Improvement of wavelet multi-scale and entropy in image character feature extraction method

Improvement of wavelet multi-scale and entropy in image character feature extraction method

Source: Application of electronic technology: Li Zheng Jianbin Zhou Yan Wan

Abstract: A method based on wavelet and entropy extracting image character characteristics is proposed. The method utilizes wavelet transform to multi-scale decomposition of image characters, using Marr zero cross edge detection operator extraction edge; minimizes the extraction of each scale image based on the determination entropy, the advantages and entropy energy of wavelet "digital microscope" A combination of various types of overlapping conditions and direct expression of the error rate can be expressed. Compared with other methods, the method extracted with the characteristic vectors, high recognition rate, fast algorithm, which is very conducive to classification, and feature extraction methods have human vision. Keywords: Multi-scale analysis MARR edge detection operator discriminant entropy feature extraction online signature verification is a technology of paper acquisition and verify personal signature, thereby realizing a technology of paperless office [1]. Among them, extracting a valid character tape from the collected video image is the core step of the online signature verification system. With the rapid development of computer and pattern identification technology, there have been many solutions for extracting character characteristics, and the most representative edge description method and moment description method [2]. A method of describing the edge shape can be used as a curved fit and a Fourier descriptive sub-method. Although the Fourier descriptor has better described a closed image profile, there are many characteristics, noise and quantization error have a larger impact on coefficients with lower amplitudes. When calculating the FFT, the FFT is calculated, and the length of its boundary point must be divided into two integers, and it does not have three (direction, position, size) uncapped, and cannot be directly used for target recognition, complex transformations must be performed. . These affect its use. The torque description method describes the characteristics of the image grayscale distribution using each of the stages of the image grayscale distribution. The moment is a two-point point defined on the entire image space, which also does not have three invariance, and must be normalized when used. Talllessness is just a rotational normalization method, and must be combined with a size, and the location normalization treatment has three invariability. Figure 1 Although the image recognition is made with these features, it has achieved more satisfactory results, but the definition of these features is quite complex, the amount of operation is large, and the mechanism of human cognition is also completely different, and cannot be intuitively understood. This paper proposes a new idea that combines statistical characteristics and structural characteristics, which performs wavelet multi-scale decomposition of character images, effectively suppresses noise in the image, and fully reflects the fine features of the image structure; minimize the determination Feature extraction can be exactly expressed in various types of overlapping conditions, and can directly express the error rate, thereby effectively improving the identification rate. 1 Wavelet Multi-scale Decomposition In order to find the base of the L2 of the space, first start from a sub-space of L2, first establish the substrate in this sub-space, then use simple transform to expand this substrate to the space L2 to form a group of bases . This is the multi-scale analysis method [3] [4]. For two-dimensional case, set {V2J} JEZ is a separate MRA: V2J = Vjvj, where {V2J} JEZ is a MRA of L2 (R2), whose scale function is is one-dimensional MRA {V2J} JEZ Real value scale functions, small-wave master functions use dabuechies [6] wavelet; corresponding to two-dimensional scale functions V2J = Vjvj, define three functions: constituting sub-space W2J orthogonal standard base, and their telescopic translation (short-handed) is : It is a standard orthogonal group of L2 (R2). In this system, the signature is collected to the computer by a desktop and electronic pen connected to a computer and is displayed on the screen. The image collected and entered into the computer is two-dimensional, and the image to decompose is f (x, y) εl2 (R2) in this paper. For convenience, L2 (R2) -V2N is set, that is, the FN is F, and the orthogonal projection of V2N. This is the decomposition of FN to FN.

Due to: Assuming {V2J} JEZ, the scale function φj, j (x, y) = 2jφ (2jx, 2jy) is a scale function of two-dimensional Mar {V2J} JEZ, and the wavelet function ψ (α) j, α = 1, 2, 3 has been given by equations (1) and formula (2), and from arrays {CNK1, K2}, (K1, K1εZ2), such that: where CN, K1, K2 = Similarly, it is: in the formula (6), J = N-1, λ, nm. FJ is the low pass filter signal of Fn on F2J, and gαj, α = 1, 2, 3 are three high pass filter details of Fn on W2J. There is a restricted sequence {pk1}, {pk2}, respectively, the high-pass filter coefficients in the X direction on the X, Y), and {GK1} and {GK2} are low-pass filter coefficients in the X direction and the Y direction, respectively. The equation (6) is obtained: the right portion of the arrow in the above formula is a matrix representation in the left portion, where CN is the distribution array of raw signal f (x, y), PR, PC is a row and list of CN respectively. The operator of the pass filter, while the QR, QC is an operator that is different to the CN and the list of high pass filters, respectively. Further, the J2, in the formula (7), J = N-2, λ, N-M. The formula (7) is a MALLAT tower algorithm for a limited orthogonal wave decomposition of two-dimensional signal Fn or CN [5]. Through experiments, use Daubechies 8 wavelet energy to achieve better decomposition. Wavelet decomposition of the real signature of the collected entering the computer is limited to it. This article only gives a real signature, such as the book 1. Usually in the experiment, the similar and detailed portions of the image are obtained by using the true and false character image by means of MATLAB 6.5, by two complementary filters, i.e., low pass filters, and high-pass filters, respectively. The similar sub-map is mainly the global, low frequency component of the original image, and the detail subgraph is usually local, high frequency components of the original image. The detail sub-maps include the horizontal sub-map, oblique subunit, and vertical son. The detail sub-map passes twice filtering: the horizontal direction allows the low frequency component to pass, while the high frequency component is allowed in the vertical direction. This is a horizontal stroke (the gradation variation in the horizontal direction is low frequencies, in the vertical direction is high) is enhanced, and the vertical stroke (the gradation variation is high in the horizontal direction of high frequency, in the vertical direction is low) is smooth. The pixels in the vertical direction and the oblique direction are protruded in the vertical sub-figure and the oblique diagram in the vertical subsequent diagram. This direction selectivity is consistent with human eye visual characteristics, enabling the feature based on this, with an algorithm with visual characteristics. Figure 22 The classic edge detection operator of the zero cross edge operator has a Sobel operator, a Laplace operator, a Marr operator, etc. In recent years, some scholars have proposed a broad fuzzy operator [7], the morphological edge count [8], etc. . The Marr Edge Detection Operator 2G is known as one of the best edge monitors, so this literal Marr operator. The operator is characterized by using the Gaussian filter to smooth the image. The response function of the two-dimensional Gaussian filter. To set f (x, y) to binary image functions, consolidate and differential in linear systems, 2 {g (x, y) хi (x, y)} = {▽ 2G (x, Y)} i (x, y), that is, the Gaussian smooth filter and the Laplas differential operation can be combined into a coils as follows: the above operator convolution image, determined zero by judging the symbol change The position of the intersection is the edge point. The results of the real signature after wavelet once decomposed are shown in Figure 2. As can be seen from Figure 2, the Marr zero cross edge operator simultaneously extracts strong, weak edges, and relatively clean edges, less noise interference, good continuity. 3 Extracting different types of samples with different types of feature spaces based on the characteristics of the determination entropy, as long as these areas are not overlap, they can be separated. The average distance between the samples is often used as the criterion function extracted by the feature.

The important distance has a MINKOWSKI metric ΔM, a European distance ΔE, a CHEBYCHEV distance ΔR, a square distance ΔQ and a non-linear metric Δn. When the probability distribution is not considered, various types of overlapping conditions cannot be expressed in exactly, and the error rate cannot be directly expressed. To this end, the probability distance should be considered, which is most advantageous to use uncertainty, so it is most advantageous, so that the probability distribution is verified after the entropy is used. This probability distribution density deviates from the degree of the given standard distribution, called relative entropy. This paper assumes that the probability distribution of the image function after the small wave and the Marr operator process is P (Xi, YJ), a given standard distribution ω (xi, yj), then the relative entropy between the two is : The summation should be performed on all possible values ​​of this feature. The smaller the relative entropy, the larger the difference between the two types of probability distribution, the larger value (equal to zero) of the two types of probability is completely identical. Therefore, it is possible to define the discriminant entropy W (p, q) to characterize the difference between two types of distribution P (Xi, YJ) and Q (Xi, Yi). In a variety of cases, σnσmw (p (n), Q (m)) can be used to represent the degree of separation between the various distributions. Here n, m represents the class number. In terms of feature extraction, under the conditions of a given dimension D, it is necessary to obtain such D features, which minimizes the above-described judgment entropy. For the sake of calculation, this paper uses the following functions - U (p, q) = σiσσj (pi, j-qij) 2 ≤ 0 instead of W (p, q) without affecting the result of selecting D optimal feature. In the case where the probability distribution is not estimated, the probability distribution in the above formula can be replaced by a normalized sample feature value. K is the sample number of the first type of sample, N1 is the total number of samples of the first class, i is a feature number. Because, this is reasonable. The coordinate system engineering of U-Take the minimum is composed of the intrinsic vector corresponding to the D subdiometric value of the matrix A = G (1) -g (2). Here G (1) and G (2) are the first class sample set and a second class of covariance matrices. The intrinsic value λk, k = 1, 2, λd queued of the matrix A is queued: select the intrinsic vector corresponding to the emission value as the desired coordinate shaft system, and the unusual entropy is determined in this coordinate system. Select Shannon Entropy in the experiment. Tables 1 and 2 2 lists the minimum discriminant entropy of the real signature and the forged signature decomposition. It can be seen from the calculation data of Table 1 and Table 2 that the data after the minimum discrimination entropy after wavelet can be apparently identified. Further, the minimum judgment entropy of similar pattern and detail graphics is very far, distinguishable, and the horizontal sub-map in the detail graph, the oblique subunter, and the minimum discrimination entropy of the three parts of the vertical figure are different. Therefore, the feature vector thus extracted is stable, the difference is large, and the correctness is high. Table 1 Minimum real signature entropy is determined similar to the sub-pattern level submap shaded view similar to FIG vertical sub-pattern level 0.0000 56.7827 58.371 60.5942 0.0000 1.5883 3.8115 58.371 subgraph hatched sub FIG 56.7827 1.5883 0.0000 2.2232 3.8115 2.2232 60.5942 vertical sub FIG forged 0.0000 Table 2 Signature minimum discrimination entropy