3D Shape Retrieval using Uncertain Semantic Query

A Preliminary Study

Hattoibe Aboubacar

1,2

, Vincent Barra

1,2

and Ga

elle Loosli

1,2

Clermont Universit

e, Universit

e Blaise Pascal, LIMOS, BP 10448, F-63000, Clermont-Ferrand, France

CNRS, UMR 6158, Limos, F-63171 Aubiere, France

Keywords:

3D Shape Retrieval, Uncertainty Coding, Semantic Query, SimpleMKL, SVDD.

Abstract:

The recent technological progress contributes to a huge increase of 3D models available in digital forms.

Numerous applications were developed to deal with this amount of information, especially for 3D shape

retrieval. One of the main issues is to break the semantic gap between shapes desired by users and shapes

returned by retrieval methods. In this paper, we propose an algorithm to address this issue. First the user gives

a semantic request. Second, a fuzzy 3D-shape generator sketches out suitable 3D-shapes. Those shapes are

ﬁltered by the user or a learning machine to select the ones that match the semantic query. Then, we use a

state-of-the-art retrieval method to return real-world 3D shapes that match this semantic query. This algorithm

is used to retrieve object in SHREC’07 database. The results are good and promising.

1 INTRODUCTION

With the technological progress in computer graphics

and object modeling, the number of available 3D data

has grown exponentially. It makes it essential to de-

velop effective methods and elegant modeling, analy-

sis and processing tools to allow a better understand-

ing of the phenomena involved and the interpretation

of data.

The proposed work is closely linked to the 3D-

shape retrieval problem, even though it doesn’t pro-

pose a novel algorithm for this task (examples of

retrieval methods can be found in (Tangelder and

Veltkamp, 2008) and a brief description is given in

section 3 ). Indeed, the target problem deals with the

request that is given to any retrieval machine. Usually,

this request is a 3D-shape and we propose here to start

from a (textual) semantic request and help the user to

obtain a 3D-shape that will be given to the retrieval

machine.

In the next section, the black box between the re-

quest and the generated 3D-shape is detailed. Section

3 reviews the related work. Then, we detail the differ-

ent tools used in our process in section 4. In section 5

we introduce some experiments. At last, some points

are explained and discussed in section 6.

2 FROM THE SEMANTIC

REQUEST TO A SUITABLE

SYNTHETIC 3D-SHAPE

As mentioned above, the objective is to provide a tool

that goes from a semantic request to a 3D-shape suit-

able to be an input for retrieval.

Semantic Request. This requires to deﬁne what

will be considered as a semantic request : it is re-

stricted to the association of a noun (the class) and

an adjective (the concept). For this study, the nouns

are limited to a set of known classes (although future

work is planned to extend this) and the concept is free.

Suitable 3D-shape. Let’s now deﬁne what a suit-

able 3D-shape is. Since we will use a retrieval ma-

chine based on Reeb graphs that are extracted from

the 3D-shape, we consider that texture or details are

meaningless and that the general shape and position

are sufﬁcient to deﬁne the semantic request. A suit-

able 3D shape will be a shape composed of very sim-

ple geometrical parts (like balls, cylinders, parallelo-

grams) that looks like what the user meant.

Process. It is obviously not easy or even possible

to deﬁne all concepts a priori. The choice here is to

ask the user, as in retrieval feedback processes, to give

600

Aboubacar H., Barra V. and Loosli G..

3D Shape Retrieval using Uncertain Semantic Query - A Preliminary Study.

DOI: 10.5220/0004819106000607

In Proceedings of the 3rd International Conference on Pattern Recognition Applications and Methods (ICPRAM-2014), pages 600-607

ISBN: 978-989-758-018-5

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Overview - we propose a process to go from a semantic request to a suitable 3D-shape that can be used in a retrieval

machine in order to retrive 3D-shapes matching the semantic request. We present a way to generate suitable 3D-shapes and

examples of machine ﬁlter.

precision on his request by selecting matching shapes

when a concept is unknown. The idea is to generate

several instances of the classes, based on several un-

certainties in the deﬁnition of the class (see section

4.1). This is the ﬁrst contribution of this paper. Then,

a ﬁlter is applied, in order to keep only instances of

the desired concept. This is the second contribution.

This ﬁlter takes two forms: the human one (manual

selection of the generated shapes that match the con-

cept) and the trained machine one (trained using pre-

viously selected shapes). The basic process is that the

human ﬁltering is required for any unknown concept

and used to train the machine one. If a reliable ﬁlter

has been trained for a concept, the human intervention

is not required anymore.

Figure 1 gives an overview of our process.

Tools and Open Questions. To implement our pro-

cess, we need to evaluate several points:

• the trained machine ﬁlter : since we’ll get only

good instances, we focus on one-class learning

methods (here we present results for SVDD and

SimpleMKL with One-class SVM) : see section

4.2 for details on the methods.

• the reliability of the machine ﬁlter : the question

here is to evaluate the number of good instances

that are necessary to train the ﬁlter (see experi-

ment in section 6).

• how good are the generated 3D-shape to retrieve

concept matching real 3D-shapes using a retrieval

machine : see section 5.

3 RELATED WORK

Breaking the semantic gap between users and ma-

chines has been the subject of a huge amount of works

in CAD and computer graphics in general. A brief re-

view of state-of-art methods in reducing the semantic

gap is given in (Han et al., 2008).

Recently, (Eitz et al., 2012) made a great contribu-

tion towards human’s way of seeing images. It helped

them to develop a powerful method to retrieve shape

from sketch. It is an interesting way of dealing with

uncertainty as sketches are a personal simpliﬁcation

of the way we see objects. We aim at developing a

tool that allows user to sketch out the 3D shape they

want like in the approach of (Eitz et al., 2012), more-

over we want to be able to retrieve not only objects of

the same class but shapes in a speciﬁed posture.

In this paper, we are mainly inspired by shape

content-based methods. The recent progress made

in this ﬁeld is the introduction of relevance feedback

methods. The idea behind relevance feedback is to ap-

proach the user’s query by allowing him to specify it

several times. In practice, the user gives his request.

Then ﬁrst objects that best match the query are dis-

played. Hence the user can state the ones he wants

and those which are wrong. These choices may be

reused to be more accurate on the retrieval process.

Therefore based on the iterative feedback of the user

better results can be obtained. (Giorgi et al., 2010)

proposed a relevance feedback method based on the

assumption that similarity may emerge from the in-

hibition of differences. In this approach, objects that

are wrong according to the user are not integrated in

the new retrieval process. (Zhang and Jin, 2010) used

a learning technique to learn through the different re-

sponses of the user. This technique used a Gaussian

kernel coupled with a method of gradient descent to

improve the learning step. The results were very en-

couraging as these of (Giorgi et al., 2010).

Moreover, CAD-oriented works gradually and in-

directly integrated uncertainty in the modeling of 3D

shapes. (Funkhouser et al., 2004) was one of the ﬁrst

to propose the construction of models based on other

existing models. Several algorithms for handling 3D

shapes have been developed in this work including

smart scissors which allow the user to easily separate

parts of 3D shapes and paste one part to another using

an efﬁcient paste tool. The results are really remark-

able and let the user play with his imagination. How-

ever, despite of a shape search module, the user must

do a great job to ﬁnd all forms of possible parts of ob-

jects. More recently (Chaudhuri et al., 2011) provides

an effective response to this problem. The different

parts of 3D shapes are automatically segmented and

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classiﬁed as primitives in a relevant way according to

position, size and other parameters. In addition, as

the user manually creates a model, the method pro-

vides the user with primitives sorted by relevance se-

mantics, from most relevant to least relevant, step by

step. This work is subject to an automatic extension

in (Kalogerakis et al., 2012), where 3D shapes are au-

tomatically synthesized using existing shapes and a

probabilistic learning model. Experimental creation

of planes, cars and boats have been made and the re-

sults are mind-blowing. Furthermore, the method al-

lows different kinds of imaginable objects for each

class to be computed and there is a great time saving

as thousand of possible realistic models are created in

a few minutes. It is a powerful tool, but the user still

has to look at several models to ﬁnd what he wants.

The process proposed in this paper is a comple-

mentary approach to that ones. Most of the time peo-

ple does not think of one object but different possible

objects. We think that trying to model the requested

object from simple part before searching for real ob-

jects will help pass the hurdle. Our main intention is

to explicitly deal with uncertainties in modeling, cod-

ing and processing. Thus, we will be able not only to

design objects but ideas.

So far, there has not been yet a black box that cap-

tures the semantic request of a user and returns ex-

actly what he wants. Our purpose is to provide tools

to help taking a step towards this black box.

4 PROCESS DEPLOYEMENT

We introduce here all the different tools that are used,

from 3D-shape modeling to the retrieval method, in-

cluding a brief description of the one-class learning

methods.

4.1 Modeling Process

We consider that most of 3D shapes can be robustly

segmented. This brings the idea that a shape is a com-

bination of several simple shapes joined according to

some rules. Therefore, we model 3D shapes as a com-

bination of simple shapes we call primitives. In order

to introduce some uncertainties, these primitives can

be altered by pattern maker called modiﬁers, before

being pieced together according to random spatial re-

lations. Doing this, we are able to design all possible

postures of the same object. As a result, we create a

fast and ﬂexible 3D shapes generator which randomly

produces uncertain shapes allowing the user to select

the ones that correspond to his semantic query.

Here, we choose to model a simple manufactured

class of objects: chair in section 4.1.1, and a more

complex one: humanoid in section 4.1.2. To model

these uncertain 3D shapes we use four primitives

which are spheres, cylinders, parallelograms and el-

lipsoids. One has to note that our 3D models are quite

simple and do not satisfy all real constraints inherent

to each object. However, this is not annoying in our

case because we want to learn semantic concepts and

we assess that our semantic concepts only embed re-

alistic models so our methods have to be robust with

unrealistic ones.

4.1.1 Design of a Generic Chair

A chair is modeled as a combination of three prim-

itives representing the back, the chair seat and the

feet. We assume the feet are symmetrical and have

the same characteristics, therefore only information

on one foot is needed. Otherwise, we consider only

two kind of primitives in our chair modeling process

which are cylinder and parallelogram. Indeed, the

back, the chair seat and the feet are each one indepen-

dently from the other a cylinder or a parallelogram.

In addition, characteristics of cylinder and parallelo-

gram are randomly deﬁned. Of course, we include

in our implementation some constraints to ensure that

our uncertain chairs are like realistic ones. These con-

straints ensure that primitives do not have abnormal

size according to realistic characteristics of a chair.

This is made using uniform distribution to draw the

sizes under speciﬁed bounds. Furthermore, we make

sure the back is linked with the chair seat and the feet

are located below the chair seat. Then we randomly

select angles to ﬁx the orientation between the primi-

tives.

Figure 2 shows some examples of designed chairs.

Figure 2: Examples of designed chairs.

4.1.2 Design of a Generic Humanoid

Humanoid are modeled using eleven body parts mod-

eled as primitives: two arms, two forearms, two

thighs, two legs, one chest, one neck and a head. We

choose to model limbs and neck as cylinders, head

as sphere and chest as ellipsoids. Quite naturally, the

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motion of each limb is independent of other limbs.

As for chairs, the characteristics of primitives are set

up randomly to bring some size uncertainties. We

start modeling a humanoid from the chest which is

always vertical. Then we add neck and head which

do not need to be oriented, so we just ﬁx neck to

chest and head to neck. We add limbs and orient

each one independently which allows to obtain ran-

dom postures. Furthermore, we ensure that corre-

sponding limbs have the same characteristics as for

realistic humanoid, and we enable independent orien-

tation from one to another.

Figure 3 shows an example of designed humanoid.

Figure 3: Example of designed humanoid.

4.1.3 Suitable 3D-shape Features

Each suitable 3D-shape is represented by its features

in the learning process. The features of a suitable 3D-

shape is the set of features of the primitives the shape

is composed of, plus angles between primitives. A

primitive is characterized by its type of shape and its

size. Thus, there are sixteen features for a chair and

forty four for an humanoid. Then, an harmonization

step is performed in order to have the same number of

features for each kind of shape in the data. It consists

in repeating information on primitive in each model

as much as needed to have the same number of prim-

itives in both. After this step we then worked with

a hundred and sixteen features for each shape. These

features were the inputs used in our learning methods.

4.2 Learning Semantic Concept:

Creating a Machine Filter

Learning a semantic concept from a sample of 3D-

shapes is equivalent to learning the characteristics of

objects supposed to belong to the same class. It is

a standard problem in machine learning called one-

class classiﬁcation problem also known as problem

of data description. We refer to (Khan and Madden,

2009) to have a glimpse at recent one class classiﬁ-

cation methods. We investigated two methods which

address this problem in order to create a machine ﬁl-

ter.

Here, we choose to use only Support Vector Ma-

chine (SVM) based methods. SVM-based methodol-

ogy for one class classiﬁcation was ﬁrst introduced by

(Schlkopf and Smola, 2001). Schlkopf’s approach is

to ﬁnd an separation hyperplane between targets and

outliers. This is the most widely used approach in the

literature. We also concentrate here on another ap-

proach, proposed in (Tax and Duin, 2004), called Sup-

port Vector Data Description (SVDD). This method

aims to ﬁnd a hypersphere which contains all possible

targets. This approach has proved to be efﬁcient and

SVDD is part of top methods when it comes to one-

class classiﬁcation. SVDD is detailed in section 4.2.1

and SimpleMKL in section 4.2.2.

When a user asks for a semantic concept. First,

he has to choose manually a sample of suitable 3D-

shapes that match his query. This sample is learned

and saved using a learning method. Hence, the next

time the same concept is asked, we use our fuzzy

shape generator to produce several shapes. Then the

same learning method is used to determine which

shapes belong to this concept. The best matching

shapes are the ﬁltered suitable 3D-shapes.

4.2.1 SVDD

SVDD (Tax and Duin, 2004), solves a multidimen-

sional outlier detection problem. The aim here is

not to estimate a probability density like in standard

methods, but rather to construct a spherically shaped

boundary around the target set. Hence, the following

optimization problem is solved:

Minimize R

∑

subject to k x

− a k

≤ R

+ ξ

, ξ

≥ 0 ∀i

(1)

Where x

are the targets, R is the radius of the spher-

ically shapes boundary, ξ

are slack variables and C

controls the trade-off between the volumes and the er-

rors.

One of the advantages of this method is that it

allows the possibility of outliers in the training set.

Then the optimization is modiﬁed as explained in

(Tax and Duin, 2004). However, it still well performs.

Furthermore, it is really ﬂexible as one can choose to

use his kernel function instead of the inner product

used by default.

4.2.2 SimpleMKL

SimpleMKL is a Multiple Kernel Learning (MKL)

method introduced by (Rakotomamonjy et al., 2008).

MKL was ﬁrst introduced in (Lanckriet et al., 2004),

then it was subject to enhancements, extensions and

algorithms to solve the problem in (Bach et al., 2004;

Sonnenburg et al., 2006), before (Rakotomamonjy

et al., 2008) propose a new formulation and a new

algorithm. SimpleMKL uses the same approach as

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traditional SVM but instead of looking for only one

kernel it looks for several kernels and linear combi-

nations of these kernels then ﬁnds the best one and

optimizes it.

The idea behind MKL as summarized in (Rako-

tomamonjy et al., 2008) is to look for a different so-

lution of the learning problem. Indeed in one class

learning problem the solution is of the form

f (x) =

∑

i=1

∗

K(x, x

) (2)

where α

∗

are some coefﬁcients to be learned from ex-

amples x

and K(., .) is a given deﬁnite kernel associ-

ated with a reproducing kernel Hilbert space (RKHS),

H. (Lanckriet et al., 2004) proposed to consider the

kernel K(., .) as a convex combination of basis kernels

K(x, y) =

∑

m=1

(x, y)

with d

≥ 0,

∑

m=1

= 1

(3)

where M is the total number of kernels, K

, which are

classical kernels. Hence, MKL is learning both the

coefﬁcients α

∗

and d

in a single optimization prob-

lem. To work out this problem, and following (Rako-

tomamonjy et al., 2008) that claims that their method

can be extended to a one-class problem, we used the

following extension of SimpleMKL:

Minimize

{ f

},ξ

,ρ

∑

k f

νn

∑

− ρ

subject to

∑

) ≥ ρ − ξ

, ∀i,

≥ 0, ∀i,

∑

= 1, d

≥ 0, ∀m,

(4)

where n is the number of examples and ν the error

allowed. H

are the RKHS associated to each K

(., .)

and each function f

belongs to a different H

. It is

assumed that one looks for a decision function of the

form f (x) =

∑

(x).

4.3 Retrieval

After learning the semantic concept, we retrieve real-

world shapes that match this semantic concept using

our designed suitable shapes. Here we introduce the

method we use to retrieve real world 3D-shapes.

We perform retrieval with a recent unsupervised

method for 3D retrieval using Kernels on Extended

Reeb Graphs from (Barra and Biasotti, 2013). This

method used some real functions to perform differ-

ent Extended Reeb Graphs (ERG) of each 3D model.

This family of Extended Reeb Graphs is considered as

the graph representation of those 3D models. Hence,

in order to assess similarity of 3D models, a Gaus-

sian kernel similarity measure is deﬁned on the set of

graphs. The measure is based on a representation of

graphs in terms of bag of shortest paths with bounded

maximal length. It is used to determine similarity be-

tween ERG of the same real function. Therefore, the

r nearest neighbors of a query 3D-shape, where r is an

integer, can be computed according to the ERG simi-

larity of each real function. Then, an aggregated func-

tion is used to sum up the outcomes for each real func-

tions and solve the 3D retrieval problem, that is to say

giving the overall r nearest neighbors. This method

has been compared with state-of-the-art methods and

performs very well, as most of the time it outperforms

reference methods. We refer to (Biasotti et al., 2008)

for Extended Reeb Graphs.

This method is the one we use to run experiments

presented in this article.

5 EXPERIMENTS

In this section, we investigate how our process can be

useful to retrieve semantic concept. Doing this, we

learned three concepts (Figure 4) which correspond

to the following semantic requests:

• high chair: chair with a seat raised at a fair dis-

tance from the ground or with high feet length.

• low chair: chair with small feet length.

• stand up humanoid (stand hum).

Figure 4: Examples of high chair, low chair and stand hum.

Then we used our algorithm to retrieve match-

ing shapes in the database of the watertight track of

the Shape Contest SHREC’07 (Giorgi et al., 2007).

We give details of the comparison between our three

learning methods in section 5.1. Section 5.2 gives

some examples of designed shapes, afterwards re-

trieval outputs are detailed in section 5.3.

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Figure 5: Precision/Recall graphs for each concept. Precision is the fraction of relevant retrieved objects to a given query, and

recall is the fraction of relevant objects which have been retrieved from the database. If O is the set of relevant objects to the

query, A is the set of objects retrieved, O

is the set of relevant objects in the result set then P =

|OA|

|A|

and R =

|OA|

|O|

5.1 Choice of the Learning Method

In order to test our algorithm, we compared the learn-

ing methods presented in section 4.2 to choose the

best one to learn our semantic concepts. A cross vali-

dation was performed to determine which parameters

were the best for each learning method. We worked

with a training dataset of a hundred of shapes of each

concept: stand up humanoids, low chairs and high

chairs. The test dataset was composed of a hundred

of instances of each concept and one hundred shapes

of non stand up humanoids.

We assumed that a standard user will provide

at most ﬁve instances representing the concept he

wants to be learned. Therefore, for each concept we

randomly partitioned our training data into twenty

subsamples of ﬁve instances. Then, we repeatedly

learned each subsample and test our precision using

the remaining subsamples.

We only mention here the average error obtained

for each method. Figure 5 shows the precision and

recall graphs for each concept. SVDD has the best

precision recall curves. It outperforms SimpleMKL

for the three concepts. SimpleMKL performs well for

both chair concepts but give poor performances for

the stand up humanoid concept.

Table 1 summarizes the overall precision on the

testing database. SVDD has the lowest error for high

chair and stand up humanoid concepts. However,

SimpleMKL is the best for the low chair concept.

Both methods have approximately the same error for

chair concepts but SVDD outperforms SimpleMKL

for the humanoid concept.

Hence, based on these observations, we chose to

use SVDD as our method to learn semantic concept.

Table 1: Percentage errors for each concept.

Concept MKL SVDD

High chair 12.58 12.29

Low chair 13.43 13.46

Stand hum 39.70 23.11

5.2 Suitable 3D-shapes

SVDD was run to select the three best matching ob-

jects from a random dataset of two hundred chairs and

two hundred humanoids for each of our three con-

cepts. Figure 6 shows the ﬁrst three selected high

chairs, ﬁgures 7 and 8 the ﬁrst three selected shapes

for respectively low chairs and stand hum.

Figure 6: Examples of ﬁrst three selected high chairs

(ranked from left to right).

Figure 7: Examples of ﬁrst three selected low chairs (ranked

from left to right).

Figure 8: Examples of ﬁrst three selected stand hum (ranked

from left to right).

The outcomes are good according to what we ex-

pected. These shapes are used to retrieved object in

the next section.

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5.3 Retrieval Outputs

We did a retrieval in SHREC’07 database with the

method of (Barra and Biasotti, 2013) to see what we

can get from a thorough database with our designed

shapes. We chose SHREC’07 (Giorgi et al., 2007) be-

cause it is a 3D-shape database which was manually

established with enough variation in order to evalu-

ate the effectiveness of 3D-shape retrieval algorithms.

The collection is composed of 400 mesh models, sub-

divided into 20 classes of 20 elements each.

Figure 9: Instances used to retrieve 3D-shapes in

SHREC’07.

The three shapes showed in Figure 9 were the

one used to retrieve 3d-shapes. Figure 10 shows the

ﬁrst retrieved shapes for each concept. The retrieved

Figure 10: The ﬁrst retrieved shapes for each concept.

shapes are on the top shapes we expected to have in

our ﬁrst retrieved one. This shows arguably that we

can connect our suitable 3D-shapes with state-of-the-

art designed one.

6 DISCUSSION

This paper presents results of a prototype phase. The

learning and retrieval methods used were chosen not

only because they are widely used in the literature and

perform very well but also because they are easy and

fast to implement. Readers can feel free to replace

those methods by methods of their choice.

Similarly, here only chairs and humanoids are

modeled but new objects can be added quickly be-

cause our method does not require thorough models.

Moreover, we said that we used ﬁve learning ex-

amples to build our ﬁlter because we thought that a

user will arguably select at least ﬁve elements. How-

ever, there is another reason: we ran some experi-

ments to know with how many learning examples we

were able to build a reliable machine ﬁlter. Hence, we

splitted up our learning database of one hundred ex-

amples in several set of the same number starting by

set of one element to set of 50 elements. These pro-

cess was done for each concept. Then, we did a cross

validation for each set to determine the best parame-

ters to use to learn with according to the number of

element in the set. The same test data used in section

5 has been used to perform tests and we gathered the

average learning error obtained for each number of

learning examples. This was repeated for each con-

cept and each learning method. Figure 11 shows the

average test error according to the number of learn-

ing examples used to build the machine ﬁlter. The

results show that we are able to build a reliable ﬁlter

with less than ﬁve learning examples for each concept

but the number of learning examples that performs the

best depends on the learned concepts and the learning

method used. For instance, when learning the high

chair concept, SVDD has better performances with 30

learning examples and SimpleMKL with 10 learning

examples. However, If we look at the error obtained

when learning with less than ﬁve elements, the best

performances are obtained when learning with three

or ﬁve elements. We chose to learn with ﬁve exam-

ples but one may prefer to learn with only three.

Another issue is the number of semantic requests

presented. This choice has been driven by the large

degree of freedom of our generator. The probability

to get shapes matching the concept the user wants is

really low, even if we already know which class of ob-

ject he wants, there are thousand of possible postures.

One of our futur work is to develop a tool that allows

the users to specify what he wants without choosing

between thousand of models. However, theoreticaly

user who wants to ask for 3D-shapes representing a

new semantic request just needs to select a sample of

3D-shapes. Then those shapes are processed and ana-

lyzed as explained in the former section.

7 CONCLUSIONS

An algorithm to generate suitable 3D-shapes corre-

sponding to a speciﬁc semantic concept is proposed

in this article. The principle is to allow the user to

specify his semantic query by selecting representing

3D-shapes designed by a 3D-shapes generator that in-

tegrates a part of randomness, enabling to explore the

uncertainty characteristic of such a request. The con-

cept behind the selected shapes is learned to create

automatic ﬁlters for future usage and used to retrieve

shapes in SHREC’07 database.

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Figure 11: Evolution of the test error according to the number of learning examples used to build the machine ﬁlter.

We plan to make numerous improvements in our

work. We are currently working on a method allow-

ing the user to more easily select suitable shapes for

concept matching. Moreover, we hope to run directly

our algorithms to retrieve uncertain shapes.

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