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脉冲图像不变性人脸表述
绽琨
兰州大学信息科学与工程学院，兰州 730000
摘要：本文以生物启发的方法进行人脸识别。脉冲发放皮层模型演化自对猫等哺乳期视觉皮层
电化学特性的研究，已证实脉冲发放皮层模型可有效地提取图像中几何不变性的特征。提取到
的特征由富含图像本质特性如形状、边缘和纹理等的脉冲图像得到。在本文中，脉冲发放皮层
模型输出的脉冲图像被用于人脸图像特征提取，在研究了几何不变性的基础上，也研究了特征
的光照不变性。以脉冲图像得到的特征来进行人脸识别时，得到比较高的实验结果。
关键词：脉冲图像，人脸分析，脉冲耦合神经网络，复合相关滤波器
中图分类号： TP391
Invariant Face Representation via Pulse Images
ZHAN Kun
School of information science and engineering, Lanzhou University, Lanzhou 730000
Abstract: This paper show how biologically inspired methods can be applied to a variety of
face image analysis. Spiking cortical model (SCM) based on the observation of the visual
cortex nerve cell of cats and simulating the activities of the visual nerve cell. It has
demonstrated that SCM can effectively extract invariant image feature. The feature is
inherent in an image, and describes the regional information, edges, shapes, segments and
textures in the image. In this paper, the pulse images, output of the system of SCM, are
developed for face image representation. The experimental results show that pulse images
very suitable to process face images, and its application on face recognition achieve high
accuracy and it is a robust scheme for face modeling systems.
Key words: Pulse images, Face analysis, PCNN, Composite correlation filters
0 Introduction
Identification and verification of a person’s identity are very important for applications of
face recognition systems. Human face recognition is currently a popular research area [1, 2, 3]
with focus on ways to perform robust identification. However, face recognition is a challenging
task because of the variability of the appearance of face images even for the same subject as it
changes due to expression, pose, aging, size, shift, skew, rotation, mingle with noisy etc.
基金项目： This work has been supported by the Specialized Research Fund for the Doctoral Program of Higher
Education under the Grant No. 20120211120013
作者简介： Kun Zhan, male, assistant professor. His main research interests include image processing and neural
networks
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In this paper we explore face images analysis based on pulse images. The feature calculated
by the pulse images is invariant to images that were shifted, rotated, scaled and skewed [4, 5, 6,
7, 8, 9]. This paper using composite correlation filters try to obtain the feature with illumination
invariant. The image feature extracting from the PCNN with time-sequence were proposed by
Johnson [4, 5, 6]. Images are converted to small one-dimensional sequences, however, the time-
sequence has a low accuracy because it describes the pulse images too simple. In [9], Zhan et
al. attains a conclusion that the entropy and standard deviation are more accurate than the
time-sequence, especially, Intersecting Cortical Model (ICM) [10, 11] with standard deviation
obtain a high accurate rate. An optimized modified PCNN, spiking cortical model (SCM), is
used for image recognition and classification [9]. We present a comparison of SCM and the two
former models.
According to the regional information, edges, shapes, and textures of the pulse images
which contain the facial feature points, in the end this paper also explored to extract the feature
points on human face for Three-Dimensional face modeling from Two-Dimensional image.
Firstly, These experiments realize face recognition system that is illumination invariant
and could avoid background affects. Secondly, we explore a face molding systems by Pulse
images that are the regional information, edges, shapes, and textures in original images. These
experimental results show that it is very suitable for face processing systems.
1 Spiking Cortical Model
If a neuron receives a stimulus in its resting state, its membrane potential is mainly charged
by the stimulus directly. At the same time, the membrane potential is modulated by the
postsynaptic action potential from its neighborhood neurons. The membrane potential of SCM
is calculated by the combination of the stimulus and the synaptic modulation, which is similar to
the actual neuronal electrical activity [9]. The threshold of SCM complies with the mechanism of
relative and absolute refractory periods of a real neuron [12, 13, 9]. When the neural membrane
potential is rising up over the threshold, the neuron produces an action potential (spike). SCM
is proposed based on these comprehensive characteristics of the neuronal electrical activity and
the mathematical description is given by,
Uij(n) = fUij(n− 1) + Sij
∑
kl
WijklYkl(n− 1) + Sij (1)
Xij(n) = 1/(1 + exp(−γ(Uij(n) −Θ(n)))) (2)
Yij(n) =
1, if Xij(n) > , otherwise (3)
Θij(n) = gΘij(n− 1) + hYij(n) (4)
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where each neuron is denoted with indices (i, j) and one of its neighboring neurons is denoted
with indices (k, l); Sij is the external stimulus received by a neuron at the (i, j) coordinate;
Uij(n) is the membrane potential when the iterative times is n; Θij(n) is the threshold; Yij(n)
is the output spike; the modulation on the center neuron by its neighborhood neurons is repre-
sented by the convolution of W and Y , and the synaptic weighted matrix W has the property
of Gaussian kernel simulated the receptive field and its size is decided by kl; β is the linking
coefficient; f(0 < f < 1) is the attenuation constant of the membrane potential and f reflects
the increasing speed of the membrane potential; g(0 < g < 1) denotes the attenuation constant
of the threshold and decides the relative refractory period, which means that a neuron with a
larger g produces its next spike much earlier; and h is designed for absolute refractory period,
which denotes that a neuron that produced spike just now cannot produce spike again in a
short while, even though it has a stronger stimulus.
A two dimensional image with sine of m× n can be thought as a neuromime with m× n
neurons, and the gray level of pixels can be thought as Sij , the input of the neuron. Obviously,
W is the interior linking matrix. When there are pixels whose gray levels are approximately in
the neighborhood of W , one pixel’s pulsating output can activate other corresponding pixels
having the approximate gray level in the neighborhood and let them generate pulsating output
sequence Yij(n). Obviously Yij(n) contains some information about this image such as regional
information, edge, segment and texture features. Then the binary image constructed by Yij(n),
Yij(n) is a binary 2-D matrix, the output, is the segmented image.
2 Algorithms
SCM generates series of pulse images which bring out different features of original image,
such as texture, edge and segment features. For an input image Sij , a series of pulse images
Yij(1), Yij(2), …, Yij(n) are outputted when SCM is iterated for n times, and the series of
pulse images can be computed to a unique feature.
Pulse images are calculated to be sequences as signatures of the original images. The first
approach to calculate signatures was the integration of neural activity for iteration of PCNN by
Johnson [24][25]. In [6][7] it is demonstrated that the accuracy would be higher when employs
the entropy (5),
E(n) = p1(n) log2 p1(n) + p0(n) log2 p0(n) (5)
or the modified standard deviation (6),
σ(n) =
√∑
ij
(Yij(n) − µ(n))2 (6)
where
p1(n) = µ(n) =
∑
ij Yij(n)
m× n (7)
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p0(n) = 1− p1(n) (8)
These signatures are effective to geometry, noise and background invariants, but they are
sensitive to the illumination (intensity and contrast). In order to overcome the illumination
these experiments explored composite correlation filters [14].
图 1: Schematic for Correlation Process.
shows schematically how the cross-correlation is obtained using Fast Fourier Trans-
forms (FFT).The composite correlation filter is given by,
h = D−1X(XHD−1X)−1c (9)
where h is composite correlation filter, D is a diagonal matrix; X is the Fourier transform of
images, and typically all the entries of the column vector c is set to 1.
The composite correlation filter to produce sharp peaks that resemble 2-dimensional delta-
type correlation output when the input image belongs to the class of images. The output of
an authentic would produce strong peaks, usually, peak to sidelobe ratio (PSR) is applied to
discriminate authentic. PSR is defined by,
PSR =
peak − µ
σ
(10)
3 Experimental Results
Geometric Invariant
Taking a sample face (s2) form the ORL album for example, got the same effect from
different facial expression. As shown in Table 1, it means that these methods are strongly
flexible to resist variance, and then select ten images from database; each image represents a
unique feature. As can be seen from the Table 2, these experiments could obtain the conclusion
that the method in this paper is greatly robust to face identification. A series of experiments
has been carried out to calculate Euclidean distances from different facial expression. In these
experiments applies PCNN, or ICM, or SCM extraction algorithm to each face image from
database. The Euclidean distances results are summarized in Table 1 and Table 2.
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图 2: Correlation output of a sample s2 from the ORL album in different illumination for a
well designed correlation filter
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图 3: Correlation output of s1 to s10 from the ORL album for a well designed correlation filter
by s2
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表 1: Euclidean distance between and to of a sample face (S2) from the
ORL album, Entropy (e), Deviation (d)
表 2: Euclidean distance between and to of a sample face (S2) from the
ORL album, Entropy (e), Deviation (d)
表 3: psr of s2 (0 255) in different illumination
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表 4: psr of s1 to s10 (0 255) for a correlation filter by s2
Invariant experiments are represented. Rotation, scale, shift, skew invariant experiments
were presented by [4 7], and avoid noisy affects experiments could be seen from Zhan ’s exper-
iments [6 7].
Illumination Invariant
Experiments explored to avoid background affects and illumination (intensity and con-
trast). It is can be seen from Table 1 that the three models could avoid background variety. It
is used the composite correlation filters to solve the illumination invariant, as shown in ,
using face image to of s2 ORL database to train a composite correlation filters
and sampling some image to test the correlation peak. The PSR results are summarized in
Table 3. If other images input to test the peak, it would no shape peak and their PSR is very
low. And the results can be seen from and Table 4. Different illuminations were obtained
by increase the intensity with a range of 0 to 180, if some intensity of pixel were higher than
255, cut their values to 255.
Conclusions
The proposed face identification Algorithms based on pulse images were very effective with
only 37 energy values compare to traditional feature extraction methods which need more than
one hundred energy values, or need train the database of face images. These features were
rotation, scale, shift, skew invariant and that could be anti noise and background, this paper
was involved in composite correlation filters to solve the illumination invariant, its results shown
that the methods are robust to illumination invariant. But composite correlation filters need
train the images and it has a high computational complexity. In the future works it can be
explore to reduce the computational complexity and use the pulse images to train the filter. In
this paper, it tried to show a summarized method to Three-Dimensional face modeling from
Two-Dimensional image, and there are more works can be done in detail.
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