Face liveness detection by learning multispectral reflectance distributions

Abstract

Existing face liveness detection algorithms adopt behavioural challenge-response methods that require user cooperation. To be verified live, users are expected to obey some user unfriendly requirement. In this paper, we present a multispectral face liveness detection method, which is user cooperation free. Moreover, the system is adaptive to various user-system distances. Using the Lambertian model, we analyze multispectral properties of human skin versus non-skin, and the discriminative wavelengths are then chosen. Reflectance data of genuine and fake faces at multi-distances are selected to form a training set. An SVM classifier is trained to learn the multispectral distribution for a final Genuine-or-Fake classification. Compared with previous works, the proposed method has the following advantages: (a) The requirement on the users' cooperation is no longer needed, making the liveness detection user friendly and fast. (b) The system can work without restricted distance requirement from the target being analyzed. Experiments are conducted on genuine versus planar face data, and genuine versus mask face data. Furthermore a comparison with the visible challenge-response liveness detection method is also given. The experimental results clearly demonstrate the superiority of our method over previous systems.

Full text

Page 1

Face Liveness Detection
by Learning Multispectral Reflectance Distributions
Zhiwei Zhang, Dong Yi, Zhen Lei, Stan Z. Li*
Center for Biometrics and Security Research & National Laboratory of Pattern Recognition
Institute of Automation, Chinese Academy of Sciences
{zwzhang,dyi,zlei,szli}@cbsr.ia.ac.cn
Abstract—Existing face liveness detection algorithms adopt
behavioural challenge-response methods that require user co-
operation. To be verified live, users are expected to obey
some user unfriendly requirement. In this paper, we present
a multispectral face liveness detection method, which is user
cooperation free. Moreover, the system is adaptive to various
user-system distances. Using the Lambertian model, we analyze
multispectral properties of human skin versus non-skin, and the
discriminative wavelengths are then chosen. Reflectance data
of genuine and fake faces at multi-distances are selected to
form a training set. An SVM classifier is trained to learn the
multispectral distribution for a final Genuine-or-Fake classifi-
cation. Compared with previous works, the proposed method
has the following advantages: (a) The requirement on the users’
cooperation is no longer needed, making the liveness detection
user friendly and fast. (b) The system can work without
restricted distance requirement from the target being analyzed.
Experiments are conducted on genuine versus planar face data,
and genuine versus mask face data. Furthermore a comparison
with the visible challenge-response liveness detection method is
also given. The experimental results clearly demonstrate the
superiority of our method over previous systems.
I. INTRODUCTION
Existing face recognition (FR) systems [1] are fragile to
attacks of fake faces, since the detection of liveness of the
captured faces has not been a built-in module. A typical
FR system can be deceived by printed face pictures, video
replays, or mimic masks. In general, fake faces have two
main properties:
1) Large variations. Although the positive class, namely
the genuine face, has limited variation (all genuine
faces are human skins), the negative class, i.e., the fake
faces, can range from photos, videos to masks and so
on. When it comes to material level, the variety is even
larger: take face mask for example, there are rubber
mask, plastic mask, silica gel mask, etc. It’s almost
impossible to give a complete list. Some examples of
fake faces are shown in Fig.1.
2) Indistinguishable under visible light. Fake is, by its
definition, indistinguishable for human eyes. There-
fore, without extra aid, only visual face images are
insufficient and impossible for the detection of fake
faces.
Previous works can be classified as visible liveness detec-
tion methods and multispectral liveness detection methods.
*Stan Z. Li is the corresponding author.
Fig. 1.
silica gel, rubber, photo and video replay
Some fake face examples. Materials from left column to right are:
The former is applied to face recognition systems which
work under visible light. For methods of this kind, human-
computer interaction (HCI) is almost indispensable to detect
users’ biological motion. The most commonly used motion
types include eye blinking [5], [6], head rotation [6], [7],
and mouth movement [8], and these motions are mainly
detected by adopting optical flow. One main problem of these
methods is that users need to be highly cooperative and the
duration of liveness detection is relatively long, which will
make users feel uncomfortable when using such a system.
Another kind of problem is that they can only detect planar
faces such as photos. If the fake face is a mask, or even
more simpler, some photos over a genuine face with eyes
and mouth cut out as illustrated in [6], these methods will
definitely fail. Therefore, the applications of such kind of
methods are limited. It is also noticed that some researchers
attempt to detect liveness from a single image [9], [10].
The clue they use is the illumination factor of the image.
Apparently they can only be used for photo face detection
and actually, at many times, these methods won’t work well
because photos can be made very vivid as genuine faces.
The other class is the multispectral methods, which de-
tect the reflectance of object surface. To the best of our
knowledge, there have been very few papers published in this
field, among which two papers are most representative. In [3]
Pavlidis and Symosekuses uses light at two wavelengths, and
a simple threshold method to detect the genuine and fake
faces. No experiments but only illustrations were reported
in their paper. The second one [4] also selects light at two

Page 2

different wavelength and then LDA is used to make the final
decision. However, this paper requires the distance between
the user and the system is exactly 30cm, and they utilize
users’ forehead region to measure reflectance. Not only the
forehead may be occluded, but also the exact distance is
quite demanding and is impossible to execute in practice.
Furthermore, the wavelengths they select are actually not
as optimal as in [3], which we will show in section II-
B. Thermal information is another choice, and we refer
readers to a common facial thermal imagery database in [16].
However, it is clear that thermal radiation can pass through
the wearing, such as the clothes, therefore it may not detect
the case when attackers wear masks. Furthermore, the high
cost also prevents its usage in real practice.
In this paper, we propose a novel liveness detection
method using multi-spectral lighting. We start by analyzing
how to distinguish fake faces multispectrally based on Lam-
bertian model when the user-system distance is unlimited and
variable. Then after measuring the albedo curves of different
materials(skin and non-skin), two discriminative wavelengths
are selected . A device is built to capture multi-spectral data
of the face to be recognized and a classifier is trained on
the multi-distance reflectance data set for the final liveness
detection.
Compared with previous works, the advantages of our
methods are obvious. Firstly, our method requires no user
cooperation, and therefore is user-friendly and fast. Secondly,
our multispectral method takes user-system distance factor
into consideration, which is novel.
The rest of the paper is organized as follows: in section II,
we analyze the problem based on the Lambertian reflectance
model, followed by the multispectral light selection and
classification process; in section III the system construction is
given as well as three different experiments conducted under
different cases, which show the superior of our method; in
section IV, we conclude the paper.
II. MULTISPECTRAL LIVENESS DETECTION
Light beyond visual spectrum gives us hope to tackle the
liveness detection problem. Indistinguishable fake faces may
exhibit quite different properties under invisible light. In this
section, we first give a reflectance analysis at multi-distances
using Lambertian reflectance model in section II-A. Based
on the analysis, the albedo curves of some materials and
selection of the proper wavelengths are given in section II-
B. In section II-C, the learning and classification process is
presented.
A. Reflectance Analysis
According to the Lambertian reflectance model [14], the
reflectance light intensity I at a location (x,y) is:
I(x,y) = A0(x,y)r(x,y)cosθ(x,y)
(1)
in which A0(x,y) is the input light intensity at the facial
location (x,y), r(x,y) is the object albedo, and θ(x,y) is
the angle between surface normal vector and the receiver’s
viewpoint.
According to the Beer-Lambert law [15], the attenuation
of light through the air is
A0= Ae−cd
(2)
in which A is the light source intensity, c is the attenuation
coefficient in the air and d is the distance traveled. For
simplicity, (2) is replaced by a function D, which is
a monotone decreasing function of distance d, and by
combining (1), we have:
I(x,y) = A(x,y)r(x,y)cosθ(x,y)D(d)
(3)
in which d is the distance between the object and the receiver.
The average value ave of I over an area Ω is,
?
(x,y)∈Ω
?
(x,y)∈Ω
assuming the uniform distribution of A, r and D in Ω. The
average value ave is more robust and useful than I at a single
point, and is used to represent reflectance intensity.
Given a genuine face f1 and a fake face f2, due to
different material, rf1 ?= rf2 exists under most of the
wavelengths. Given a wavelength w1, from (4) we have
ave =
I(x,y)dxdy =
?
Ω
(ArcosθD(d))dxdy
= ArD(d)
cosθ(x,y)dxdy
(4)
ave(f1,w1)= Aw1r(f1,w1)D(d1)
?
?
(x,y)∈Ω
cosθf1dxdy
(5)
ave(f2,w1)= Aw1r(f2,w1)D(d2)
(x,y)∈Ω
cosθf2dxdy
(6)
If there is no distance requirement, then f1 and f2 are
undistinguishable because there always exist proper distance
d1 and d2 (d1 is unnecessarily equal to d2) which makes
ave(f1,w1)= ave(f2,w1)→r(f1,w1)
r(f2,w1)
=D(d2)?cosθf2
D(d1)?cosθf1
(7)
In order to handle the problem imposed by distance, we
refer to a multispectral solution. If another wavelength w2
is added and received at the same area Ω, then we have
ave(f1,w2)= Aw2r(f1,w2)D(d1)
?
?
(x,y)∈Ω
cosθf1dxdy
(8)
ave(f2,w2)= Aw2r(f2,w2)D(d2)
(x,y)∈Ω
cosθf2dxdy
(9)
In order to distinguish f1 and f2 at wavelength w2,
similar with (7) we get
ave(f1,w2)?= ave(f2,w2)→r(f1,w2)
r(f2,w2)
?=D(d2)?cosθf2
D(d1)?cosθf1
(10)

Page 3

(a)
(b)
Fig. 2.
reflectance-distance curves of a genuine face and a photo face at wavelength
850nm are given; then for a fixed reflectance value, two distances are
obtained. In (b) the reflectance-distance curves at wavelength 1450nm are
given; when the two distances of (a) are fixed, the reflectance values are
different.
An example for reflectance analysis at multi-distances. In (a), the
Combing (7) and (10), obviously if proper wavelengths
w1 and w2 are selected which satisfy
r(f1,w1)
r(f2,w1)
then f1 and f2 can be distinguished without any distance
requirement.
In Fig.2 an example is given for illustration. Fig.2(a) shows
the reflectance1curves of a genuine face and a photo face
at wavelength 1450nm as the distance increases (the choice
of the wavelengths will be explained in next subsection).
Given a reflectance value, 30 for example, the corresponding
distance is about 22cm and 34.1cm for the genuine face and
the photo face(the undistinguishable case). With the distance
unchanged, now another light source of 850nm is added,
and the reflectance curve is shown in Fig.2(b). Obviously, at
the unchanged distance, the reflectance values at 850nm are
different. Therefore, the genuine face can be classified from
the fake photo face.
?=r(f1,w2)
r(f2,w2)
(11)
B. Select discriminative wavelengths
From section II-A, it is clear that proper wavelengths are
crucial to correct classification of genuine-fake faces when
1the reflectance is represented by the electrical value(voltage in this case)
measured by a hardware system.
Fig. 3.
from [11]
The skin albedo curve of Caucasian and Negro, reproduced
Fig. 4.
two kinds of silica gel.
We test the albedo curves of three materials, which are paper, and
there is no distance limitation. Also as stated in section I,
there are great varieties for fake faces while the genuine
faces are relatively constant, therefore it is better to analyze
the reflectance properties of the skin rather than fake faces,
based on which the proper wavelengths are to be selected.
From [11], a skin albedo curve can be found spanning a
wide range, as shown in Fig.3. Wavelengths below 400nm
is not considered because the ultraviolet rays are harmful
to human beings. Visible wavelengths between 400nm and
700nm are not considered as well, because visible light
source will make the users feel uncomfortable when lighting.
One can easily notice that at wavelength 1450nm, the albedo
of human skin is very low while at 800nm∼900nm, the
albedo is quite high. As current near-infrared face recognition
systems also adopt 850nm as light source [2], we choose
1450nm and 850nm as our consideration. To further verify
the choice, the albedo curves of some common materials,
which are paper from a photo face, and two kinds of silica gel
from two mask faces, are also tested and measured by us. The
curves can be seen in Fig 4. Obviously the other materials
do not possess such a high-low relationship at wavelength
850nm and 1450nm as human skin does, and these two
wavelengths can satisfy (11). Therefore, our proper choice
is 850nm and 1450nm. Obviously, the more light sources
at different wavelengths are added, the more discriminative
the reflectance value vector {ave(f,w1),...,ave(f,wn)} is. But
for the sake of simplicity, only two wavelengths are selected

Page 4

in this paper. Although there are only two wavelengths, the
experiments show the discriminative power of our selection.
In [4], however, the selected two wavelength is not the
best. Besides 850nm, they select visible light at wavelength
560nm , which is not only uncomfortable to human eyes
during experiment but also not as powerful as 1450nm when
combined with 850nm.
C. Learning and classification at multi-distances
Based on the above discussion, with proper wavelengths,
the fake faces can be detected very easily. However, as
some simplifications and assumptions are added into the
reflectance analysis, as well as the measure error in real
practice, a learning and classification process has to be
executed to achieve a high detection accuracy.
At the learning step, both positive and negative samples are
measured at multi-distances to form a training database. It is
believed that the multispectral facial reflectance distribution,
namely the avew1 and avew2, can be learned from the
training database. Then an SVM classifier is trained as the
Genuine-Or-Fake classifier. The reason for choosing SVM is
that it is impossible to learn the multispectral reflectance
distribution beforehand, and probably the distribution of
genuine and fake faces are linearly inseparable. SVM is
capable of calculating a nonlinear classifier, which is surly
better than the mere threshold method in [3], and also better
than a linear LDA method in [4]. Even if the distribution can
be separated linearly, SVM is as good as LDA.
It is important to point out that in practice most of the face
recognition systems require a proper face size, for example,
with the eye distance more than 60 pixels. Similarly, we
also expect that the distance between the face and the
liveness detection device is about 20 ∼ 35cm. Such a broad
requirement is clearly only a little deviation from the original
intention of distance robust liveness detection.
III. EXPERIMENTS
In this section, the system construction is firstly introduced
in details in subsection A; then an experiment on detecting
genuine faces and planar fake faces is conducted in B; in C
we further test the effect of detecting genuine faces and many
kinds of mask faces; in D a comparison between previous
visible liveness detection method and our method is also
given.
A. System Construction
The system is constructed on the near infrared face recog-
nition system [2] with modifications. The system includes
two groups of LED lights to provide active light sources. The
two groups of LED are interweaved and evenly located as a
rectangle. Because it is impossible to purchase any cameras
corresponding to 1450nm light, two photodiodes are used
instead to receive the reflectance light at both wavelengths.
For photodiodes, the electrical values(voltage in this case),
which is measured by a circuit, represent the sum of light
intensity over certain areas, which equals ave explained in
section III.A. If the receiving area of the photodiodes are
Fig. 5.System Overview
restricted to a certain size by limiting the receiving angle
of the photodiode, then the two photodiodes have the same
size of receiving area, making the electrical value at two
wavelengths could represent the average facial reflectance
properly. A view of our system is shown in Fig.5.
B. Genuine faces vs Planar faces
In this section we mainly concentrate on the planar faces,
the most common fake face type. Planar faces are named
because the faces are in 2 dimensional plane rather than
in 3 dimensional space. Common planar faces are photos,
and video replays. 40 face images from FRGC database are
selected and are printed as photos, among which 20 are
printed on high-quality paper and the other 20 are printed on
normal paper. 20 faces are also shown on a laptop screen as
the video replays. Each photo and video replay is measured
5 times, each time at different distances ranging from 20cm
to 35cm. We also selected 40 persons to form the genuine
face database. Each person is measured 3 times, each time at
different distances as well. Therefore a database containing
300 negative samples (200 for photos and 100 for video
replays) and 120 positive samples is built. A 5-fold cross
validation is taken to give the final testing results, which is
shown in Table 1. LibSVM 2.89 [12] is used as the classifier
with default parameters.
The multispectral reflectance distribution of the photo
faces and genuine faces are shown in Fig 6. In experiment
it is found that the electrical values of the video replays
are much higher than these of the photos and genuine
faces (approximately 3 times more than the photos). If
the electrical values of video replays as well as those
of the genuine and photo faces are plotted in the same
image, the latter will become unclear to see. Therefore the
distributions of the video replays are simply omitted in Fig 6.
C. Genuine faces vs Mask faces
We further test the genuine faces versus mask faces.
Compared with planar faces, mask faces are less common
and more difficult to detect. Firstly, masks are 3D objects,
whose surface terrain are more like a genuine face than a 2D
planar face; secondly, the materials of masks, such as silica

Page 5

Fig. 6.The reflectance distribution of genuine faces and photos
gel and rubber, is more closer to human skins in reflectance
than paper-based photos and glass-based video screens.
As it is quite difficult for us to acquire face-like masks,
only 20 masks are selected, each sampled 5 times at different
distances to form a 100 negative database. The materials of
the 20 masks are: 4 plastic masks, 6 silica gel masks, 4 paper
pulp masks, 4 plaster masks and 2 sponge masks. Once again
5-fold cross validation is taken to give a final testing results.
Because each material class only contains a few masks, it
is meaningless to calculate a detection accuracy for each
class. Instead a detection accuracy treating all masks as a
whole is given in Table 2 and the multispectral distribution is
shown in Fig.7. From Fig.7 it can be seen that the distribution
difference between genuine faces and mask faces are not as
much as that of the planar faces. This is mainly because there
are more material types for mask faces than mere plane faces,
and the 3D surface also makes them more similar to genuine
faces. Our result is not as high as that in [4], but it cannot
be asserted that our method is worse. Reasons for different
detection accuracy between ours and [4] are: 1) the mask
faces used in the experiments are different; 2) they fix the
distance as 30cm, and use the forehead for test. On the other
hand, our method has no such fixed distance requirement
and is based on the whole face. Actually, our method is
more convenient in real practice, yet their requirement is too
heavy for the users.
TABLE I
DETECTION ACCURACY OF GENUINE FACE VS PLANAR FACE
5 cross12345
genuine vs photo
G vs P average
genuine vs video
G vs V average
93.6% 92.9%89.6%
92.2%
100%
100%
93.9% 91.0%
100%100%100% 100%
TABLE II
DETECTION ACCURACY OF GENUINE FACE VS MASK FACE
5 cross
accuracy
average
12345
90.5%87.8%90.4%
89.18%
90.2% 87%
Fig. 7.The reflectance distribution of genuine faces and mask faces
D. Comparison with visible liveness detection
To present a complete comparison of current face liveness
detection methods, a comparison experiment is also con-
ducted between the visible liveness detection method and our
multispectral one. As stated above, visible liveness detection
method is essentially to find the biological facial motions.
The motion detected here is the most frequently used motion
type – eye blinking. During experiment, a period of 10
seconds is set for the users to blink in front of the camera.
10 photos, 10 photos with eyes cut out and 10 genuine
faces are used during the experiment, as shown in Fig.8.
With eyes cut out on the photos, people can hide behind the
photos to show blinking, as does in [6]. For visible liveness
detection, a Haar + GentleBoost [13] classifier is trained to
detect the blinking. The classifier, also known as eye state
classifier, is trained on an eye state database as does in [5],
and is used to give a blink score to each eye state image:
positive scores mean open state and negative scores mean
close state. A training database containing 2000 open eye
images and 1000 close eye images is collected; a testing
database of the same size is also collected, on which the
classifier achieves an accuracy of 98.7% in classifying open
eyes and an accuracy of 98.3% in classifying close eyes. A
complete blink process shown in Fig.9; for the multispectral
liveness detection, our method is employed and the training
data is from the above experiments. The liveness detection
results are shown in Table 3.
From Table 3 it can be seen that with eyes cut out
from the photos, traditional visible liveness detection method
can still detect motion, namely the blinking. In this case,
visible liveness detection method cannot even detect photos
properly, let alone other types of fake faces which are
capable of exhibiting motions as well. On the other side, our
multispectral method only depends on the material covering
the faces, and therefore can properly detect fake faces.
Furthermore, waiting for the users’ interaction is quite time-
consuming, which is set to be 10 seconds in this experiment;
yet our method only takes 1 second to measure reflectance.
This comparison experiment proves the superior of our
method than the visible liveness detection method.
However, an important note should be declared: challenge-

Page 6

Fig. 8.
method. From left to right are photos, photos with eyes cut out,and the
genuine faces.
Fake faces attacking the blinking-based visible liveness detection
4.817 -0.257 -6.573-6.046
-3.612-1.275 -1.3691.959
Fig. 9.
classifier in a complete blink process..
Every eye state is given a Blink Score by the Haar+GentleBoost
response based visible liveness detection method is not the
competitor of the multispectral livenss detection method but
a useful complement. The combination of the two methods
will produce more precise results: when any of them fails
the detection, the other one may work well to prevent any
wrong decision, because the attackers have to pass both of
the two methods to be verified alive.
IV. CONCLUSION
In this paper we propose a distance robust face live-
ness detection method, which performs better than previous
works. Firstly an analysis on facial reflectance at multi-
distances is given and after measuring the albedo curves of
some materials, two discriminative wavelengths are selected
to build our multispectral system. Samples are measured
at multi-distances, and then a SVM classifier is trained to
learn the distribution. Experiments are conducted on genuine
faces vs plane faces, genuine faces vs mask faces, showing
the effectiveness of our method. Furthermore we make a
comparison with visible liveness detection method, proving
the power of our method. Compared with previous works, our
method does not adopt time-consuming and user-unfriendly
interactions; and we consider the distance factor, which is
crucial in real practice.Our future work will lie on improving
the detection accuracy on mask faces.
V. ACKNOWLEDGEMENT
This work was supported by the Chinese National Natural
Science Foundation Project #61070146, National Science
and Technology Support Program Project #2009BAK43B26,
and AuthenMetric R&D Funds.
REFERENCES
[1] Stan Z. Li and Anil K Jain, Handbook of Face Recognition , Springer,
New York, 2004.
TABLE III
VISIBLE VS MULTISPECTRAL LIVENESS DETECTION
genuine detected
visible
multipsepctral
photo(10)
0%(0/10)
0%(0/10)
cutted photo(10)
90%(9/10)
0%(0/10)
genuine(10)
100%(10/10)
100%(10/10)
[2] Stan Z. Li, RuFeng Chu, Shengcai Liao and Lun Zhang, ”Illumination
Invariant Face Recognition Using Near-Infrared Images”, IEEE Trans-
action on Pattern Analysis and Machine Intelligence, vol. 29, no. 4,
April 2007.
[3] Ioannis Pavlidis and Peter Symosek, ”The imaging issue in an auto-
matic face/disguise detection system”, proceedings of IEEE workshop
on Computer Vision Beyond the Visible Spectrum: Methods and
Applications, 2000.
[4] Youngshin Kim, Jaekeun Na, Seongbeak Yoon, and Juneho Yi,
”Masked fake face detection using radiance measurements”, Journal
of the Optical Society of America A, vol. 26, no. 4, 2009.
[5] Gang Pan, Lin Sun, Zhaohui Wu and Shihong Lao, ”Eyeblink-based
Anti-Spoofing in Face Recognition from a GenericWebcamera”, the
11th IEEE International Conference on Computer Vision, Rio de
Janeiro, October, 2007.
[6] K. Kollreider, H. Fronthaler and J. Bigun, ”Verifying Liveness by
Multiple Experts in Face Biometrics”, IEEE Computer Vision and
Pattern Recognition Workshops, Anchorage, 2008.
[7] K. Kollreider, H. Fronthaler and J. Bigun, ”Evaluating Liveness by
Face Images and the Structure Tensor”, Fourth IEEE Workshop on
Automatic Identification Advanced Technologies, October, 2005.
[8] G. Chetty and M. Wagner, ”Liveness Verification in Audio-Video
Speaker Authentication”, In 10th Australian Int. Conference on Speech
Science and Technology, December, 2004.
[9] J. W. Li, Y. H. Wang, T. N. Tan, and A. K. Jain, ”Live Face Detection
Based on the Analysis of Fourier Spectra”, In Proc. SPIE Biometric
Technology for Human Identification, vol. 5404, pp. 296–303, January
1999.
[10] Xiaoyang Tan, Yi Li, Jun Liu and Lin Jiang, ”Face Liveness Detection
from A Single Image with Sparse Low Rank Bilinear Discriminative
Model”, In Proceedings of the European Conference on Computer
Vision, 2010.
[11] R. Rox Anderson, B.S. and John A. Parrish M.D., ”The Optics of
Human Skin”, The Journal of Investigative Dermatology, vol.77, no.1,
1981.
[12] Chih-Chung Changand
http://www.csie.ntu.edu.tw/ cjlin/libsvm/
[13] Jerome Friedman, Trevor Hastie and Robert Tibshirani, ”Additive
Logistic Regression: a Statistical View of Boosting”, In Annals of
Statistics, vol. 28, pp.2000-2043, 1998.
[14] Ronen Basri and David W. Jacobs, ”Lambertian Reflectance and Lin-
ear Subspaces”, IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol.25, no.2, 2003.
[15] J. D. J. Ingle and S. R. Crouch, ”Spectrochemical Analysis”, Prentice
Hall, New Jersey, 1988.
[16] OSUThermalImagery
state.edu/otcbvs-bench/.
Chih-JenLin,LIBSVM,
Database.http://www.cse.ohio-