The document describes an image pattern matching method using Principal Component Analysis (PCA). It involves preprocessing training images by converting them to grayscale, resizing them, and storing them in a matrix. PCA is then performed on the training images to extract eigenfaces. Test images are projected onto the eigenfaces to obtain a projection matrix. The test image with the minimum Euclidean distance from the training projections in the matrix is considered the best match. The method provides fast and robust image pattern matching through PCA dimensionality reduction and efficient preprocessing.

1. Image Pattern Matching Using Principal Component
Analysis Method
Lalita Kumari, Swapan Debbarma, Nikhil Debbarma, Suman Deb
Department of Computer Science, NIT Agartala, India
Abstract— Pattern matching in image refers to searching a set of images to find out a particular image matching most with
required image. Computer vision can‘t be implemented successfully until fast and effective pattern matching algorithm is
successfully used. Fast pattern matching algorithm can be used with the help of Principal Component Analysis (PCA)
method. In this paper we described pattern matching algorithm, based on PCA method, which is less time consuming at
run time.
Keywords— Image Processing, Pattern Matching, PCA method, Image matching
I. INTRODUCTION succeeding component in turn has the highest variance
Pattern matching in the area of image processing is possible under the constraint that it be orthogonal to
current trend of research and development. Pattern (uncorrelated with) the preceding components. Principal
matching or pattern analysis is widely being used in the components are guaranteed to be independent only if the
area of Digital Image Processing. Some example of its data set is jointly normally distributed. PCA is sensitive
domain, where it is used is Optical Character to the relative scaling of the original variables.
Recognition, Human body gesture recognition, facial Depending on the field of application, it is also named
expression detection, computer vision, human-machine the discrete Karhunen–Loève transform (KLT), the
interaction, etc. Each of these areas is current research Hotelling transform or proper orthogonal decomposition
topic around the world. (POD).
Pattern matching can be done by Principal PCA was invented in 1901 by Karl Pearson.[1] Now
Component Analysis, Neural Network, Fuzzy Logic it is mostly used as a tool in exploratory data analysis
Principal, etc. In terms of space/time complexity of and for making predictive models. PCA can be done by
algorithms, PCA algorithm is fast as well as efficient. eigenvalue decomposition of a data covariance matrix or
Principal component analysis (PCA) is a mainstay singular value decomposition of a data matrix, usually
of modern data analysis - a black box that is widely used after mean centering the data for each attribute. The
but (sometimes) poorly understood. Principal component results of a PCA are usually discussed in terms of
analysis (PCA) is a standard tool in modern data analysis component scores (the transformed variable values
- in diverse fields from neuroscience to computer corresponding to a particular case in the data) and
graphics - because it is a simple, non-parametric method loadings (the weight by which each standardized original
for extracting relevant information from confusing data variable should be multiplied to get the component
sets. With minimal effort PCA provides a roadmap for score) (Shaw, 2003).
how to reduce a complex data set to a lower dimension PCA is the simplest of the true eigenvector-based
to reveal the sometimes hidden, simplified structures that multivariate analyses. Often, its operation can be thought
often underlie it. of as revealing the internal structure of the data in a way
Principal component analysis is a variable reduction which best explains the variance in the data. If a
procedure. It is useful when you have obtained data on a multivariate dataset is visualised as a set of coordinates
number of variables (possibly a large number of in a high-dimensional data space (1 axis per variable),
variables), and believe that there is some redundancy in PCA can supply the user with a lower-dimensional
those variables. In this case, redundancy means that picture, a "shadow" of this object when viewed from its
some of the variables are correlated with one another, (in some sense) most informative viewpoint. This is
possibly because they are measuring the same construct. done by using only the first few principal components so
Because of this redundancy, you believe that it should be that the dimensionality of the transformed data is
possible to reduce the observed variables into a smaller reduced.
number of principal components (artificial variables) PCA is closely related to factor analysis; indeed,
that will account for most of the variance in the observed some statistical packages (such as Stata) deliberately
variables. conflate the two techniques. True factor analysis makes
Principal component analysis (PCA) is a different assumptions about the underlying structure and
mathematical procedure that uses an orthogonal solves eigenvectors of a slightly different matrix.
transformation to convert a set of observations of The principal component analysis (PCA) is one of
possibly correlated variables into a set of values of the most successful techniques that have been used to
uncorrelated variables called principal components. The recognize faces in images. However, high computational
number of principal components is less than or equal to cost and dimensionality is a major problem of this
the number of original variables. This transformation is technique.
defined in such a way that the first principal component
has as high a variance as possible (that is, accounts for as II. METHOD FOR PATTERN MATCHING
much of the variability in the data as possible), and each Pattern matching using Principal Component
Published in International Journal of Advanced Engineering & Application, June 2011 Issue 6

2. Analysis (PCA) method consists of following steps: X(i-1)*m+j = I(i,,j)
1. Convert images from color to gray scale image.
A(i,,j) = Xi for image number j.
2. Resize all images to a fixed size image by
Mi =
scaling/cropping.
I(i,,j) represents pixel value of one gray scale image at
3. Read all images and store its pixel values into array
forming a matrix having row equal to total number of row i and column j.
mXn is size of gray scale image.
images read.
X is row matrix representing one gray scale image.
4. Calculate mean of this matrix.
Size of X is tX1 where t = m*n.
5. Find deviation matrix from its mean matrix.
Here A(i,,j) represents ith row and jth column of matrix
6. Calculate Eigenface of this deviation matrix.
7. Project each image into Eigenface of deviation A. And Mi represents ith row of mean matrix M.
matrix. Equation-1
8. Read image to be match and convert into gray scale.
9. Calculated difference matrix from mean matrix. Mi =
10. Find minimum difference with projected test image. Here A(i,,j) represents ith row and jth column of matrix
11. Image with minimum difference will represent A. And Mi represents ith row of mean matrix M.
desired image with most probability of match. Equation-2
In this paper image matching algorithm discussed, is
not matching exact pixels to pixels. Instead of it, there is Next step is to calculate deviation of each image
pattern matching where principal components are from mean matrix calculated above. For this we find
matched with that of training database. The most difference of each column of main image matrix (i.e. M)
matching components with training database are desired with mean matrix (i.e. m). Matrix obtained (say B) is
matched image. calculated as each column of B is equal to each column
There is a training database which contains set of of A minus column matrix m.
images from which we have to match pattern of another B(i,,j) = A(i,,j) –Mi
images to know which image from training database has Here B(i,,j) and A(i,,j) represents ith row and jth column
best match. of matrix B and A respectively. Mi represents ith row
Before matching with training database, there is pre-
of row matrix M (mean matrix).
processing on images of training database, which is done
Equation-3
once for one set of training database. This pre-processing
the quality of individual sentences. Score obtained in
is not done again until training database is not changed. Calculate Eigenface of deviation matrix: is always a
Now image to be matched with training database is MT evaluation using BLEU method
Next step is to calculate face of deviation matrix
projected and matched by use of pre-processed data. number between 0 and 1.Its value indicates how
obtained in previous step. For this fist we have to
similar the candidate and reference texts are, with
calculate Eigen values and eigenvector of deviation
Image read, resize, and gray scale conversion: matrix. Then we 1calculate Eigen face by multiplying
values closer to representing more similar texts. The
All images of training database are read one by one eigenvector 1, image matrix A. there is with a human
closer to to the more overlap
and are converted into gray scale. Colour image gives 3- reference translation and thus the better the system is.
D matrix of data (showing RGB values of each pixel) E =aA * Ev the BLEU metric measures how many
In nutshell,
after reading. RGB values are normalized to obtain gray Here E overlap, giving deviation matrix; And Ev is
words is Eigenface of higher scores to sequential
scale image (Represented by 1-D matrix i.e. row matrix). words. Here intelligibility or grammatical correctness
eigenvector of deviation matrix.
After that, all images of database are reshaped into a is not taken into account. Score calculation method in
Equation-4
fixed size images. Suppose there is n number of images BLEU is shown in figure 1.
in training set i.e. We have to take one image and match Project imagesnumber of words from the candidate that
Here m is from training database into Eigenface of
this selected image with n number of images from deviation matrix: reference. Wt is the total number of
are found in the
training set to find best match. Gray scale images from Every gray scale image is orthogonally projected
words in the candidate. r is the effective length of the
training database is read and stored into a matrix (say A) into Eigenface of deviation matrix. For this, gray scale
reference corpus, and c the total length of the
of column n where n is number of images from training image converted into row matrix is multiplied with
database. Here each column of this matrix represents one transpose of corpus. Pnmatrix calculated in previous
translation Eigenface is geometric average of the
modified n-gram precision. N is length of n-grams
step.
gray scale image from training database.
used to compute Pn.
Pj = E‘ * Aj is a metric for the evaluation of output,
METEOR
Mean calculation of image matrix:
obtained from machine translation system. The metric
Mean matrix is determined from the Matrix
Here E‘ on the harmonic mean matrix, obtained by
is based represents transpose of unigram precision
obtained from previous step of image matrix. Mean is
transpose with recall weighted higher than precision.
and recall, operation on Eigenface of deviation
calculated along rows of matrix. Here in this step we
determine average/mean value of pixels value at each matrix.
It has various features, such as stemming and
co-ordinate location of image i.e. here we calculate mean Pj and Aj represent all rows of jth column of matrix P
synonymy matching, along with the standard
image from images of training database. Mean matrix and A respectively.
exactprojection matrix obtained is not available in
P is word matching which by projecting every
calculated in this step is a row matrix (say M).
grayscale images score is calculated,
BLEU metric. A (orthogonally) into E‘. on the basis
of which, grading isEquation-5 translation system.
given to
Score
Published in International Journal of Advanced Engineering & Application, June 2011 Issue 7

3. The row containing minimum value in matrix
Processing up to this step is termed as pre- Euc_dist, is matched image of our interest
processing for pattern recognition, because pattern
matching is not started yet and this processing is done If
once for one set of training database. Once these
Euc_dist (1,k) has smallest value, the kth image from
processing is completed, there is no need to analyse/read
training set is best matched image
images from training database. This is valid until we do
not change training database regardless of images which Equation-9
we have to match with training database.
III. IMPLEMENTATION DETAILS
Read, resize, and gray scale conversion of image, which Figure1 shows MATLAB implementation of
has to be matched with training database. described algorithm. Training database of 12 RGB
Next step is to select target image, to be matched image having size 640 X 480 pixels taken for
with training database. Read selected image and convert experimental purpose. After conversion of images into
it into gray scale, and resize this image to same size that gray scale, resizing to 80 X 60 and storing into matrix
was used for pre-processing of training database. form, matrix ―A‖ is obtained as of dimension 4800 X 12.
Convert this resized gray scale image into 1-D matrix Mean matrix m is obtained as of size4800 X 1.
(row matrix). Difference matrix ―B‖ is again of same size as ―A‖.
Eigen value matrix and eigenvector matrix obtained is of
Z(i-1)*m+j = T(i,,j) size 12 X 12. Eigenface matrix ―E‖ calculated from
matrix B is obtained as of size 4800 *12. Projection
Here T is gray scaled target image. T (i,,j) represents matrix P is obtained as of size 12 *12.
pixel value of T at location ith row and jth column. Now for matching an image, we have taken one
Z is row matrix having number of rows equals to m * image which is resized to 80 X 60 pixels and converted
n where m and n are number of rows and column of into gray scale. It is stored into matrix T of size 4800 X
target image T. 1. Difference matrix and the projection matrix is
Equation-6
calculated which is of size 12 X 1 Euclidian distance
matrix is obtained as of size 12 X 1.
Calculate difference matrix from mean matrix. Now this matrix has minimum value at row number
Next step is to find difference matrix by subtracting 5. That means that selected matrix is best matched with
mean matrix of training database from target image image number 5 from training dataset.
matrix Z (row matrix). Now this test image is projected
on Eigenface of training data base. IV. CONCLUSION
Described method in this paper, is very fast as well
Q = E‘ * Z as robust technique of pattern matching. Since pre-
processing is done only once for a set of training
Here E‘ represents transpose matrix, obtained by database, processing time turns very low after
transpose operation on Eigenface of deviation initialization. Therefore this method gives result is very
matrix. fast. Even with its simplicity, described method is robust
Q is projection matrix (projected test image) and always gives better result.
obtained after projecting test image into Eigenface of
deviation matrix. REFERENCES
[1] A. Jain, R. Duin, and J. Mao, "Statistical Pattern Recognition: A
E‘ is transpose matrix of E.
Review", IEEE Transactions on Pattern Analysis and Machine
Intelligenve, vol. 22, no. 1, pp. 4-37, 2000.
Equation-7 [2] H. Bay, A. Ess, T. Tuytelaars, L. Van Gool, Speeded-up robust
features (SURF). Comp. Vision and Image Understanding
Find match between training database and target test 110(3), 346–359 (2008).
image. [3] Chi-Fa Chen, Yu-Shan Tseng and Chia-Yen Chen, 2003.
Combination of PCA and Wavelet Transforms for Face
Final step of pattern matching using PCA method is Recognition on 2.5D Images. Conf. of Image and Vision
set of sub steps as stated below. Computing '03 26-28 November 2003.
Find difference between projected image and [4] Imran S. Bajwa, S. Irfan Hyder [2005], ―PCA based Image
projected test image and calculate mean of each column Classification of Single-layered Cloud Types‖, Journal of Market
Forces Vol.1 No.2, pp. 3-13
by considering magnitude only. [5] M. Turk, A. Pentland, Eigenfaces for Recognition, Journal of
Cognitive Neurosicence, Vol. 3, No. 1, 1991, pp. 71-86
Euc_dist (1,j) = – [6] Fukunaga, Keinosuke (1990). ―Introduction to Statistical Pattern
Here Euc_dist is column matrix of size 1 row and j Recognition.‖ Elsevier. ISBN 0122698517.
http://books.google.com/books?visbn=0122698517.
column. [7] Jolliffe I.T., Principal Component Analysis, Series: Springer Series
Here j equals size of column matrix Q. in Statistics, 2nd ed., Springer, NY, 2002, XXIX, 487 p. 28 illus.
N is total number of images in training data base. ISBN 978-0-387-95442-4
Equation-8
Published in International Journal of Advanced Engineering & Application, June 2011 Issue 8

4. Fig 1. MATLAB implementation of fast PCA method for image pattern matching
Published in International Journal of Advanced Engineering & Application, June 2011 Issue 9