Journal of Software Engineering and Applications, 2011, 4, 306-310
doi:10.4236/jsea.2011.45033 Published Online May 2011 (http://www.SciRP.org/journal/jsea)
3D Object Recognition by Classification Using
Neural Networks
Mostafa Elhachloufi1, Ahmed El Oirrak1, Aboutajdine Driss2, M. Najib Kaddioui Mohamed1
1University Cady Ayyad, Faculty Semlalia, Department of Informatics, Marrakech, Morocco; 2University Mohamed V, Faculty of
Science, Department of Physique, LEESA-GSCM, Rabat, Morocco.
Received March 27th, 2011; revised April 28th, 2011; accepted May 12th, 2011.
ABSTRACT
In this Paper, a classification method ba sed on neural networks is presented for recognitio n of 3D objects. Indeed, the
objective of this paper is to classify an object query against objects in a database, which leads to recognition of the
former. 3D objects of this database are transformations of other objects by one element of the overall transformation.
The set of transforma tions considered in this work is the general affine group.
Keywords: Recognition, Classification, 3D Object, Neural Network, Affine Transformation
1. Introduction
The growing number of 3D objects available on the
Internet or in specialized databases, mandates the es-
tablishment of methods to develop techniques for rec-
ognition and description to access the content of these
smartly objects. However the objects’ 3D object rec-
ognition has been as extensive and has become very
important in many areas.
In this framework, several approaches exist: In terms
of statistical approaches, the statistical shape descrip-
tors for recognition generally consist of either calcu-
lating various statistical moments [1-3] or estimating
the distribution of the measurement of a given geomet-
ric primitive, which is deterministic [3] or random [2].
Among the approaches by statistical distribution, we
mention the specter of a 3D shape (3D SSD) [4] which
is invariant to geometric transformations and algebraic
invariants [5], providing of global descriptors, ex-
pressed in terms of moments of different orders. For
structural approaches, the approaches representing the
segmentation of a 3D object into plot of land and rep-
resentation by the adjacency graph are presented in [6]
and [7].
In the same vein, Tang elder et al. [8] have devel-
oped an approach based on representations by points of
interest. In approaches by transformation a very rich
literature emphasizes any interest in approaches based
on Haugh transformation [9-11] which include detect-
ing different varieties of (n − 1) dimension diving into
the space.
In the same vein, this work focuses on defining a
method that allows the recognition of 3D objects by
classification based on neural networks. Classification
is a computing tool that expects as input a list of num-
bers, and which provides, at its output, an indication of
class. A classifier must be able to model the best bor-
ders that separate classes from each other. This model-
ing uses the concept of discriminant function, which
allows to express the classification criterion. Its role is
to determine, among a finite set of classes, to which
class a particular item belongs.
2. Representation of 3D Objects
3D object is represented by a set of points denoted


1, ,
ii
MP n


 where

3
,,
iiji
Pxyz

 , arranged in
a matrix
X
. Under the action of an affine transforma-
tion, the coordinates


,,
x
yz are transformed into other
coordinates


,,
x
yz
 by the following procedure:
      
  
33
:
,, ,,
,,
f
x
tytzt fxtytzt
xtyt zt




 


XXY
YAX B


with


,,1,2,3 ij ij
a A
3

invertible matrix associated with
and is a vector translation in . B3 

3D Object Recognition by Classification Using Neural Networks307
3. Classification
Classification is a research area that has been developed
in the sixties. It is the basic principle of multiple support
systems for diagnosis. It assigns a set of objects to a set
of classes according to the description thereof. This de-
scription is done through properties or specific conditions
typical to these classes.
Objects are then classified according to whether or not
they check these conditions or properties. Classification
methods can be supervised or unsupervised.
Supervised methods require the user a description of
the classes while those unsupervised are independent of
the user. Rather they are methods of statistical grouping
that sort objects according to their properties and form
sets with similar characteristics.
4. The Artificial Neural Networks
The artificial neural networks (ANN) are mathematical
models inspired by the structure and behavior of bio-
logical neurons [12]. They are composed of intercon-
nected units called artificial neurons capable of perform-
ing specific and precise functions [13]. ANN can ap-
proximate nonlinear relationships of varying degrees of
complexity and significant to the recognition and classi-
fication of data. Figure 1 illustrates this situation.
4.1. Architecture of Artificial Neural
Networks
For an artificial neural network, each neuron is inter-
connected with other neurons to form layers in order to
solve a specific problem concerning the input data on the
network [14,15].
The input layer is responsible for entering data for the
network. The role of neurons in this layer is to transmit
the data to be processed on the network. The output layer
can present the results calculated by the network on the
input vector supplied to the network. Between network
input and output, intermediate layers may occur; they are
called hidden layers. The role of these layers is to trans-
form input data to extract its features which will subse-
quently be more easily classified by the output layer. In
these networks, information is propagated from layer to
layer, sometimes even within a layer via weighted con-
nections.
A neural network operates in two consecutive phases:
a design phase and use phase. The first step is to choose
Figure 1. Black box of artificial neura l networks.
the network architecture and its parameters: the number
of hidden layers and number of neurons in each layer.
Once these choices are fixed, we can train the network.
During this phase, the weights of network connections
and the threshold of each neuron are modified to adapt to
different conditions of input. Once the training on this
network is completed, it goes into use phase to perform
the work for which it was designed.
4.2. Multilayer Perceptron
For a multilayer network, the number of neurons in the
input layer and output layer is determined by the problem
to be solved [14-16]. The architecture of this type of
network is illustrated in Figure 2. According to R.
LEPAGE and B. Solaiman [14],the neural network has a
single layer with a hidden number of neurons appro-
ximately equal to:

12JNM

where:
N: number of input parameters.
M
: the number of neurons in the output layer.
4.3. Figures and Tables
The learning algorithm used is the gradient back propa-
gation algorithm. [17] This algorithm is used in the feed
forward type networks, which are networks of neurons in
layers with an input layer, an output layer, and at least
one hidden layer. There is no recursion in the connec-
tions and no connections between neurons in the same
layer.
The principle of backpropagation is to present the
network a vector of inputs to the network, perform the
calculation of the output by propagating through the lay-
ers, from the input layer to the output layer through hid-
den layers. This output is compared to the desired output,
an error is then obtained. From this error, is calculated
the gradient of the error which in turn is propagated from
the output layer to the input layer, hence the term back
propagation. This allows modification of the weights of
the network and the refore learning. The operation is
repeated for each input vector and that until the stop cri-
ter ion is verified [18].
4.4. Learning Algorithm
The objective of this algorithm is to minimize the maxi-
mum possible error between the outputs of the network
Figure 2. Architecture of a multilayer perceptron network.

3D Object Recognition by Classification Using Neural Networks
308
(or calculated results) and the desired results. We spread
the signal forward in the layers of the neural network:
j
 
1n
kn
x
x
 The spread forward is calculated using the
activation function, the aggregation function (often a
scalar product between the weights and the inputs of the
neuron) and synaptic weight
h
j
kbetween the neuron
and the neuron
w

1n
k
x

n
j
x
as follows:
 

 
1nnn nnn
kj jkk
k
xghgwx





 (1)
When the forward propagation is complete, we get the
output result. It then calculates the error between the
output given by the network and the desired vector
y
y
s
.
For each neuron i in output layer is calculated:



sortie sortie
iii
eghs

i y (2)
It propagates the error backward through
the following formula:
 
1nn
ij
ee


 


 111nnn
ii
eghwe


n
iji
(3)
It updates the weights in all layers:
 
1nnn
iji j
weX 

 (4)
where is the learning rate (of low magnitude and less
than 1.0).

5. Principle of the Proposed Method
The principle of the proposed method is as follows:
Step 1:
Given two 3D objects (object of database)
X
and Y
(query object) that seeks to verify if they are related by a
linear transformation and therefore are part of the same
class (class of objects and transformed by an affine
transformation), so we take as a first step r random
samples of size of points
p
X
respectively points
named 12 r
ee e
Y

,

,...,
x
xx respectively12 r
ee e
After that we study the association between the samples
0
e

.y, ,yy...,
x
and 0
e
y


0, 2,...,
0
e
1ir. To do this we extract the
parameters

and 0
e

that can transmit 0
e
x
to 0
e
y
as follows :
0
00
ii
eie
yx
0
i

  (5)
using neural networks as shown in the Figure 3.
Step 2:
In this step, we first calculates the points of the vector
using the previously extracted parameters
i
c
e
y0
i

and
0
i

by the Formula (1) as follows:
0jj
c
eie
yx
Figure 3. Parameters extraction 0
i

and 0
i

.
and


1, 2,,jr

 as such 0, then we proceed to
calculate the errors
ji
j
err defined as follows:

2
() ()
jjj j
c
je eee
k
erryyy ky k 
c
(7)
corresponding to the pairs of samples which

,
je
j
c
e
yy k
represents the number of vector elements
j
e
x
.
Step 3:
This step involves the classification of objects using mul-
tilayer neural networks whose input vector is the vector
of errors:


01
,,..., r VectErrerr errerr
1cand the output is the class c, with

(class 1) if c

VectErr



else 0c

(class 0) where c

a preset threshold small
enough (very close to zero).
If 1c

so all errors are part of the same class, a class
where errors are very close to zero, i.e. that:
0
0,
kk kk
c
keeeie
erry yyx0
i

 (8)


1, 2,...,kr
This means that all points of
X
are converted into
points of Y by the same parameters 0
e

and
0
e

Y is an affine transformation
X
. Else, this is
not the case of an affine transformation of
X
into Y.
6. Results and Discussion
Consider two 3D objects X (object of a database) and Y
(query object) related by an affine transformation (Fig-
ure 4 and Figure 5) and divided into 20 samples. The
goal is to reach neural structures capable of recognizing
0
i

  (6) Figure 4. Origin Object.

3D Object Recognition by Classification Using Neural Networks309
Figure 5. Transformed object.
Figure 6. Representation errors .
i
err
Figure 7. Affect of error classes built.
the errors corresponding to samples of objects belonging
to the same class. The learning base is comprised of input
variables (errors) and desired outputs variables (classes).
The desired output will serve as a comparison with the
calculated output during the learning phase. After train-
ing the network, tests were conducted on a number of
data (errors) to check their performance. According to
the results (Figure 6 and Figure 7) of the validation test
we notice that over 95% of errors are classified in the
class 1, which shows that according step 3 is an
affine transformation of
cY
X
.
7. Conclusions
In this work, we presented a classification method for
recognizing 3D objects. Indeed, we have developed an
approach based on neural networks which is a first step
to split the objects into n samples and then calculate the
errors for these samples. Using the proposed method,
they will be subject to classification for the recognition
of these objects. Recognition is performed using the
classification errors rate corresponding to objects (object
of origin and its clone) as shown in Figure 6. The simu-
lation results were presented and an evaluation of the
designed system has been made. They were generally
satisfactory and show the validity of the proposed
method.
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