CN107578049B

CN107578049B - Circular symmetry Gabor wavelet depth decomposition image classification method

Info

Publication number: CN107578049B
Application number: CN201710775527.5A
Authority: CN
Inventors: 李朝荣; 樊富有; 黄东
Original assignee: Yibin University
Current assignee: Yibin University
Priority date: 2017-09-01
Filing date: 2017-09-01
Publication date: 2020-06-05
Anticipated expiration: 2037-09-01
Also published as: CN107578049A

Abstract

The invention proposes an image classification method using a depth decomposition scheme based on Circularly Symmetric Gabor Wavelets (CSGW), called DD-CSGW. Because the CSGW has a rotation invariant characteristic, the DD-CSGW is also a rotation invariant decomposition method. Deep decomposition refers to iterative and hierarchical decomposition by using the CSGW, which means that coarser subbands can be decomposed successively into several finer subbands by the CSGW. Since there is a strong dependency relationship in the DD-CSGW transform domain, we use Copula model to capture these proportional dependencies, i.e. the Copula model is used to delineate the decomposition subbands of each layer. The Copula model parameters and the mean and variance of the DD-CSGW sub-band are used for representing the image, and SVM is used for image classification. The deep decomposition method has good performance in the aspect of image classification, has high speed in the classification stage, and has the characteristic of selection invariance.

Description

Circular symmetry Gabor wavelet depth decomposition image classification method

Technical Field

The invention relates to the field of image classification, in particular to a rotation-invariant image classification method by utilizing circular symmetry Gabor wavelet depth decomposition.

Background

Image classification is an important research direction in computer vision. A key task of classification is how to efficiently represent a given image using less discriminative information, often referred to as features of the image. For most feature representation methods, the extracted features will be significantly different if the images are taken at different directional perspectives. Therefore, designing a rotation-invariant approach for image representation remains an important and challenging task. It is known that wavelet transform based methods, including discrete wavelet transforms and Gabor wavelet transforms, are not rotation invariant, since different sub-bands will produce different features under rotation conditions. Some rotation invariant technologies are researched on the basis of wavelet transformation at home and abroad. Despite the multi-resolution nature, wavelet-based methods (e.g., discrete wavelets and Gabor wavelets) still have performance that is to be improved.

Disclosure of Invention

In view of this, the invention designs an image classification method based on a Circularly Symmetric Gabor Wavelet (CSGW). CSGW is a Gabor filter-based rotation invariant approach designed by Porter and Canagarajah. The CSGW is designed for the purpose of the obtained rotation invariance. However, without directional selection characteristics like Gabor wavelet, the CSGW will yield less identification information when applied to image analysis. Therefore, the efficiency of the CSGW for non-rotated image representation is relatively low compared to the Gabor wavelet. The CSGW is determined by the following expression:

h_m(x，y)＝λ^-mh_C(x′，y′)

wherein

Is a Circularly Symmetric Gabor Filter (CSGF). x ═ λ^-mx，y′＝λ^-my；λ^-m(m-0, …, S-1) is a scale parameter; m is the scale parameter and J is the number of scales of the decomposition. W is the center frequency and σ is the variance.

In order to obtain more discriminative information, the invention provides a deep decomposition method based on CSGW, which is called DD-CSGW. Deep decomposition refers to iterative and hierarchical decomposition by using the CSGW, which means that coarser subbands can be decomposed successively into several finer subbands by the CSGW. It should be noted that the depth decomposition is not simply a decomposition of the image into more scales with the CSGW. Since the performance of the CSGW does not always improve as the number of decomposition scales increases, experiments have shown that a 5-scale segment decomposition will reach the best performance. However, the deep decomposition proposed by the invention is far better than the CSGW decomposition performance of 5 scales and the performance of Gabor wavelets.

Since the CSGW transform domain has strong dependency relationship, we use Copula model to capture these proportional dependencies, i.e. the Copula model is used to delineate the decomposition sub-bands of each layer. The Copula model belongs to a multidimensional statistical model and comprises two parts of a Copula function and a plurality of edge distribution functions. Copula model h (x) is expressed as follows:

wherein f is_i(x_i) And F_i(x_i) Edge distribution density function and cumulative distribution respectively representing modelA function. c (F)₁(x₁)，…，F_d(x_d) Is a Copula density function consisting of F_i(x_i) And (4) determining. According to the invention, Gaussian Copula is used as a Copula density function; the density function of the Weibull distribution was used as the edge distribution. Gaussian Copula is expressed as follows:

wherein ξ ═ ξ₁，…，ξ_d]，ξ_i＝Φ^-1(u_i) I is 1, …, d, Φ and Φ^-1Representing a normal distribution and its inverse function. R is the correlation matrix of Gaussian Copula. The density function and cumulative distribution function of the Weibull distribution are as follows:

wherein α and β are shape parameters and scale parameters, respectively.

To further improve the performance, in addition to using Copula model parameters, we propose to use the mean and standard deviation of the DD-CSGW decomposition subband coefficients as features of the image at the same time.

For the image classification phase, the parametric features of the Copula model based on DD-CSGW, and the mean and standard deviation features of DD-CSGW are normalized to [0, 1], and SVM (support vector machine) is used as the classifier.

Drawings

FIG. 1 is a flow chart of the method of the present invention

FIG. 2 is a decomposition diagram of DD-CSGW in the method of the present invention

Detailed Description

The method of the invention is implemented by the following steps (see figure 1):

step 1, performing depth decomposition on the image by using the CSGW, namely performing DD-CSGW decomposition (see FIG. 2, wherein a scheme of two-layer decomposition is given).

Step 1.1, the first layer is decomposed. The input image I (x, y) is decomposed by CSGW, the image is decomposed into J-scale subbands and its amplitude is taken, and the decomposition scales are denoted by S [ I ], I being 1,2, …, J, respectively. The invention takes J to 5, and the formula is as follows:

S[i]＝|h_m(x，y)*I(x，y)|

step 1.2, the second layer is decomposed. And continuing to perform J-scale decomposition on the sub-band Si by using CSGW, and calculating the amplitude Si, J of the decomposition sub-band of the layer.

S[i，j]＝|h_m(x，y)*s[i]|

And 1.3, decomposing the L-th layer. Continuing to perform J-scale decomposition on the sub-bands S [ i, J, …, k ] by using CSGW, and calculating the amplitude values S [ i, J, …, k, l ] of the decomposed sub-bands. The invention takes L as 3, namely 3 layers of decomposition are carried out.

S[i，j，…，κ，l]＝|h_m(x，y)*s[i，j，…，k]|

And 2, calculating image characteristics.

And 2.1, constructing a Copula model. The decomposition subbands for each layer are first characterized by a Copula model. The Copula density function in the model is a Gaussian Copula, and the edge density function is a Weibull distributed density function. Thus, the L-level decomposition will have L Copula models as parameters. For one image, the depth decomposition of the present invention will produce 3 Copula models. The parameters of the Copula model include Copula density function parameters and edge density function parameters. Parameters of Copula model were estimated with two-stage (two-step) maximum likelihood method: the first stage estimates the parameters of the edge density; the second stage estimates the parameters of the Copula function. Since the estimated parameters R are matrices (symmetric matrices), it needs to be straightened into vectors, which are expressed as follows:

from this Copula model parameter X_CPCan be expressed as:

wherein L represents the number of decomposition layers,

and

parameters respectively expressed as edge distribution of the l-th layer decomposition;

represents the element in Copula density function parameter R of the l-th layer decomposition.

And 2.2, calculating the mean value and the standard deviation of the DD-CSGW decomposition sub-band. The mean and standard deviation of each subband coefficient for each layer of decomposition is calculated separately. Mean and standard deviation features of model X_enIs represented as follows:

and step 3, combining the characteristics. Using Copula model parameter characteristic X_CPAnd the mean and standard deviation features X of the model_enThe image features X obtained by the combination are expressed as follows:

X＝[X_CP，X_en]

and 4, classifying by using an SVM. And (4) extracting image features in the training set by using the method in the step 1-3, and training the SVM classifier. And after the SVM classifier is trained, inputting the features extracted from the current image into the SVM for classification and judgment. When SVM training and discrimination are performed, the features are normalized to [0, 1 ].

Claims

1. The circular symmetry Gabor wavelet depth decomposition image classification method comprises the following steps:

step 1, carrying out depth decomposition on the image by using a circular symmetric Gabor wavelet CSGW, namely carrying out DD-CSGW decomposition:

step 1.1, a first layer decomposition, decomposing an input image I (x, y) with CSGW, decomposing the image into J-scale subbands and taking the amplitudes thereof, where S [ I ], I ═ 1,2, …, J respectively denote the decomposition scales, where J ═ 5, expressed by the formula:

S[i]＝|h_m(x，y)*I(x，y)|

wherein h is_m(x, y) is CSGW;

step 1.2, the second layer of decomposition, continuing to use CSGW to respectively carry out J-scale decomposition on the sub-band Si, and calculating the amplitude value Si, J of the decomposed sub-band:

S[i，j]＝|hm(x，y)*s[i]|

step 1.3, performing L-th decomposition, continuing to perform J-scale decomposition on the sub-bands S [ i, J, …, k ] by using the CSGW, and calculating the amplitudes S [ i, J, …, k, L ] of the decomposed sub-bands, wherein L is 3, that is, performing 3-level decomposition;

step 2, compute image features, S [ i, j, …, k, l ] ═ hm (x, y) S [ i, j, …, k ] |:

step 2.1, constructing a Copula model, firstly, depicting a decomposition subband of each layer by using the Copula model, wherein a Copula density function in the model is a Gaussian Copula, and an edge density function is a Weibull distributed density function, so that L-layer decomposition can be used for obtaining parameters of L Copula models, for an image, deep decomposition can be used for generating 3 Copula models, parameters of the Copula model comprise a Copula density function parameter and an edge density function parameter, and parameters of the Copula model are estimated by using the maximum likelihood of two stages: the first stage estimates the parameters of the edge density; the second stage estimates the parameters of Copula function, and because the estimated parameters R are symmetric matrices, it needs to be straightened into vectors, which are expressed as follows:

from this Copula model parameter X_CPCan be expressed as:

wherein L represents the number of decomposition layers,

and

elements in a Copula density function parameter R representing the l-th layer decomposition;

step 2.2, calculating the mean value and standard deviation of the DD-CSGW decomposition sub-band, respectively calculating the mean value and standard deviation of each sub-band coefficient of each layer of decomposition, and the mean value and standard deviation characteristic X of the model_enIs represented as follows:

step 3, combining the characteristics, namely combining the parameter characteristics X of the Copula model_CPAnd the mean and standard deviation features X of the model_enThe image features X obtained by the combination are expressed as follows:

X＝[X_CP,X_en]

and 4, classifying by using an SVM, extracting the image characteristics in the training set by using the method in the step 1-3, training an SVM classifier, inputting the characteristics extracted from the current image into the SVM for classification and judgment after the training of the SVM classifier is finished, and normalizing the characteristics to [0, 1] when the SVM training and judgment are carried out.

2. The method for classifying the circularly symmetric Gabor wavelet deep decomposition images as claimed in claim 1, wherein: and (3) extracting image characteristics by using a circularly symmetric Gabor wavelet deep decomposition method called DD-CSGW, wherein the DD-CSGW has rotation invariant characteristics.

3. The method for classifying the circularly symmetric Gabor wavelet deep decomposition images as claimed in claim 1, wherein: meanwhile, the image is represented by using the parameter characteristics, the mean value characteristics and the standard deviation characteristics of the Copula model of the DD-CSGW decomposition sub-band.