3-D Face Recognition Using Improved 3D Mixed Transform

Mr. Hamid M. Hasan , Prof. Dr. Waleed A. AL.Jouhar & Dr. Majid A. Alwan
International Journal of Biometrics and Bioinformatics (IJBB), Volume (6) : Issue (1) : 2012 278
3-D Face Recognition Using Improved 3D Mixed Transform
Mr. Hamid M. Hasan Hamid2012net@gmail.com
College of Eng./ Electrical Eng. Dept.
Basra University
Basra , Iraq
Prof. Dr. Waleed A. AL.Jouhar Profwaleed54@yahoo.com
College of Eng. /Electrical Eng. Dept.
Baghdad University.
Baghdad , Iraq
Dr. Majid A. Alwan Altimimee@yahoo.com
Electrical Eng. Dept
Basra University, college of Eng.
Basra , Iraq
Abstract
This paper deals with the using of Improved 3D Mixed Transform (3D-IMT) for face recognition
problem. The mixed transform consists Fourier based 3D radon transform plus 1-D Wavelet
transform (which is also known as 3D Ridgelet transform). The Mixed Transform is improved by
using the Particle swarm optimization ( PSO) technique. The improvement involves the selection
of the best of directions for smart rectangle-to-polar transform as a part of the 3D Radon
Transformation. The 3D-IMT is applied to the 3D representation of face images, and yields a few
number of features, these features is projected into the maximized projection that achieves good
recognition rate using the Linear Discriminant Analysis (LDA).
Keywords: Face Recognition, 3-D Radon Transform, Particle Swarm Optimization (PSO),
Wavelet Transform ,Linear Discriminate Analysis (LDA) .
1. INTRODUCTION
1.1. Face Recognition Problem
Face recognition is one of the most important biometrics which seems to be a good compromise
between actuality and social reception and balances security and privacy well. It has a variety of
potential applications in information security law enforcement, access controls. Face recognition
systems fall into two categories: verification and identification, Face verification is 1:1 match that
compares a face images against a template face image. On the other hand face identification is
1:N problem that compares a probe face image against all image templates in a face database.
Face recognition is a very difficult problem due to a substantial variation in light direction
(illumination) , different face poses , and diversified facial expressions, Aging ( changing the face
over time), Occlusions (like glasses, hair, cosmetics ) , so building an automated system that
accomplishes such objectives is very challenging. In last decade many systems with recognition
rate greater than 90% has been done. However a perfect system with 100% recognition rate
remains a challenge. Face recognition algorithms are divided by [1,2] into three categories, as
follows:-
1. Holistic methods: These methods identify a face using the whole face images as input
and extract the overall features.
2. Feature based methods: these methods used the local facial features for recognition (
like eyes , mouths, fiducial points ..etc.)

3. Hybrid methods: these methods used both feature based and holistic features to
recognize a face. These methods have the potential to offer better performance than
individuals.
1.2. Three Dimensional (3D) Face Recognition
The vast majority of Researches deal with methods based on 2D image processing using
intensity or color images which reached higher than 90% recognition rate under controlled lighting
conditions whoever the performances drop in case of pose, illumination and expression variation.
Almost the 2D techniques still encounters many difficulties. On the other hand the three
dimensional (3D) face recognition technologies is now emerging, in part, due to the availability of
improved 3D imaging devices and processing algorithms. The main argument in favor of using 3D
information for face recognition appears to be that it allows us to exploit feature based on shape
and the curvature of the face without being plagued by the variances caused by lighting also the
pose variation can be corrected by rigid rotations in 3D space they also provide structural
information about the face (e.g., surface curvature and geodesic distances) which cannot be
obtained from a single 2D image. The 3D face recognition algorithms can be broadly classified
into three groups [3], first, there are the 3D appearance based techniques these techniques
include the statistical methods like PCA and 3D PCA, ICA, LDA, 3D techniques based on ICA
and LDA have been reported to perform better than 3D PCA. The second class use a 3D facial
surfaces to represents individuals these 3D models are rotated and translated using Iterative
Closest Point (ICP) algorithm the ICP based algorithms are reported to be robust to variable facial
poses and illumination the expression variation can be deal with using intrinsic representation of
facial surfaces. The third class is the local feature based 3D face recognition techniques that
employ structural properties of local regions of the 3D face. Some of techniques in this class
employ facial profiles for matching 3D faces it is reported that the central vertical facial profile has
been noted to be effective at uniquely identifying individuals. Other using local geometric
characteristics of facial sub regions including their positional coordinates, surface areas and
curvatures , and the 3D Euclidean distances, ratios of distances, joint differential invariants, and
angles between the local facial regions. A few attempts have been made to automatically locate
facial landmarks on 3D models using surface. A number of techniques based on local facial
features have been reported to perform better than 3D PCA and ICP [4].
1.3.Three Dimensional (3D) Image Representation Techniques
Two main representations are commonly used to model faces in 3D space [5]. These are the
Point clouds or triangulated surface meshes and Range Images (also referred to as a 2.5D
surface or depth map). The point cloud representation contains the (x, y, z) coordinates of a set of
points on the facial surface. A range image consists of (x, y) points on a regular rectangular grid
each (x, y) point is associated with a z value of the point on the surface closest to the acquisition
device. The Techniques which are currently being used to obtain 3D information include [6]:-
• Scanning systems: using Laser face scanner.
• Structured light systems: These systems make use of the principles of stereo vision to obtain
the range data.
• Stereo vision systems: These systems that attempt to extract 3D information from two or more
2D images taken from different angles.
• Reverse rendering/shape from shading.
1.4. A Brief Historical Review of 3D Faces Recognition
Many surveys has been published [6,7,8] about the 3D Face Recognition most papers report
performance as rank-one recognition rate although some report equal-error rate or verification
rate at a specified false accept rate but on a limited number of persons and only a few have dealt
with data sets that explicitly incorporate pose and/or expression variation.
Cartox et al. [9 ]approached 3D face recognition by segmenting a range image based on principal
curvature they reported 100% recognition rate for either in small data set ( 5 persons and
database size was 18 images).

Nagamine et al.[10] approach 3D face recognition by finding five feature points, using those
points to standardize face pose.
Experiments are performed for 16 subjects with 10 images per subject the reported performance
was 100% but the computational requirements were apparently regarded as severe.
Hesher et al. [11] explore PCA style approaches the image data set has six different facial
expressions for each 37 subjects the reported performance is 97%.
Lu et al.[12] , using ICP-based approach performed on point set Images the approach assumes
that the gallery 3D image is a more complete face model and the probe image is a frontal view
that likely a subset of gallery image. In experiment with 18 persons a recognition rate of 96% was
reported.
Russ et al.[13] presented results of Hausdorff matching on range images they used portions of
FRGC v1 dataset they reported 98% as a probability of correct verification.
Chang et al. [14] describe a "multi-region" approach to 3D face recognition. It is a type of
classifier ensemble approach in which multiple overlapping sub regions around the nose are
independently matched using ICP and the results of the 3D matched are fused. The experimental
evaluation using the FRGC v2 data set was conducted in which one neutral-expression image is
enrolled as the gallery for each person. Performance of 92% rank-one recognition rate was
reported.
Passalis et al.[15] described an approach to 3D face recognition that uses annotated deformable
models. An average 3D face is computed on a statistical basis from a training set. Landmarks are
selected based on descriptions by Frakas. Experimental results are presented using the FRGC
v2 data set. For an identification experiment in which one image per person is enrolled in the
gallery (466 total) and all later images(3541) are used as a probe, performance reaches nearly
90% rank-one recognition.
Gupta S. et al.[3] they present a novel anthropometric 3D ( Anthroface 3D) face recognition
algorithm. It is a completely automatic face recognition algorithm that employs facial 3d Euclidean
and geodesic distances between 10 automatically located anthropometric facial fiducial points
and a linear discriminant classifier. On a database of 1149 facial images of 118 subjects the
EER=1.98% and rank one recognition rate of 96.8% was achieved.
Sina Jahanbin et al.[16] They present a novel identity verification system based on Gabor
features extracted from range image . Multiple landmarks (fiducials) on face are automatically
detected the Gabor features on all fiducials are concatenated to form a feature vector then the
LDA is used. The novel features were tested on 1196 range images from Texas 3DFRC database
the reported EER was 2.2%.
Hengliang Tang et al.[17] They presented a novel 3D face recognition algorithm based on sparse
representation. First, a 3D face normalization deal with the raw faces. Then, three types of facial
geometrical features are extracted to describe the 3D faces after that a feature ranking is
performed using (FLDA). Finally, the sparse representation framework is used to collect all the
face features. The experiments tested on the BJUT-3D and FRGC v2 databases. The reported
recognition rate is 95.3% for the method of fusing the three types of features.
2. THE PROPOSED METHOD
Our approach for 3D Face Recognition is depicted in figure (1). The range Images were used
from the Texas3DFR Database [38]. Firstly, the images were preprocessed by interpolation
method in order to remove the holes due to spikes these Range images are translated into 3D
space using topography representation as 3D array these 3D data is transformed into 3D Radon
space using 3D Radon Transform (3DRT). The (3DRT) is optimized by Particle Swarm
Optimization (PSO) to select the best directions (i.e. θ, ϕ). These directions achieve a high
recognition rate as well as the minimum number of features. The selected features in Radon

space is translated into two parts using 1-D Wavelet Transform then only one part is selected so
only a half number of features are used. These features are projected into maximized
discriminate projection using Linear Discriminant Analysis (LDA).
FIGURE 1: The system block diagram.
2.1 The 3D Radon Transform
2.1.1 Introduction
The 3D Radon Transform integrates on planes. Let f(X) be a three dimensional signal where
X=[x, y, z]. Let, also ζ be a unit vector in R3 and ρ a real number. The 3D Radon Transform
RT( ζ , ρ ) of the f(x), is a function which associates to each pair (ζ , ρ) the integral of f(x) on the
plane Π(ζ , ρ)={x | x . ζ=ρ } [18] .
The 3D Radon Transform is given by the formula:
RT(ζ , ρ)=‫׬‬ fሺxሻδሺX. ξ െ ρሻdx
ାஶ
ିஶ
(1)
Since ζ can be written in spherical coordinates as ζ=[ cosϕsinθ ,sinϕcosθ,cosθ] then equation (1)
can be rewritten:
RT(ρ,θ,ϕ)=‫׬‬ ‫׬‬ ‫׬‬ fሺx, y, zሻ
ାஶ
ିஶ
ାஶ
ିஶ
ାஶ
ିஶ
. δሺxcos‫׎‬sinθ ൅ ysin‫׎‬sinθ ൅ zcosθ െ ρሻdxdydz ሺ2ሻ
Each value of the RT(ρ,θ,ϕ) expresses the summation of the values of f(x,y,z) which lie on the
plane defined by the parameters (ρ,θ,ϕ ).
2.1.2 Radon Transform Using Fast Fourier Transform
A tight relationship exists between Fourier transform (FT) and Radon transform (RT) of a function.
The 1D FT of n-dimensional RT(f) along the radial direction ρ represents a radial sampling of the
n-dimensional FT of f. This is the central-slice theorem. With the central-slice theorem the 3D
Radon transform can be computed equivalently by performing a 3D DFT, a Cartesian-to-polar
mapping, and a 1D DFT. This process requires 3D interpolation in real space which is a
computation intensive. The computing cost is substantially reduced in a two-step process. In the

first step rotate the structure stepwise around one axis and obtain a set of projections. In the
second step compute the 2D Radon transform of each projection.
2.1.3 Particle Swarm Optimization (PSO)
PSO was firstly introduced by Kenny and Eberhart in 1995 [20] it is one of the evolutionary
computation technology based on swarm intelligence. In a PSO system each solution called a
"particle". Particles fly around in the problem search space to look for the optimal solution. Each
particle adjusts its position according to the flying experience of its own and the experience of
neighboring particles. Each particle updates its velocity and position using the following equation
[21]:-
Vi(k+1) = Vi(k)+c1* rand1( pbest(k) - Xi(k)) + c2* rand2( gbest(k) - Xi(k)) (3)
Xi (k+1)=Xi(k) + Vi(k+1) (4)
Where ,
Vi is called the velocity for particle i;
Xi is represent the position of particle i ;
Pbest is the best position of ith particle ;
gbest is the global best position ;
rand is random variable in [0,1];
c1 and c2 are the learning factors;
w is called the inertia weight .
To search for optimal solution each particle changes its velocity according to Eq (3). The value of
Vi is clamped to the range [Vmin, Vmax] to avoid excessive roaming of particle outside the
searching space. Then each particle moves to a new potential solution using Eq. (4). This
process is repeated until a stopping criterion is reached. The above equations (3,4) are the basic
Equation and not guarantee the global solution is reached and may trapped in local minima. To
avoid the local minima there are many variations for the basic equations have been suggested
like (QPSO ) which adding quantum behavior to basic PSO[22,23,24], (CPSO ) which add
chaotic[25] through chaos maps to basic PSO also the mixing of the two previous methods is
suggested in [23] , There are an efforts to add the crossover and mutation used in GA to be used
with PSO which improve its behavior and avoids the local minima[26]. Also a varying dimensional
particle swarm optimization (VD-PSO) was proposed by Yanjun Yan[27]. An improved PSO by
estimation of distribution was introduced in[28].
Some of PSO applications in the Face Recognition field are feature selection optimization[29],
Robust object detection scheme using Binary PSO[30], A Novel Evolutionary Face Recognition
using PSO[31], Face Recognition Using shift invariant feature transform and BPSO[32], Face
Recognition by Extending EBG matching using PSO[33], using CPSO-SVM in Face Recognition
[34], Holistic and partial facial fusion by BPSO[35].
In our project the PSO is used to select the best values of (θ, ϕ) for 3D Radon transform; that
achieve the high recognition rate. The range of (θ, ϕ) for 3D Radon transform is (-π to π) but due
to symmetry of the transform we can calculate only in range (-π/2 to π/2). Also for discrete RT
only the integer values are used. We used the PSO to select the minimum number of angles (θ,
ϕ) required to obtain the best recognition rate. A novel method of encoding the parameters (θ, ϕ)
within the particle was used which led to a reduced number of computations that are required by
3D Radon.
2.1.4 Wavelet Transform
The continuous wavelet transform (CWT) is defined as the sum over all time of the signal
multiplied by scaled, shifted versions of the wavelet function ψ:

Cሺscal, positionሻ ൌ ‫׬‬ fሺtሻψሺscal, positionሻ
ାஶ
ିஶ
(5)
The results of the CWT are many wavelet coefficients C which are a function of scale and
position calculating wavelet coefficients at every possible scale is a fair amount of work, and it
generates an awful lot of data. What if we choose only a subset of scales and positions that if we
choose scales and positions based on powers of two so called dyadic scales and positions then
our analysis will be much more efficient and just as accurate[36]. An efficient way to implement
this scheme using filters was developed in 1988 by Mallat. The Mallat algorithm is in fact a
classical scheme known in the signal processing community as a two-channel sub band coder for
many signals and the low-frequency contents is the most important part. It is what gives the
signal its identity. On the other hand the high-frequency contents impart flavor or nuance In
wavelet analysis. We often speak of approximations and details. The approximations are the
high-scale low-frequency components of the signal. The details are the low-scale high-frequency
components see figure (2). In our project only the approximations signal (A) is used and the
details signal (D) is ignored this achieves two goals. The first is that the features produced will
maintain a high classification rate. The second is the number of features are reduced into one
half. The mother wavelet (ψ) used is Daubechies (db1) also known as Harr which has been
proven effective for image analysis and feature extraction.
FIGURE 2: Level one Discrete Wavelet Transform (DWT)
2.1.5 Linear Discriminant Analysis (LDA)
The LDA finds a set of basis vectors which maximizes the ratio of the between-class scatter and
within–class scatter [37]. Given N samples of C classes and let Ni be the number of samples in
the ith class( ci). let Mt be the mean of the whole data set and mi be the mean of the ith class (ci)
then the between-class scatter matrix is defined by:
SB ൌ ∑ N୧ሺmi െ Mtሻ ሺmi െ MtሻTୡ
୧ୀଵ (6)
And the within-class scatter matrix is defined by

(7)
Then the basis vectors is:
(8)
3. THE EXPERIMENTS
Three different experiments were conducted using Texas 3DFR Database [38]. The Texas 3D
Face Recognition Database contains 1149 range and portrait mage pairs of adult human subjects
each image is (751 x 501) 8-bit. A Sample image and its 3D representation is shown in figure
(3).The database images are scaled down into (94 x 63). Each scaled image is transformed into
3D space as (94, 63, 90) array of real numbers these 3D arrays were transformed into 3D radon
space as (90, 90, 90) real numbers. This means that each image is represented as (729000) real
numbers. A features vector of length (90) real numbers was selected from (72900) real numbers
by using PSO. Those (90) value vectors was further reduced into (45) value vectors after Wavelet
Transform. These feature vectors were projected into the maximized discrimination projection
using the Linear Discriminante Analysis (LDA) and stored into the database .
FIGURE 3: left one is the Range Image and right one is the 3D representation of the left.
3.1. Experiment No.1
In this experiment 100 subjects were selected with two different images for each subject one for
the gallery and one as a probe image for testing. In this experiment the LDA stage is not used
because there is only one sample per class is used. The other stages depicted in fig(1) were
used. The recognition rate achieved conducting this experiment was RR=86% .
In this experiment 18 subjects were selected with 10 images per subject as a gallery and more
than 10 images as a probe. The gallery set and probe set are disjoint; see figures (4, 5). The
complete system was used In this experiment. The recognition rate achieved was 100%.

FIGURE 4: The upper 10 range images are a samples of images for a person used in the
gallery , the lower 10 are the portrait for the same range images in the upper part.
FIGURE 5: The upper range images are a samples of images for a person used as Probes ,
the lower are the portraits for the same range images in the upper part.
In this experiment an (18) subjects were used with 10 images per subject as a gallery. The probe
set was composed of 180 images for authorized users and 180 image for imposters (not
authorized). All sets were disjoint . The Receiver Operating Condition ROC was illustrated by the
figure(6). The verification rate is 98.34% or ( FRR=1.66% , at zero FAR).

FIGURE 6: Receiver Operating Condition for experiment 3
4. DISCUSSION AND COMPARATIVES
The first and second experiments are recognition test for our method and the third one is for
verification test. The results are promise and even the comparison in not easy task because the
many differences between evaluation scenarios due to the different data set available and
different scenarios in partitioning those data sets between training and gallery and probe data
sets but we can depict the validity of our work as following
A. The first and second experiments can be compared with some related works as shown
in table(1). Some works used a controlled environment for the data set ( i.e. equal in
illumination and pose and expression ) some other not. The images we used are
selected randomly from the data base with different conditions.
B. The third experiment can be compared with some related works as shown in table(2).
Some of them follow the Face Recognition Grand Challenge (FRGC V2.0) ROC III
protocol they report the False Rejection Rate (FRR) at False Acceptance Rate (FAR)
equal to 0.1%. We report the Equal Error Rate (EER=1.3%) and the FRR=1.64% at
FAR=0.1% and FRR=1.66% at FAR=0%.
All the experiments are carried out using MATLAB software R2010a on a laptop computer with i3
CORE @ 2.4 GHz speed and 2 GB RAM. The time required to process one image approximately
equal to 5.56 msec and to process all the 180 images to be stored in the gallery was approximate
to 1 sec. The recognition or verification time is a faction of second and depends on the size of the
data base used which must be investigated further. Also this method need to be tested on large
data set that agrees with the used scenario to test its validity.

author database #subject #Training
images
#Gallery
images
#Probe
images
Performance
Chang[41] Notre Dame 166 278 1/subject
controlled
1/subject
controlled
RR= 83.7%
Godil [42] CAESAR 200 - 1/subject 1/subject RR= 68%
Gupta[40] Texas
3DFR
12 360 1/subject
neutral
29/subject RR= 98.6%
Gupta[39] Texas
3DFR
105 - 1/subject
neutral
663 RR=98.64%
Our
experiment(1)
Texas
3DFR
100 No
training
1/subject
uncontrolled
1/subject
uncontrolled
RR = 86%
Our
experiment(2)
Texas
3DFR
18 180 10/subject
uncontrolled
10+/subject
uncontrolled
RR=100%
TABLE 1: A Comparison between some reported Face Recognition rates and the recognition
rate in experiment 1&2.
Author #subjects #Gallery
images
#Probe
images
Performance
Passalis [15] 466 FRGC v0.2 4007 4007 FRR = 3.6%
FAR = 0.1%
Husken [43] 466 FRGC v0.2 4007 4007 FRR = 2.7%
FAR = 0.1%
Maurer [44] 466 FRGC v0.2 4007 4007 FRR = 6.5%
FAR = 0.1%
Jahanbin[16] 109 109 382 + 424
imposters
EER= 2.2%
Our
experiment(3)
18 180 180 + 180
imposters
FRR=1.64%
FAR=0.1%
EER=1.3%
TABLE 2: Comprison between some reported Face Verification rates and the Verification rate in
experiment 3.
5. CONCLUSIONS
In this work an Improved 3D Mixed Transform (3D IMT) is used for 3D face recognition. The 3D
mixed Transform is also known as 3D Ridgelet Transform. It is composed of 3D Radon Transform
(3DRT) plus 1D Wavelet Transform. The 3D Radon that we are used is Fourier based. This
transform is improved by using (PSO) to select the best directions (θ, ϕ) along which the 3DRT is
performed. By this method the number of features is reduced to a vector of (45) elements as well
as achieved a maximized discrimination based on the Linear Discriminant Analysis (LDA) as a
consequence this leads to a high recognition rate. Three experiments were conducted:
1. In the first experiment a single image per person (i.e. a vector of 45 elements) is stored in the
database and another one is used for testing. The gallery set and probe set were disjoined.
The number of subjects used were 100 and the recognition rate was RR=86%.
2. In the second experiment ten images per person are used for training and more than ten for
testing. All images have different expressions, illuminations and poses. The training and
testing sets are non-overlapped. The number of subjects used were 18 subjects and the
recognition rate was RR=100%.
3. The third experiment was the same of the experiment 2 but the test set was different. Her test
set contains 180 imposters (no subject is stored in the database) and 180 images of
authorized subjects (stored in the database). The Receiver Operating Condition (ROC) is
illustrated in figure (6). The verification rate is 98.34% or (False Rejection Rate (FRR) =1.66 %
at zero False Acceptance Rate).

6. ACKNOWLEDGMENT
We would like to appreciate the support of DR. Alan C. Bovik and DR. Shalini Gupta. for
permission to used the TEXAS3DRF Database.
7. REFERENCES
[1] Nilima B. Kachare, Vandana S. Inamdar, 2010, " Survey of Face Recognition
Tecchniques", International Journal of Computer Applications(0975-8887), Volum 1-
No.19,2010.
[2] Patil A.M., Kolhe S.R. and Patil P.M., 2010,"2D Face Recognition Techniques:A Survay",
International Journal of Machine Intelligence.
[3] Gupta,S. Mia K. Markey and Alan C. Bovik,2010, " Anthropometric 3D Face Recognition",
Int. J. Comput. Vis, Springer Science+Business Media LLC 2010.
[4] Irfanoglu, M. O. Golberk, B., & akarun L.(2004)." 3D shape based face recognition using
automatically registered facial surfaces", in proceeding of the 17
th
international conference
on pattern recognition, IEEE computer Society.
[5] Andera F. Abate, Michele Nappi, Daniel Riccio, Gabriele Sabatino, 2007, "2D and 3D face
recognition: A survey", Pattern Recognition Letters 28(2007) 1885-1906.
[6] Rabia Jafri and Hamid R. Arabnia , 2009,"A Survey of Face Recognition Techniques",
Journal of Information Processing systems, Vol 5, No.2, June 2009.
[7] Kevin W. Bowyer, Kyong chang, Patrick Flynn, 2006, " A survey of approaches and
challenges in 3d and multi-modal 3D+2D face recognition", Computer Vision and Image
Understanding 101(2006) 1-15.
[8] Gupta,S. Mia K. Markey and Alan C. Bovik,2007 ," Advances and Challenges in 3D and
2D+3D Human Face Recognition", In Pattern Recognition Research horizons, New York:
Nova Science.
[9] J. Y.Cartoux, et al., 1989," Face authentication or recognition by profile extraction from
range images, in: proceedings of the Workshop on interpretation of 3D Scenes, 1989,
pp.194-199.
[10] T. Nagamine, et al. "3D facial image analysis for human identification, in International
Conference on Pattern Recognition (ICPR 1992), pp.324-327.
[11] C. Hesher, et al." A novel Technique for face recognition using range imaging", in: Seventh
International Symposium on Signal Processing and Its Applications",2003 , pp.201-204.
[12] Lu et al.,"Matching 2.5D scans for face recognition " in: International conference on
Patteren Recognition(ICPR 2004),pp.362-366.
[13] Russ et al."3D facial recognition: a quantitative analysis, in 45-th Annual Meeting of the
Institute of Nuckear Material Management (INMM), July 2004.
[14] Chang et al."Adaptive rigid multi-region selection for handling expression variation in 3D
face recognition, in IEEE Workshop on Face Recognition Grand Challenge Expermints,
June 2005.

[15] Passalis, et al." Evaluation of face recognition in presence of facial expressions: an
annoted deformable model approach, in: IEEE Workshop on FRGC Expermints,
June,2005.
[16] Jahanbin S. et al."Automated facial Feature Detection and Face Recognition using Gabor
Features on Range and Portrait Images",2008,(ICIP 2008),pp.2768-2771.
[17] Tang H. et al. 2011" 3d face recognition based on sparse representation", J.
Supercomputer 58:84-95. Springer science+Business Media. LLC 2010.
[18] Dimitrio Zarpalas, et al., 2004," 3D Model Search and Retrieval Based on the 3D Radon
Transform",IEEE Communication Society.
[19] Slvatore lanzavicchia and pier luigi " fast computation of 3D Radon Transform via a direct
Fourier method",BIOINFORMATICS, vol.14 no.2 ,1998 pp212-216.
[20] Alec Banks, et al. " A review of particle swarm optimization. Part II: hybridization,
combinatorial, multicriteria and constrained optimization, and indicative applications", Nat
Comput (2008) 7:109-124, DOI 10.1007/s11047-007-9050-z.
[21] Shih wei Lin and shih chieh Chen, " PSOLDA: A particle swarm optimization approach for
enhancing classification accuracy rate of linear discriminant analysis", Applied Soft
Computing 9 (2009) 1008-1015.
[22] Millie Pant et al, "A New Quantum Behaved Particle Swarm Optimization",GECCO'08,July
12-16, 2008 Atlanta, Georgia. USA.
[23] Leandro dos Santos Coelho," A quantum particle swarm optimizer with chaotic mutation
operator", Chaos, Solutions and Fractals 37 (2008) 1409-1418.
[24] O. Togla altinoz, et al. " Chaos Particle Swarm Optimization PID Controller for the Inverted
Pendulum System", 2
nd
International Conference on Engineering Optimization, September
6-9, 2010, Lsbon, Portugal.
[25] Leandro dos Santos Coelho and Viviana Cocco Mariani, " A novel chaotic particle swarm
ooptimization approach using Henon map and implicit filitering local search for load
dispatch", Chaos, Solutions and Fractals 39(2009) 510-518.
[26] Qing Zhang, et al. " Fast Multi swarm Optimization with Cauchy Mutation and Crossover
operation", Puplications of China University of Geosciences, School of Computer, Wuhan,
P.R.China, 430074.
[27] Yanjun Yan and Lisa ann Osadciw, "Varying Dimensional Particle Swarm Optimization",
2008 IEEE swarm Intelligence symposim , St. Louis Mo USA, September 21-23,2008.
[28] R. V. Kulkarni and G.K. Venayagamoorthy, " An Estimation of Distribution Improved
Particle Swarm Optimization Algorithm", ISSNIP 2007.
[29] Yanj Yan, Ganapathi Kamath and Lisa ann Osadciw, " Feature Selection Optimization by
Discrete Particle swarm Optimization for Face recognition", Syracuse University , Syracuse
, NY, USA 13244.
[30] Hong Pan, LiangZhengXia, and Truong Q.Nguyen," Robust Object detection Scheme using
feature selectin", Proceeding of 2010 IEEE 17th
International Conference on Image
Processing , September 26-29, 2010, Hong Kong.

[31] Osslan Osiris Aergara Villegas and Viancy Guadalupe," a Novel Evolutionary Face
algorithm Using Particle Swarm Optimization ", 2009 Fith International Conference on
Signal Image Technology and Internet Based Syetems.
[32] Lanzarini Laura , et al. " Face Recognition Using SIFT and Binary PSO Descriptors", 2010
Proceedings of the ITI 2010 32th Int. Conf. on Information technology Interfaces, June 21-
24,2010, Cavtat, Croatia.
[33] Rajinda Senaratne, et al. " Face Recognition by Extending Elastic Bunch Graph Matching
with Particle Swarm Optimization", Journal of Multimedia , VOL. 4, No. 4, August 2009.
[34] Ming Li, et al. " Application of Improved CPSO-SVM Approach in Face Recognition", 2009
Internaltional Conference on Artificial Intelligence and Com[utational Intelligence.
[35] Xiaorong Pu, Zhang YI, Zhongjie Fang," Holistic and partial facial features fution by binary
particle swarm optimization", Neural Comput & Applic (2008) 17:481-488.
[36] C.Valens,1999-2004,"A Really Friendly Guide to Wavelets", ,available on Internet,
questions goto wavelets@polyvalens.com.
[37] Belhumeur PN, Hespanala JP, Kriegman DJ (1997) Eigenfaces vs. fisherfaces: recognition
using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711-720.
[38] Gupta, S. et al., 2010,"Texas 3D face recognition database", In Image analysis and
interpretation ,2010 IEEE southwet symposium on, Austin,TX.
[39] S. Gupta, M. K. Markey, J. K. Aggarwal, and A. C. Bovik. Three dimensional face
recognition based on geodesic and euclidean distances. In Electronic Imaging, Vision
Geometry XV, volume 6499 of Proc. of SPIE, San Jose, California, USA, Jan 28 -Feb 1
2007.
[40] S. Gupta, M. P. Sampat, Z. Wang, M. K. Markey, and A. C. Bovik. 3d face recognition using
the complex-wavelet structural similarity metric. In IEEE Workshop on Applications of
Computer Vision, Austin, TX, 2007.
[41] K. I. Chang, K. W. Bowyer, and P. J. Flynn. Multimodal 2d and 3d biometrics for face
recognition. In Analysis and Modeling of Faces and Gestures, 2003. AMFG 2003. IEEE
International Workshop on, pages 187–194, 2003.
[42] A. Godil, S. Ressler, and P. Grother. Face recognition using 3d facial shape and color map
information: comparison and combination. In Proceedings of the SPIE – The International
Society for Optical Engineering, volume 5404, pages 351–361, Nat.Inst. of Stand. &
Technol., Gaithersburg, MD, USA, 2004. SPIE-Int. Soc. Opt. Eng.
[43] M. Husken, M. Brauckmann, S. Gehlen, and C. Von der Malsburg. Strategies and beneﬁts
of fusion of 2d and 3d face recognition. In Computer Vision and Pattern Recognition, 2005
IEEE Computer Society Conference on, volume 3, pages 174–182, 2005.
[44] T. Maurer, D. Guigonis, I. Maslov, B. Pesenti, A. Tsaregorodtsev, D. West, and G. Medioni.
Performance of geometrix activeidTM 3d face recognition engine on the frgc data. In
Computer Vision and Pattern Recognition, 2005 IEEE Computer Society Conference on,
volume 3, pages 154–161, 2005.

3-D Face Recognition Using Improved 3D Mixed Transform

Recommended

More Related Content

What's hot (17)

Viewers also liked (7)

Similar to 3-D Face Recognition Using Improved 3D Mixed Transform (20)

Recently uploaded (20)

3-D Face Recognition Using Improved 3D Mixed Transform