Statistical Feature Fusion for Sassanian Coin Classification Seyyedeh-Sahar Parsa1, Maryam Rastgarpour1, and Mohammad Mahdi Dehshibi2 1
Department of Computer Engineering, Islamic Azad University, Saveh Branch, Saveh, Iran {sahar.parsa,m.rastgarpour}@iau-saveh.ac.ir 2 Pattern Research Center (PRC), Iran
[email protected]
Abstract. Ancient coins classification has attracted increasing attention for the benefits which it brings to numismatic community. However, high betweenclass similarity and, in the meantime, high within-class variability make the problem a particular challenge. This issue highlights the importance of extracting discriminative features for ancient coins classification. Therefore, in this paper, the capability of statistical feature fusion was examined. First, a representation of the coin image based on the phase of the 2-D Fourier transform of the image is using so that the adverse effect of illumination was eliminated. The phase of the Fourier transform preserves the locations of the edges of a given coin image. The problem of unwrapping is avoided by considering two functions of the phase spectrum rather than the phase directly. Then, BDPCA approach which can reduce the dimension of the phase spectrum in both column and row directions is used and an entry-wise matrix norm calculates the distance between two feature matrices so as to classify coins. Extensive experiments are conducted on a database of Sassanian coins in order to compare the performance of proposed method with the other feature extraction method which are used in other works. The results show the proposed method is promising. Keywords: Ancient coins classification, BDPCA, Cultural Heritage, Entrywise matrix norm, phase representation.
1
Introduction
Nowadays, applications of machine vision can be found in every aspect of life [1216]. Ancient coins classification is one of the most important activities in the fields of cultural heritage and numismatics which can be benefited by machine vision, pattern recognition and other related fields. More precisely, an accurate automated coins classification system significantly improves the classification accuracy, speeds the process, and reduces the processing time. In addition, such a system can be used for classifying and documenting large collections of unclassified coins which are being kept in the museums. Furthermore, illegal trade of stolen coins can be detected and prevented as the great majority of them are being sold through the Internet and, therefore, manual tracking of the trade is almost impossible. © Springer International Publishing Switzerland 2015 H. Unger et al. (eds.), Recent Advances in Information and Communication Technology 2015, Advances in Intelligent Systems and Computing 361, DOI: 10.1007/978-3-319-19024-2_8
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Classification of ancient coins is not a trivial task and encounters many difficultties. On the one hand, irregularr shape of coins caused by manual minting, fractures, and erosions leads to consideraable variation within class samples which, in some cases, can be increased by proto otyping the same person at different ages with variious clothes, hairstyles, crowns and a decorations. On the other hand, between-class simillarity is also high, especially in n cases in which the rulers belong to the same dynasty and therefore their coins follow w almost similar patterns. Fig. 1 shows examples of m mentioned challenges in Sasanian coins. It is worth noting that the coins with the saame person prototyped on their obverses, who is often a ruler or a king, usually go to the same class.
Fig. 1. (a) Similar coins belon nging to three different classes (b) Three dissimilar coins from m the same class
Developed ancient coinss classification methods have mainly utilized local featuures in order to build a discrim minative feature space. For example in [1], different loocal descriptors are used as featture extractors for ancient coins recognition and it was observed in the course of expeeriments that SIFT descriptor has the capability of prodducing a promising result. In another attempt, Arandjelovic [2] can achieve the ratee of 57% in Roman’s coins claassification with a view to utilizing the visual words and locally biased directional histograms. h Although local features are typically suggessted for this application, global features are less taken into account and have been ovvershadowed by local featurees. Although the latter work conducted experiments oon a database with 65 classes and examined different features for comparing the end results, it is similar to Kamp pel work in performing local features and the experimeents are not reproducible. The reason is that the detail of feature’s parameters and ddata distributions corresponded to between/within classes are left in doubt. Allahverddi et al. [3], [4] did the first attem mpt in ancient Persian coins classification in the Sasaniaan’s era. They used statistical methods m in their works; these methods were Eigen analyysis and Discrete Cosine Transform, respectively, in conjunction with Support Vecctor Machine. They achieved th he recognition rate of 21.7% and 86.21%, in turn. In adddition to ancient coins, severral works have been reported on classifying modern cooins.
Statistical Feature Fusion for Sassanian Coin Classification
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For instance, Huber et al. [5] utilize Eigen analysis in order to construct a discriminative model which has the capability of classifying coins from their diameter and thickness. Another identification system for matching EURO coins is presented by Khashman et al. [6] in which a neural network is trained with images relate to the both side of EURO in different rotated positions. In [7], angular and distance information of coin’s edge image are encoded in histograms; then, a 3-nearest neighbor approach is utilized on two sides of the coin to construct a classification pilot socalled COIN-O-MATIC. In this paper, we explored the effectiveness of the dimensional reduction approach in a phase of the 2-D Fourier transform representation of the coin image. BiDirectional Principal Component Analysis (BDPCA) approach [8] is used because its power in reducing the dimension of the phase spectrum in both column and row directions. Finally, entry-wise matrix norm calculates the distance between two feature matrices so as to classify coins. In order to compare the features comprehensively, extensive experiments are conducted on a database of Sasanian coins. The experiments include performance of each group while considering obverse and reverse sides of coins, and capability of each one in making distinction between samples of each class and other classes. The organization of this paper is as follows. Section 2 briefly describes the proposed method. Experimental results are illustrated in Section 3. Finally, in section 4, results are discussed and a conclusion is drawn.
2
Proposed Method
Feature extraction is a key step in any pattern recognition problem. In particular, performance of a method is directly dependent on how discriminative the extracted features are. An appropriate feature extraction method has to minimize the overlap or similarity between classes while maximizing the similarity within each class. This is a particular challenge especially in cases in which the nature of the problem itself leads to a large overlap between classes like ancient coins classification as foreshadowed. Therefore, exploring discriminative feature extraction methods for the purpose of ancient coins classification is of great importance. 2.1
Preprocessing and Region Extraction
The areas of the coins under study have to be extracted from cluttered background images. In fact, backgrounds of images under this study have been cluttered with some 4-digit numbers, as is shown in Fig.1, indicating the coins’ record IDs. These numbers have to be removed from the backgrounds as they can introduce correlation and similarities between images and therefore will affect the classification rate. To do this, Sobel operator is firstly applied to create a binary gradient mask which represents lines of high contrast; i.e. edges; in the image. This mask is later enhanced by being dilated as well as filling holes and removing small undesired objects. Finally, the binary mask is applied to the image and the coin’s region is extracted. This process is illustrated in Fig. 2.
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Fig. 2. Preprocessing steps. (aa) Original image; (b) Binary gradient mask; (c) Dilated graddient mask; (d) Gradient mask aftter filling holes; (e) Gradient mask after removing undessired connected components; (f) Seg gmented image.
2.2
Phase of the Fourieer Transform
The most common way of representing an image in the spatial domain is by a tw wodimensional array of positiv ve numbers, corresponding to the gray levels of the pixxels. An image can also be reprresented in the frequency domain as the discrete Fouurier transform (FT) of the two-d dimensional array of pixels [9]. The Fourier representattion involves complex numberss, i.e., the magnitude and phase parts. The relative importance of the magnitude and a phase of the FT of a signal/image under different sittuations was studied in [10], [11]. It is difficult to visualize how the information in thhese two components are related d, because the magnitude and phase are not directly com mparable. Let us represent an imag ge by x [n1, n2], n1 = 0, 1, …, R − 1, n2 = 0, 1, …,C − 1. Here R and C are the numb ber of rows and columns of the given image, respectively. The discrete Fourier transfo orm (DFT) [9] of x [n1, n2] is given by: X[k1, k2] = DFT D {x[n1, n2]} = Xr [k1, k2] + Xi [k1, k2] (1)
= |X[k1, k2]|×exp[θ[k1, k2]] where |X[k1, k2]| = ((Xr [k1, k2])2 + (Xi [k1, k2])2)0.5, and θ[k1, k2] = arctan{Xi [k1, k2]/ Xr [k1, k2]} are the magnitude and the phase of the DFT, respectively. The real and im maginary parts of the DFT are denoted d by Xr and Xi, respectively. The original image can be obtained from X[k1, k2] by b inverse DFT relation [9] which is abbreviated as ID DFT. The information contained in the magnitude and phase of the DFT can be visualiized using either magnitude-only y synthesis of the image or the phase-only synthesis of the image, as are shown in Fig g. 3. The phase-only image gives more crucial featuress as compared to the magnitudee-only image. But computation of the phase spectrum ussing arctan leads to the problem m of phase wrapping [9]. One way to resolve this problem m is to use a function of the phase spectrum as follows:
Staatistical Feature Fusion for Sassanian Coin Classification
,
= ,
(a)
+ ×
, =|
, ,
|
,
(b)
, ,
=|
,
=|
,
, ,
|
79
(2)
(3)
|
(c)
mage. (b) Magnitude-only synthesis of coin image. (c) Phase-oonly Fig. 3. (a) Gray-level coin im synthesis of coin image
2.3
BDPCA with Entry y-Wise Matrix Norm
The cosine and sine functiions of the phase spectrum accentuate the high frequeency components. Hence they emphasize e noise also. The effect of noise can be reduuced using Eigen analysis. Let th he training coin images for the coin i be denoted by sett Di. The cosine and sine functio ons of the phase spectrum are computed using Eq. 3. T The DFT of a real image exhibiits conjugate symmetry [9]. Hence only the non-redunddant coefficients (the shaded reg gion in Fig. 4) of the cosine and sine functions of the phhase spectrum are used in the Eig gen analysis.
Fig. 4. DFT coefficients X[k1, k2] in the shaded area determine the remaining coefficientts
Here, we use an extend model of Eigen analysis method, so-called Bi-Directioonal PCA, for achieving the aim m of noise reduction as well as the feature extraction. Thhen,
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an entry-wise matrix distance metric is used to calculate the distance of two feature matrices. BDPCA directly extracts feature matrix Y from image matrix D by, =
(4)
and are the column and row projectors. In order to calculate these where projectors, given a training set {D1, ..., DN} where N is the number of samples and each sample is m×n, we must first define total scatter matrix for rows and columns of the data matrix as follows: =
∑
(
− ) (
=
∑
(
− )(
− )
(5)
− )
(6)
where is the mean matrix of all training images. We choose the row and columns eigenvectors corresponding to the first krow and kcol largest eigenvalues of and to construct the row (Wrow) and column (Wcol) projectors, respectively. Finally we use Eq. 4 to extract feature matrix Y from image D. BDPCA just produces a feature matrix, with which doing a classification task needs to define a matrix distance. Therefore, we use a sort of entry-wise matrix norm so as to increase the recognition rate. This distance is defined as follows and its efficiency is subjected to several experiments: ( , )=
∑
It is worth mentioning = ( matrixes. A matrix norm on ℝ lowing properties [6]:
∑ )
×
−
(7)
and = ( ) is a function : ℝ ×
×
×
are two feature → ℝ with the fol-
1. ( ) ≥ 0, ∈ ℝ × ( ( ) = 0 ⇔ = 0) 2. ( + ) ≤ ( ) + ( ), , ∈ ℝ × 3. ( ) ≤ | | ( ), ∈ ℝ, ∈ ℝ × Theorem 1: Theorem 2: The
= (∑ | | ) ,
=
is a vector norm. The proof is discussed in [6].
∑
∑
function is a matrix norm.
Proof: It can be easily shown that ─ ||A||p, q ≥ 0, ─ ||A||p, q = 0 A = 0, ─ ||αA||p, q = |α|.||A||p, q. Now, we prove ||A+B||p, q ≤ ||A||p, q + ||B||p, q. +
,
=
+
≤
( )
+
( )
Statistical Feature Fusion for Sassanian Coin Classification
where
( )
( )
and
81
denote the jth column vectors of A and B, respectively. From The-
orem 1, we know ∑
( )
and ∑
( )
are vector norms
for a and b, respectively. Therefore, the following property is reasonable:
( )
+
( )
=
≤
+
( )
( )
+
=
,
+
,
Consequently, ||A||p, q is a matrix norm and can be used to find out an input image belongs to which class. 2.4
Eigenanalysis Using Fourier Phase
We only used the non-redundant coefficients (the shaded region in Fig. 4) of the co∈ℝ × = sine and sine functions of the phase spectrum in the Eigenanalysis. Let × ,…, ∈ℝ = ,…, and be the eigenvectors corresponding to the m, where m = min{krow, kcol}, largest eigenvalues derived from Wrow and Wrow of the given training images, respectively. Here, N = (row × col/2) + 2. The eigenvectors are used to represent the image approximately in cosine and sine domain with respect to Eq. 4. These new representations are used for matching in a coin recognition task. The effect of noise is reduced as only the first m (m ≤ N) coefficients are considered for matching. The proposed representations have another advantage in the context of Eigenanalysis, as the size of resulting scatter matrixes is approximately one fourth as compared to the scatter matrixes [(row × col) × (row × col)] obtained using gray level values of the coin images. Thus, the estimation of the eigenvectors may be more accurate for same number of training images.
3
Experiments
This section describes experiments with the proposed method. The extracted cosine and sine features are investigated in the Bi-Directional PCA algorithm so as to find the right classes. In addition, the classification rate of the system is compared with classification rates obtained from applying different feature extraction and classification methods. It is worth mentioning that in these experiments, both sides of coins were considered. 3.1
Database
The experiments are conducted on a database with 570 coins images in JPEG format with resolution 1014×1014 pixels. The images are equally distributed in three classes. In other words, there are 95 coins, i.e. 190 images, in each class. Each class corresponds to a
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Sasanian king namely, Khossrow I, Khosrow II and Hormizd IV. Two third of the dataa are allocated to training set and d the remaining part is considered as test set. Fig. 5 deppicts sample coin images of each class in the database.
Fig. 5. Database samples. Obv verse and reverses of (a) Khosrow I; (b) Khosrow II; (c) Horm mozd IV.
3.2
Significance of DFT T Coefficients and BDPCA Features
The spacing of the edges will w be inversely proportional to the frequency in the phhase of the Fourier transform. As A a result, the low frequency DFT coefficients correspoond to events/edges separated by b large spacing, and the high frequency DFT coefficieents for events/edges separated by small spacing. The effect of the different DFT coeefficients can be seen in the phase-only synthesis of the image. Matching true class coin n images having some variation with respect to training images can be improved by reemoving some high frequency DFT coefficients. This iss an advantage because noise and a events with small spacing are given less importannce. Experiments were conducteed by considering only the first k DFT coefficients aloong both the axes of the Xc[k1, k2] and Xs [k1, k2] representations of the given training ccoin image. Only non-redundan nt coefficients are used for Eigenanalysis. The recognittion performance is improved by y removing some high frequency DFT coefficients. In general the performan nce increases with m, but after some value of m the perfformance reaches a maximum m value. The performance can be improved further by removing some high frequen ncy DFT coefficients. In fact the performance improoves from 79.31% to 87.35% ussing k 128 for choosing the number of DFT coefficieents and decreasing the size of feature vector to krow = 4, kcol = 18, and setting p1=2 and p1= 0.25. Performance comparison n with other methods is given in Table 1. The results shhow that the proposed method peerforms better than the existing methods.
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Table 1. Average recognition rate in % Methods Principal Component Analysis (PCA) 2D PCA Bi-Directional PCA Indipent Component Analysis (ICA) Discrete Cosine Transform + SVM Wavelet + SVM Proposed
4
Set of reference coin images Khosrow I Khosrow I Hormozd IV 68.96 79.31 79.31 62.06 79.31 65.51 82.75
82.75 82.75 93.10 82.75 93.10 93.10 93.10
44.82 65.51 86.20 62.06 65.51 79.31 86.20
Conclusion
Ancient coins classification is one of the most important activities in the fields of cultural heritage and numismatics which can be benefited by machine vision, pattern recognition and other related fields. This paper presented an efficient ancient coins classification method. This method utilizes a representation of the coin image based on the phase of the 2-D Fourier Transform (FT) of the image so that the adverse effect of illumination was eliminated. The phase of the Fourier transform preserves the locations of the edges of a given coin image. The problem of unwrapping is avoided by considering two functions of the phase spectrum rather than the phase directly. Then, BDPCA approach which can reduce the dimension of the phase spectrum in both column and row directions is used and an entry-wise matrix norm calculates the distance between two feature matrices so as to classify coins. Effect of different number of FT as well as BDPCA coefficients was examined in order to find the best choice. The highest classification rate of 87.35 % was obtained with 128 DFT coefficients and 4×18 Eigenvectors where were extracted from row and column scatter matrixes, respectively. In addition, we have compared performance of the system with 6 other cases. It was observed in the course of experiment that the proposed method outperformed others in spite of the smaller feature vector.
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