighted to favor larger part count, with α a user-tuned
parameter to control the influence. In all of our experiments, we set
the range for n to IAP S = [2, 6] and α to 1.6.
With the APS style distance computed between each pair of shapes,
we perform standard spectral k-means clustering [Ng et al. 2001]
and determine the number of clusters k by observing the k-means
cost curve and finding the first point at which the curve starts to
level off; this is a fairly standard heuristic for determining k [Everitt
et al. 2009] and has worked well in our examples.
A last note on style clustering is related to computational efficiency.
Instead of exhausting all possible part compositions, we only look
through ones that preserve the major symmetries of the original
shape [Podolak et al. 2006]; for man-made shapes, this was proven
to be an effective pruning heuristic. Under the parameter setting
Smax = 15 and 2 ≤ n ≤ 6, there are typically only hundreds
of part compositions to consider per shape. Since n is quite small,
comparing a pair of APS signatures consists of only solving a few
small-scale eigenvalues problems (see below). The time taken to
compare two part compositions for n = 6 is about 9 milliseconds.
APS style signature. Given an OBB graph representing a part
composition of size n, we wish to design a signature that captures
the anisotropic part scale information in a way that is independent
of part permutations. To this end, we resort to results from spectral
graph theory [Chung 1997] on the usefulness of Laplacian eigenvalues in characterizing graphs. The Laplacian graph spectra are
permutation-independent and as signatures, they are generally discriminative since it is known that iso-spectral cases are rare.
Figure 3: Ten possible OBB-to-OBB transformations. 1D, 2D, and
3D OBBs are colored in yellow, red, and blue, respectively.
First, we encode binary or relative anisotropic part scale information into three graph Laplacians, one per direction of the OBB. Each
Laplacian matrix is n × n and specifically,

2
2
 −e−||si (u)−sθ(i) (v)|| /σ
if u ∼ v,
P
Si (u, v) =
−Si (u, z)
if u = v,
z∼u

0
otherwise,
where ∼ is the graph adjacency relation, the Gaussian width σ is
set to be the maximal scale difference among all the OBBs, si (u)
is the scale of the OBB u along the i-th direction (i = 1, 2, 3), and
this direction is aligned with θ(i), one of the scale directions of the
OBB v; sθ(i) (v) is the scale of OBB v along direction θ(i). Here
the alignment of the axes of two adjacent OBBs is computed using
the optimal rotation alignment method of [Kazhdan 2007].
The Laplacian graph spectra of S1 , S2 , and S3 contribute 3n eigenvalues to the signature. The three spectra are concatenated into a
length-3n vector with eigenvalues sorted in ascending order in each
spectrum. However, to compare the signatures from two shapes, the
three Laplacians need to be brought into proper correspondence.
Since the input sets are composed of man-made objects, it is usually possible to compute their upright orientations [Fu et al. 2008].
These upright orientations may be used as a reference to sort the
Laplacians. As an alternative, which is what we have chosen to
do in this paper, we simply take the ordering which results in the
smallest Euclidean distance between the spectral signatures.
The signature constructed so far is seen to vary with change of
angles between the OBBs. It is possible to encode intrinsic OBB
scales as unitary characteristics of the OBBs. To this end, we consider measures of linearity, planarity, and sphericity of an OBB and
encode them as vertex weights into graph Laplacians. Our approach
is inspired by the work of [Chung and Langlands 1996] which defined certain combinatorial Laplacians with vertex weights. We define three such Laplacians to suit our problem setting, one for each
of the above intrinsic scale measures:
 p
 P
− αj (u)αj (v) if u ∼ v,
Aj (u, v) =
if u = v,
z∼v αj (z)

0
otherwise,
where the index j is one of L, P , and S for linearity, planarity, and
sphericity, respectively, and αj (u) = vob(u) · cj (u) is the volumeweighted anisotropy of the OBB u, where vob(u) is the volume of
Figure 4: OBB-based part correspondence via deform-to-fit (D2F).
Left: three chairs with functional part compositions and their OBB
representations. Middle: results of D2F where the red parts are
deformed to fit the blue ones; matched parts are colored green;
unmatched parts retain their original color. Right: final part correspondences where those parts in the same color are in correspondence while parts in grey are left unmatched.
the OBB u. Assuming that the three scales of u are sorted such that
s1 ≥ s2 ≥ s3 ≥ 0, then
cL =
2(s2 − s3 )
s1 − s2
3s3
, cP =
, cS =
.
s1 + s2 + s3
s1 + s2 + s3
s1 + s2 + s3
We sort the three spectra for A1 , A2 , A3 in some arbitrary yet
agreed-upon order when comparing the signatures of two shapes.
The complete APS signature thus contains 6n eigenvalues. The
distance between two APS signatures is their Euclidean distance.
Within a style cluster obtained from the previous style separation step, we perform co-segmentation, which
computes a consistent segmentation across all shapes in the style
cluster. Such a co-segmentation obviously leads to an intra-cluster
part correspondence. Since style separation serves to remove nonhomogeneous part scaling from the analysis, co-segmentation under this setting is expected to be an easier problem.
Co-segmentation.
We follow the same approach as [Golovinskiy and Funkhouser
2009] for consistent segmentation. The method first over-segments
each shape in the input set (in our experiments, we over-segment
each shape to Fmax = 25 segments). Then it performs hierarchical clustering of the resulting segments based on a cost combining
two factors: a) adjacency, which accounts for how connected two
segments from the same shape are for the purpose of mesh segmentation; surface concavity can be used — the more concave the angle between the segments, the larger the cost. b) correspondence,
which accounts for how well two segments from different shapes
correspond; here global rigid alignment is used — the better the
two segments can be aligned, the smaller the cost. It is worth noting that it is the rigid alignment step that may render the method
unreliable under part stretching, as shown in their work. Style separation provides exactly the right remedy for this very issue.
To adapt the above method to our setting, we need to work at the
OBB level, that is, to define the adjacency and correspondence costs
based on the OBBs. Since the number of OBBs is typically much
smaller than the number of faces, the clustering process is efficient.
Given two adjacent segments p1 and p2 (initial or clustered) on the
Figure 5: Comparison of co-segmentation results between (a)
[Golovinskiy and Funkhouser 2009] and (b) our method. Note the
adverse effect of non-homogeneous part scaling on the former and
our method’s ability to correct the problem.
same shape, we define the adjacency cost by a convexity measure
(vob(p1 ) + vob(p2 ))/vob(p), where p is the result of clustering
segments p1 and p2 .
If p1 and p2 belong to different shapes, we first find the optimal
global alignment between the OBBs of the two whole shapes (by
aligning their major axes) using rigid ICP [Besl and Mckay 1992].
Then we define the correspondence cost as
1
arob(p1 ) + arob(p2 )
X
area(f1 ) + area(f2 ),
(f1 ,f2 )∈CF O(p1 ,p2 )
where arob(p) is the area of the OBB of segment p and
CF O(p1 , p2 ) is the set of compatible face pairs between the OBBs
of p1 and p2 — a pair of faces from these OBBs are compatible if
the Euclidean and normal distances between them each falls below
a threshold. In our experiments, we set the distance threshold to be
10% of the length of the OBB diagonal for the whole shapes and
measure the normal distance by the dot product between normals,
setting the threshold at 0.75.
Inter-style part correspondence via deform-to-fit. With cosegmentations computed for the style clusters, we now establish
correspondence between these segmentations or part compositions.
In general, part correspondence searches for the best match between
two given models. We take a deform-to-fit (D2F) approach, finding
the best deformation between the matched entities in the source and
target models and use certain deformation energy or cost to evaluate
the correspondence. Our technique extends the deformation-driven
correspondence method of Zhang et al. [2008] to deal with manmade models and to operate at the OBB level. The approach of
[Zhang et al. 2008] is that of a pruned priority-driven search. While
generally slow due to the exhaustive nature of the approach, it is
able to find quality partial correspondences.
The two given models to be brought into correspondence are the
co-segmentations from two style clusters and each of them is represented by an OBB graph. We classify each OBB into three types:
1D, 2D and 3D, roughly corresponding to linear, planar, and spherical objects, respectively. To classify the OBBs into these types,
we use the three measures cL , cP , and cS defined for APS signatures. Typically, one of the three values is much larger than the rest,
uniquely determining the OBB type. However, some OBBs may be
regarded as of more than one type, such as the leg part of a stool
shown in Figure 1 — since both cL and cS are large, the OBB is
regarded as both a 1D-type OBB and a 3D-type OBB.
The OBBs and the relation among them define an attributed graph
in a straightforward way. Since the number of OBBs is rather small,
the search space is small and an exhaustive search is viable [Zhang
et al. 2008]. To reduce search time, we select the node with the
largest number of edges as the root of the source model. In the
Figure 6: Comparison of content classification on a set of kitchen
utensils. Left: with style clustering, D2F, and part-level LFD distances. Right: direct LFD distances measured on whole shapes.
Our method does a much better job in separating the spoon, knife,
three- and two-pronged fork sets, even under style variations.
target model, we use all the nodes whose types are the same as the
root of the source as the candidates for correspondence.
In addition to considering unary characteristics of the OBBs, we
also define allowable binary relations; this further reduces the
search time during D2F. Specifically, two neighboring OBB nodes
have a valid relation if their types can be transformed to fit by a
rotation or sliding operation. We define ten possible OBB-to-OBB
transformations as shown in Figure 3. These OBB-to-OBB transformations always exist between functional parts of man-made objects and they seem sufficiently representative, which is the very
reason why we have identified these transformations. During D2F,
before measuring the deformation between two matched OBB subgraphs, we first validate the OBB-to-OBB correspondence relations; invalid relations lead to pruning of the search subtree.
The quality of each valid correspondence between two sub-graphs
is measured by ED2F = αEmatch + βEvolume , where Ematch is
the volume percentage of unmatched parts and Evolume is the sum
of squared volume differences of all matched parts; ED2F can be
seen as the deformation energy. Throughout our experiments, we
simply set α = β = 0.5. Figure 4 illustrates some results of OBBbased part correspondence through D2F. Results on consistent cosegmentation, which are enabled by style-content separation and
inter-style correspondence via D2F, can be found in Figure 8.
Most content-based classification algorithms seek to identify the right class for a query [Tangelder and
Veltkamp 2008]. For our current problem however, we are faced
with an input set already belonging to a class, e.g., chairs, and our
goal is to further refine the classification. One naturally expects that
a global shape descriptor would not work well for this task so that
part-level analysis becomes necessary. The part correspondence obtained from the previous step allows us to do just that.
Content classification.
We develop a simple scheme for content clustering. First, we
cluster the input shapes based on the part counts in their cosegmentations. Then within each such cluster, we define a distance
measure that is the maximum Euclidean distance between the light
field descriptors (LFD) [Chen et al. 2003] defined for the corresponding parts. However, before computing the LFDs, we first
scale the corresponding OBBs so that they align and the parts within
are space-deformed [Cohen-Or 2009]. Results from content classification are reported in Section 4.
The most difficult aspect of automatic shape synthesis is the correspondence among the example set.
With style separation, co-segmentation, and finally D2F to achieve
meaningful part correspondence between each pair of shapes, the
Synthesis by style transfer.
Figure 7: Style-content separation for a chair and stool set (row: style; column: content). Newly synthesized models (in gold) fill the table.
Figure 8: Results of co-segmentation and D2F-based inter-style part correspondence on three subsets (a-c) of the chair and stool set. In
each subset, models are grouped by style clusters.
synthesis problem by style transfer is greatly facilitated. With part
correspondence, we know precisely how each part in the modified
shape needs to be scaled. The only remaining problem is to maintain a proper connectivity between two adjacent parts under possibly different scalings, in particular between the adjoining features.
We have implemented a rather simplistic scheme to handle scaling
discrepancies between adjacent parts as it is not the focus of this
paper; more sophisticated deformation techniques [Kraevoy et al.
2008; Gal et al. 2009] may be otherwise applied. During style transfer, each part is scaled by deforming its OBB according to the style.
For all the synthesis results shown in this paper, we assume that the
scalings only cause sliding of the connection curves in an interfacing plane. Then the disconnected connection curves after scaling
are simply blended linearly to obtain the new adjoining feature. We
obtain the final surface by performing a surface deformation with
the blended curve as a handle similar to iWires [Gal et al. 2009].
4
Results
In this section, we show results of style-content separation and
shape synthesis. Models used in the example set consist of those
from the Princeton Shape Benchmark [Shilane et al. 2004] and
Gal’s iWires dataset [Gal et al. 2009], as well as ones obtained via
space deformation to enrich the styles. The sizes of the mesh models range from 5K vertices to 40K vertices. For an example set of
10 to 20 models with each containing tens of segments (typically
ranging from 2 to 25), the typical timing of the various steps of
our method are given below. Style clustering: 30-340 seconds; cosegmentation: 15-60 seconds; deform-to-fit part correspondence:
0.5-2 seconds, roughly 0.04 seconds per pair of models; content
clustering: 15-40 seconds with most of the time spent on computing LFDs. These times were measured on an Intel(R) Core 2 Duo
2.53GHz CPU machine with 2GB memory.
One of the key points of the paper is that style separation by APS
analysis facilitates shape co-analysis and we demonstrate this first.
Figure 5 compares our co-segmentation results with [Golovinskiy
and Funkhouser 2009], showing that our style separation can properly handle non-homogeneous part scaling. Figure 6 compares content classification results between with and without style clustering,
demonstrating the ability of our method to achieve much refined
classification. The main reason for such success is that style clustering, co-segmentation, and deform-to-fit, together allow to derive
meaningful part correspondence and content analysis at the part
level leads to the more refined results.
Figure 7 shows the full set of chairs and stools and the table resulting from style-content separation. Each style cluster occupies
Figure 9: A gallery of style-content tables (row: style; column: content) and synthesis results for six data sets: hammers, airplanes, tables,
kitchen utensils, goblets, and humanoids. It is especially interesting to note the ability of our method to successfully content-classify the
shapes within a class despite the rather small geometry variations among shapes in that class, e.g., see the hammer and utensil sets.
a row, while content clusters occupy the columns. Newly synthesized models fill the table and in this and all other figures, they are
shaded in gold. The table also shows results of content clustering
— shapes belonging to the same content clusters are grouped into
the same columns. Despite the large style variations in the input
example set, our method exhibits success in the results described
above. Note that since our D2F procedure is able to obtain partial
matching, we can even perform style transfer between two styles
which were not brought into full part correspondence. For example, style transfer can be performed between stools and chairs, and
between chairs with and without armrests. A side effect worth noting however is that the newly created models may not respect the
styles identified for the original example set. One may also notice
that some synthesis results contain distortions, as exemplified by
the result given in the second row, eighth column of the table of
Figure 7. This may occur due to the use of homogeneous resizing
for the matched parts which can possibly lead to distorted segments.
To stress-test our algorithm, we apply it to a diverse set of object
classes shown in Figures 9. Note that despite our focus on manmade shapes, we also ran our algorithm on a set of organic (hu-
content separation prior to co-segmentation and correspondence
computations, effectively factoring out the part scale issue from the
analysis equation. The strength of our approach stems from the
power of our style clustering scheme. Being correspondence-free,
it succeeds to reveal valuable knowledge about the set, which then
paves the way for subsequent analyses including co-segmentation,
part correspondence, and refined content classification.
Admittedly, the current work is merely making one step forward in
solving the general problem. It is important to note that our coanalysis is not expected to work on an arbitrary input set. The
set needs to contain objects in the same semantic class, and with
sufficient variety in its anisotropic part scales. In addition, the initial (over) segmentation of the input shapes needs to be sufficiently
meaningful. As we can observe from the vehicle and humanoid
sets, achieving this automatically is not always easy.
Figure 10: Unnatural part correspondence (bottom: A and B with
respect to the rest) and synthesis results (top: red background).
manoid) shapes. While the processing of all other sets were automatic, following the procedures described in the paper, the humanoid set required some manual effort to obtain reasonable results. Six out of the ten input humanoid models were segmented
manually since the particular mesh segmentation algorithm we are
adopting does not work well on the set. In particular, the segmentation boundaries obtained lack sufficient quality. Manual part stitching was also performed during style synthesis since our simplistic
linear blending between the adjoining feature curves works poorly
on organic shapes. These two issues indeed point to certain limitations of our current implementation, which we discuss in Section 5. Nevertheless, the results on all the sets in Figure 9 demonstrate success in style-content separation for co-segmentation and
content clustering, which represent the core of our contribution.
The vehicle set given in Figure 10 also presents difficulties in terms
of initial segmentation and part stitching, for which manual efforts
were involved. However, even with such efforts, we encounter a
case of unnatural part correspondence, as highlighted by the two
models marked A and B. In particular, the back wheels of these
models are not properly matched with any of the wheels of the
remaining input models. As a result of the unnatural correspondence, the synthesis results, shown by red background in the table, are also seen as unnatural. The main cause of the problem
is that our D2F-based correspondence currently does not alter the
part compositions obtained during co-segmentation. Since the latter only works within style clusters, inconsistencies between part
compositions across different clusters may occur. Having D2F
search through different part compositions can solve the problem
but would incur a high computational cost. Alternatively, we could
segment the green part of B into two parts, a cab and a trailer; this
would also fix the problem but the initial segmentation would have
been hard to obtain using only geometric cues.
5
Discussion, limitation and future work
In this paper, we deal with the difficult problem of analyzing a set of
3D objects belonging to the same class while exhibiting significant
shape variations, particularly in part scales. Existing shape analysis
algorithms have been ineffective in dealing with non-homogeneous
part scales, and the associated co-analysis problem is particularly
challenging under the unsupervised setting. Treating anisotropic
part scales as a particular shape style, we propose to apply style-
As a means to generate novel shapes, our synthesis method limits itself to creating new variations of an existing example model instead
of arriving at new contents by exchanging or shuffling parts of multiple shapes. While the latter may be able to generate more shape
varieties, it inevitably has to take care of the part stitching problem.
Stitching parts from different models, especially man-made shapes,
is quite a difficult problem in general; it may require resolving topological inconsistencies between parts and the general problem is not
even well-defined. Our current solution to part stitching is admittedly rather simplistic; tackling the general problem indeed points
to an interesting direction for future work.
We are witnessing a rapid accumulation of 3D models yet most of
these models are not tagged or segmented and their parts have no
semantic labels. We believe that co-analysis of sets of shapes, as we
do in this paper, will gain more and more interest, both for indexing
and retrieving shapes, and as a tool for generating new variations of
existing objects. As shown in this paper, style-content separation
can be an effective means to this end. However, anisotropic part
scales is only one particular shape style. We believe that our current investigation is only a start to defining and incorporating more
shape styles into the shape analysis problem.
Acknowledgments
We first thank the anonymous reviewers for their valuable comments. We are grateful to Aleksey Golovinskiy, Joshua Podolak,
Thomas Funkhouser, Michael Kazhdan, and Ding-Yun Chen for
sharing their software or source code on consistent segmentation,
symmetry detection, as well as spherical harmonics and light field
shape descriptors. Thanks also go to Yanzhen Wang and Ariel
Shamir for discussions on the topic. This work is supported in
part by grants from NSERC (No. 611370), the Israeli Ministry
of Science, the Israel Science Foundation, the 863 Program of
China (No. 2007AA01Z313 and 2009AA01Z301), NSFC (No.
60773022, 60773020, and 60970094), and the Pre-research funding
of National University of Defense Technology (No. JC09-06-01).
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