I. Introduction

Image fusion is the synthesis of image information obtained by two or more sensors to form a more accurate and richer image. Image fusion is divided into three levels from low to high: pixel level fusion, feature level fusion and decision level fusion. Wavelet transform is a commonly used method in image fusion. The research shows that wavelet transform is not an optimal function representation method in high dimension. In order to more effectively represent and process high-dimensional spatial data such as images, researchers have proposed a series of multi-scale geometric analysis tools such as Ridgelet, Curvelet, Bandelet, Contourlet, and Wavelet-Contourlet. The proposed methods laid the foundation for constructing more and more effective fusion methods in the field of image fusion.

Wavelet transform and Contourlet transform are two main and commonly used tools for image fusion. Wavelet transform is relatively mature in both theory and practical application, and it has always been a common tool for image fusion, but it can only obtain information in three directions: horizontal, vertical, and diagonal. The contourlet transform can make up for the flaw of the finiteness of the wavelet transform and obtain information in any direction of the image. At the same time, the wavelet transform and the Contourlet transform process the image in a similar manner. That is, the image is decomposed into low frequency and high frequency parts, and image fusion is performed in the low frequency and high frequency, respectively. Therefore, wavelet transform and Contourlet transform can be used together to improve the performance of the image.

The research of image fusion not only includes the research of algorithm, but also contains the research of fusion rules. Fusion rules now generally choose regional (or windowed) fusion rules. Because the low frequency mainly reflects the energy information of the image, the high frequency reflects the boundary information of the image, that is, the degree of change. The variance also reflects the overall change in image pixels. Therefore, in this paper, we choose regional variance method to select the weighted average fusion method.

Second, wavelet - Contourlet transform

Wavelet transform

In 1989, under the inspiration of Burt and Adelson's image decomposition and reconstruction pyramid algorithm (ie, the Gaussian Laplacian pyramid algorithm), Mallat introduced the idea of â€‹â€‹multi-scale analysis in the field of computer vision to wavelet analysis. The concept of resolution analysis gives the Mallat fast algorithm.

2. Contourlet transform

Because the wavelet transform can not represent the direction information of the image well. In 2002, Do and Vetterli proposed the Contourlet transform. Contourlet transform is a multi-resolution, local, and directional image representation. It can provide information in any direction and is a sparse representation of a two-dimensional image. The Contourlet transform uses a dual channel filter bank to process the image in two major steps:

1 The input image is decomposed using the Laplacian pyramid (LP). The LP decomposition includes four steps: low-pass filtering, down-sampling, interpolating amplification, and band-pass filtering. Low-frequency sub-bands continue to be LP-decomposed, and high-frequency subbands at low frequencies and a range of different scales can be obtained.

2 Directional analysis is performed on the high-frequency directional filter bank obtained by LP decomposition. The purpose of the directional filter bank is to capture the directional high-frequency information of the image and synthesize the singular points in the same direction into a single coefficient.

The directional filter bank decomposes the tree structure of the image and decomposes the frequency domain into sub-bands. Each sub-band is wedge-shaped. The method first uses the sector filter and five sampling filters shown in Fig. 1, and decomposes the input image into two horizontal and vertical sub-bands, and then introduces the Shearing re-sampling operator band.

3. Wavelet-Contourlet Transform

The LP decomposition used in the first stage of the Contourlet transform has redundancy, resulting in 4/3 redundancy of the Contourlet transform. In addition, the decorrelation of LP decomposition is not as good as the wavelet transform. To solve the above problem, Eslami R and Radha H proposed wavelet-contourlet transform. The wavelet-contourlet transform consists of a two-stage filter bank. The first stage uses wavelet transform to decompose and obtain high-frequency components of the image, thereby reducing the correlation of detail information in each subspace. The second stage uses a directional filter bank. Get subbands in all directions of high frequency.

Third, based on variance selection average fusion algorithm

The steps of the fusion algorithm given in this paper are as follows:

1 Wavelet-Contourlet transform is applied to the left blurred image and the right blurred image respectively to obtain the low frequency part and the high frequency part of the source image.

2 The low frequency part adopts a simple weighted average fusion rule.

After the wavelet-contourlet transform of the image, the low frequency coefficients mainly concentrate most of the energy of the original image, which determines the general appearance of the image. This article uses a weighted average fusion rule for low frequency subband coefficients.

3 The high frequency part adopts the variance rule to select the weighted average fusion rule.

After the image is transformed by the wavelet-Contourlet transform, the high-frequency coefficients mainly include the details of the image and the edge information. Each high frequency subband coefficient reflects the directional characteristics.

Fourth, the conclusion

This paper proposes an improved algorithm that uses weighted averaging of regional variances for high frequency coefficients and weighted average processing for low frequencies. Experiments show that the algorithm can more easily obtain the details and edge information of the image. According to the experimental data, it can also be known that the wavelet-contourlet transform has lower bias and cross entropy than the wavelet transform and Contourlet transform.

Therefore, under the same fusion rule, the image fusion algorithm based on the wavelet-contourlet transform and the weighted-average selection of regional variance can obtain better results than the wavelet transform and the Contourlet transform fusion algorithm.

Image fusion is the synthesis of image information obtained by two or more sensors to form a more accurate and richer image. Image fusion is divided into three levels from low to high: pixel level fusion, feature level fusion and decision level fusion. Wavelet transform is a commonly used method in image fusion. The research shows that wavelet transform is not an optimal function representation method in high dimension. In order to more effectively represent and process high-dimensional spatial data such as images, researchers have proposed a series of multi-scale geometric analysis tools such as Ridgelet, Curvelet, Bandelet, Contourlet, and Wavelet-Contourlet. The proposed methods laid the foundation for constructing more and more effective fusion methods in the field of image fusion.

Wavelet transform and Contourlet transform are two main and commonly used tools for image fusion. Wavelet transform is relatively mature in both theory and practical application, and it has always been a common tool for image fusion, but it can only obtain information in three directions: horizontal, vertical, and diagonal. The contourlet transform can make up for the flaw of the finiteness of the wavelet transform and obtain information in any direction of the image. At the same time, the wavelet transform and the Contourlet transform process the image in a similar manner. That is, the image is decomposed into low frequency and high frequency parts, and image fusion is performed in the low frequency and high frequency, respectively. Therefore, wavelet transform and Contourlet transform can be used together to improve the performance of the image.

The research of image fusion not only includes the research of algorithm, but also contains the research of fusion rules. Fusion rules now generally choose regional (or windowed) fusion rules. Because the low frequency mainly reflects the energy information of the image, the high frequency reflects the boundary information of the image, that is, the degree of change. The variance also reflects the overall change in image pixels. Therefore, in this paper, we choose regional variance method to select the weighted average fusion method.

Second, wavelet - Contourlet transform

Wavelet transform

In 1989, under the inspiration of Burt and Adelson's image decomposition and reconstruction pyramid algorithm (ie, the Gaussian Laplacian pyramid algorithm), Mallat introduced the idea of â€‹â€‹multi-scale analysis in the field of computer vision to wavelet analysis. The concept of resolution analysis gives the Mallat fast algorithm.

2. Contourlet transform

Because the wavelet transform can not represent the direction information of the image well. In 2002, Do and Vetterli proposed the Contourlet transform. Contourlet transform is a multi-resolution, local, and directional image representation. It can provide information in any direction and is a sparse representation of a two-dimensional image. The Contourlet transform uses a dual channel filter bank to process the image in two major steps:

1 The input image is decomposed using the Laplacian pyramid (LP). The LP decomposition includes four steps: low-pass filtering, down-sampling, interpolating amplification, and band-pass filtering. Low-frequency sub-bands continue to be LP-decomposed, and high-frequency subbands at low frequencies and a range of different scales can be obtained.

2 Directional analysis is performed on the high-frequency directional filter bank obtained by LP decomposition. The purpose of the directional filter bank is to capture the directional high-frequency information of the image and synthesize the singular points in the same direction into a single coefficient.

The directional filter bank decomposes the tree structure of the image and decomposes the frequency domain into sub-bands. Each sub-band is wedge-shaped. The method first uses the sector filter and five sampling filters shown in Fig. 1, and decomposes the input image into two horizontal and vertical sub-bands, and then introduces the Shearing re-sampling operator band.

3. Wavelet-Contourlet Transform

The LP decomposition used in the first stage of the Contourlet transform has redundancy, resulting in 4/3 redundancy of the Contourlet transform. In addition, the decorrelation of LP decomposition is not as good as the wavelet transform. To solve the above problem, Eslami R and Radha H proposed wavelet-contourlet transform. The wavelet-contourlet transform consists of a two-stage filter bank. The first stage uses wavelet transform to decompose and obtain high-frequency components of the image, thereby reducing the correlation of detail information in each subspace. The second stage uses a directional filter bank. Get subbands in all directions of high frequency.

Third, based on variance selection average fusion algorithm

The steps of the fusion algorithm given in this paper are as follows:

1 Wavelet-Contourlet transform is applied to the left blurred image and the right blurred image respectively to obtain the low frequency part and the high frequency part of the source image.

2 The low frequency part adopts a simple weighted average fusion rule.

After the wavelet-contourlet transform of the image, the low frequency coefficients mainly concentrate most of the energy of the original image, which determines the general appearance of the image. This article uses a weighted average fusion rule for low frequency subband coefficients.

3 The high frequency part adopts the variance rule to select the weighted average fusion rule.

After the image is transformed by the wavelet-Contourlet transform, the high-frequency coefficients mainly include the details of the image and the edge information. Each high frequency subband coefficient reflects the directional characteristics.

Fourth, the conclusion

This paper proposes an improved algorithm that uses weighted averaging of regional variances for high frequency coefficients and weighted average processing for low frequencies. Experiments show that the algorithm can more easily obtain the details and edge information of the image. According to the experimental data, it can also be known that the wavelet-contourlet transform has lower bias and cross entropy than the wavelet transform and Contourlet transform.

Therefore, under the same fusion rule, the image fusion algorithm based on the wavelet-contourlet transform and the weighted-average selection of regional variance can obtain better results than the wavelet transform and the Contourlet transform fusion algorithm.

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