Blur Parameter Identification using Support Vector Machine

ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012

Blur Parameter Identification using Support Vector
Machine
Ratnakar Dash1, Pankaj Kumar Sa2, and Banshidhar Majhi2
1
CSE Department, National Institute of Technology, Rourkela, India
Email: ratnakar.dash@gmail.com
2
CSE Department, National Institute of Technology, Rourkela, India
Email: {pankajksa, bmajhi}@nitrkl.ac.in

Abstract—This paper presents a scheme to identify the blur Then image is restored using any of the classical
parameters using support vector machine (SVM) Multiclass restoration methods.In the second category PSF estimation
approach has been used to classify the length of motion blur and image restoration are achieved simultaneously. Our work
and sigma parameter of atmospheric blur. Different models falls in the first category where PSF parameters are identified
of SVM have been constructed to classify the parameters. before image restoration. In this paper, we have identified the
Experimental results show the robustness of the proposed
length of motion blur and sigma parameter of atmospheric
approach to classify blur parameters.
turbulence blur which decides the severity of blur. Motion
Index Terms—Classification, support vector machine (SVM), blur parameter identification have been proposed in many
motion blur, point spread function(PSF) literature[2,3,4,5,7 ]. Hough transform has been used to
estimate blur length by detecting the lines in the spectrum of
I. INTRODUCTION the degraded image [5]. Authors in [6] have proposed an
adaptive adaline network to estimate motion length of a
The goal of image restoration is to obtain visual
degraded image. Igor Aizenberg and his team [4] developed a
information from a degraded observation. Image restoration
method to restore horizontal motion blurred image. Their work
finds application in many areas like photographic blur,
needs a rough estimation of motion length which is achieved
astronomical imaging, remote sensing, medical imaging etc.
using power spectrum. Similarly in [9] a method has been
Images may be blurred by the imaging device, or the medium
proposed to restore images degraded with atmospheric blur.
through which the light propagates. The relative motion
Principal component analysis (PCA) has been used in [8 ] to
between the imaging device and the object also leads to image
deal with the turbulence blur. The present work attempts to
blurring. In most of the applications, the blurring process is
estimate length parameter of motion blurred image and sigma
assumed to be linear and it is mathematically represented as
parameter of turbulence blurred image. We utilize the blur
2D convolution between the original image f ( x, y ) and the parameter subsequently to construct the PSF for restoration.
degradation function hx, y  also known as point spread Though there are large volume of work reported, researchers
are still active in this direction in order to improve the image
function (PSF). Thus g ( x, y ) can be written as quality and peak signal to noise ratio (PSNR). In this paper we
have utilized the support vector machine as a classifier to
classify the blur parameter.
The rest of the paper is organized as follows. Different
Where * denotes the linear convolution operator and Z is blur models are described in section II. Support vector machine
the set of integers. Image restoration techniques are oriented and multiclass approach has been provided in section III.
towards approximating the true image from the degraded Experimental results for the proposed approach have been
observation. In classical restoration, it is assumed that the provided in section IV. Finally section V gives the concluding
PSF is known apriori and the task is just to invert the remarks.
degradation process. However, in many practical situations, II. BLUR MODELS
the point spread function [1] is not available and it is difficult A. MOTIONBLUR MODEL
to obtain the sense of the original image. This situation arises
because of some practical constraints like characterizing the The point spread function for motion blur can be described
degradation function in astronomical imaging and may be by the following equation.
due to hazard of using stronger beam for a good image
resolution in medical imaging. In such situations blind image
deconvolution is inevitable for image restoration.There exists
a variety of blind image restoration schemes proposed in the
literature [8, 9, 10]. Bind image deconvolution problem has
been classified into two categories. In the first category, blur where L is the length of motion blur and  is the angle of
and its parameters are identified and the PSF is constructed. motion blur.
© 2012 ACEEE 54
DOI: 01.IJCSI.03.02.108


B. ATMOSPHERIC TURBULENCE MODEL
The point spread function for atmospheric blur is described
as

where  controls the severity of degradation.
III. SVM BASED BLUR IDENTIFICATION
A support vector machine classifies data into two classes
by separating them into two categories. SVM is also used to
perform multi class classification [11, 15]. It distinguishes
one class from others by constructing a hyper plane with
maximum margin. An optimal hyper plane is constructed by
solving a quadratic optimization problem. SVM models are
equivalent to the classical multi layer perceptron(MLP) neural
network where weights are optimized in order to classify the Figure1. Variance curve for different blurred images with blur length
test data accurately. Traditional neural networks solve a non
B. BLUR PARAMTER CLASSIFICATION
convex unconstrained minimization problem. SVM models
also use a training data set (Xi, Yi) like MLP and update the The multi class SVM has been used to classify the blur
weights. However, SVM uses a kernel function and weights parameter. Several approaches to multiclass SVM have been
of the networks are found by solving a quadratic programming proposed in the literature [12, 13, 14]. These methods
problem with linear constraints. SVM solves the following decompose the multiclass problem into number of two class
optimization problem problems. They use different decomposition methods like
one versus rest, one versus one etc. Using the SVM for blur
parameter classification is straightforward.
First we construct a training set using the feature vectors
as described above and train the feature samples with a
multiclass SVM. In the testing phase, features of the blurred
image with different blur length are collected and fed to the
trained SVM model. The output of the SVM is the identified
Where  i is the upper training error and i is the lower blur length. The sigma parameter of the atmospheric
turbulence blur has been identified in the same way by
 
training error subject to yi  W T   xi   b   and  is a constructing another multi class SVM model. Details of the
experiments conducted are described in the simulation
threshold. C is the penalty parameter.
section.
A. FEATURE SELECTION
The variance parameter decreases with the blurring III. SIMULATION RESULTS AND DISCUSSION
strength in a blurred image Change of variance with blur Experiments have been conducted in the MATLAB
length for different images are shown in Figure.1 We have environment to show that the trained SVM model can be
used variance as one of the criteria to select the samples from used to identify the blur parameter in new images. Standard
the blurred image. It is also well known that edges in an images like Cameraman, Lena and Pepper are used for both
image play a major role for image analysis. The high frequency training and testing. All the images used for training and
regions in a cameraman image for different motion blur length testing are scaled in the range [0, 1] in the spatial domain. We
are shown in Figure.2. It is evident from Figure 2 as the blur have used a window size of 7x7. So the size of one sample
length increases, edges becomes smoother. The smoothness vector used in the SVM is [49x1]. The SVM model trained
in the blurred image can be measured using variance. We with Cameraman image is tested with a different image.
construct the training set by taking the regions in the blurred
image having higher variance. Such regions are searched by A. Experiment 1: Cameraman SVM model for motion blurred
taking a 7x7 window and sliding this from top to bottom. If g image
represents the blurred image with blur length L, then we select The Cameraman image is horizontally motion blurred with
the gray values of the window gw whose variance is larger. L = 2 to 30 with a gap of 2. The 1844 samples from the blurred
The feature vector is constructed as [gw(:); L]T where gw(:) image have been taken by considering the window whose
represents lexicographic ordering of the gray values of the variance is larger than 0.02. The SVM istrained with the
window having larger variance and L is the corresponding collected samples of blurred cameraman image and a SVM
blur length. model is created.

© 2012 ACEEE 55
DOI: 01.IJCSI.03.02.108


Figure 2 Behavior of an edge under motion blur of various Blur length with 45 0 angle

The SVM model is validated by testing the samples of B. EXPERIMENT 2 PEPPER SVM MODEL FOR ATMOSPHERIC BLURRED
cameraman image as well as Lena image. The vote count for IMAGE
each of the estimated class is for cameraman image and Lena The Pepper image is degraded with atmospheric turbulence
image are noted and has been shown in TABLES I & II with different sigma (σ) values in the range [0.5 -5] using the
respectively. Values in each column show the number of inbuilt function available in MATLAB. The training samples
votes won by different blur lengths. The maximum vote of the blurred Pepper image are accumulated using the same
obtained by any row in a particular column is the estimated procedure as explained in Experiment 1 Total 1392 samples;
class which is equal to the blur length We should note that have been used for training the SVM.. To validate the
the samples from Lena image are different from the sample effectiveness of the proposed scheme, testing samples from
used in the training. It is clear from the Table 1 that the cameraman image also have been used. The performance of
proposed multiclass SVM identifies the blur length accurately the multi class SVM for different images has been shown in
for the same image as well as different image. To create the TABLE III and IV respectively. The results in the TABLE’s
SVM model LIBSVM package [16] is used with the default show that the proposed multiclass SVM also works well for
radial basis function. The value of C is chosen on a trial and images degraded with atmospheric turbulence blur and it
error basis and for the cameraman image SVM model it is achieves generalization in terms of different images. Same
taken as 1. Error tolerance and Gamma value are chosen to be voting strategy has been followed in this experiment to
0.0001 and 5 respectively. identify the actual sigma value. The value of C has been kept
TABLEI. BLUR I DETIFICATION PERFORMANCEOF MULTICLASS SVM FOR 1 and RBF kernel has been used in the LIBSVM package.
CAMERAMAN I MAGE Gamma value and error tolerance are chosen to be 4 and 0.0001
respectively. The restored image is obtained after constructing
the PSF from the identified sigma parameter. The restoration
results for Pepper image is shown in Figure4.
TABLE III. BLUR I DETIFICATION PERFORMANCEOF MULTICLASS SVM FOR
PEPPER IMAGE

TABLE II. B LUR IDETIFICATION PERFORMANCEOF MULTICLASS SVM FOR LENA
IMAGE

TABLE IV. BLUR IDETIFICATION PERFORMANCEOF MULTICLASS SVM FOR
CAMERAMAN IMAGE

These parameters can also be optimized for different
images and different degradation. After the blur parameter
is identified PSF is constructed and the degrade images are
restored. The restoration result for the cameraman image is
shown in Figure 3.

© 2012 ACEEE 56
DOI: 01.IJCSI.03.02.108


CONCLUSIONS [7] M.E.Moghaddam, M.Zamzad, “Robust estimation of motion
blur parameters” 5th International Conference on Advanced Pattern
A novel method has been proposed to identify the blur Recognition (ICAPR). 2003
parameter from the blurred images. The blur identification [8] Dalong Li, Russell M. Mersereau, and Steven Simske,
problem is modeled as a multiclass classification problem “Atmospheric Turbulence-Degraded Image Restoration Using
and has been solved using support vector machine. The Principal Components Analysis”, IEEE Geoscience and Remote
suggested scheme achieves generalization in terms of Sensing Letter, vol 4, pp 340-344, July 2007
different images and estimates the blur parameters accurately. [9] Omri Shacham, Oren Haik, and Yitzhak Yitzhaky, “Blind
The proposed scheme is applicable to images degraded with restoration of atmospherically degraded images by automatic best
step-edge detection”, Pattern Recognition Letters, vol 28,pp 2094-
horizontal motion blur and images degraded with atmospheric
2103, November 2007
turbulence blur. However, the proposed method can also be [10] Dalong Li, Russell M. Mersereau, and Steven Simske., “Blind
applied to estimate angle of motion blur by constructing Image Deconvolution Through Support Vector Regression”, IEEE
another SVM model. Transactions on Neural Networks, vol 18, pp 931-935, may 2007
[11] Vladimir N. Vapnik.,” The Nature of Statistical Learning
REFERENCES
Theory”, Springer Verlag, Neywork 1995
[1] R.C.Gonzalez, R.E.Woods “Digital Image Processing”, Addition [12] A. Bordes, L. Bottou, P. Gallinari, and J. Weston,” Solving
Wesley, 2 nd edtion Multiclass Support Vector Machines with LaRank”, In 24th
[2] Y.Zhang, C.Wen, “Estimation of motion parameters from International Conference on Machine Learning, Corvallis, USA,
blurred images” Pattern Recognition Letters, pp 425–433.. 2000 June 2007
[3] M. Chang, A. Tekalp, A. Erdem, “Blur identification using the [13] Chih-Wei Hsu and Chih-Jen Lin.,” A Comparison of Methods
bispectrum,” in, IEEE Transactions on Signal Processing vol. 39, for Multiclass Support Vector Machines”, IEEE Transactions on
pp. 2323–2325. 1991 Neural Networks, vol 13 pp 415-425, March 2002
[4] I. Aizenberg, D. V. Paliy, J. M. Zurada, J. T. Astola, “Blur [14] Ben Fei and Jinbai Liu., “Binary Tree of SVM: A New Fast
identification by multilayer neural network based on multivalued Multiclass Training and Classification Algorithm”, IEEE
neurons”, IEEE Transaction on Neural Networks. vol ,pp 883-898, Transactions on Neural Networks, vol 17, pp 694-704 May 2006
2008 [15] Kai-Bo Duan and S. S. Keerthi, “Multiple Classifier Systems,
[5] R. Lokhande, K. V. Arya, P. Gupta, “Identification of parameters chapter Which Is the Best Multiclass SVM Method? An Empirical
and restoration of motion blurred images”, in: Proceedings of the Study”, Lecture Notes in Computer
ACM Symposium on Applied Computing vol 9,pp 301-305, 2006. Science. Springer Berlin 2005
[6] W.-G. He, S.-F. Li, G.-W. Hu, “Blur identification using adaptive [16] C. C. Chang and C. J. Lin, “LIBSVM: A library for support
adaline network,” IEEE International Conference on Machine vector machines”, [Online]. Available: http://www.csie.ntu.edu.tw/
Learning and Cybernetics, Guangzhou, China, pp. 5314-5317, verb~cjlin/libsvm 2001
2005

© 2012 ACEEE 57
DOI: 01.IJCSI.03.02.108

Blur Parameter Identification using Support Vector Machine

More Related Content

What's hot (16)

Similar to Blur Parameter Identification using Support Vector Machine (20)

More from IDES Editor (20)

Recently uploaded (20)

Blur Parameter Identification using Support Vector Machine