I. Introduction
Image fusion is to synthesize the image information obtained by two or more sensors to form an image with more accurate and rich data. 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 more commonly used method in image fusion at present. Research shows that wavelet transform is not the optimal function representation method in high-dimensional situations. 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 proposition of these methods has laid the foundation for constructing more and more effective fusion methods in the field of image fusion.
Wavelet transform and Contourlet transform are currently two main and commonly used tools for image fusion. Wavelet transform is relatively mature in theory and practical application, has been a common tool for image fusion, but can only obtain information in three directions of horizontal, vertical and diagonal. Contourlet transform can make up for the defect of the limited direction of wavelet transform, and can obtain information in any direction of the image. At the same time, the wavelet transform and the Contourlet transform process images in a similar manner, that is, the image is decomposed into low-frequency and high-frequency parts, and image fusion is performed at low and high frequencies, respectively. Therefore, wavelet transform and Contourlet transform can be used in combination to improve the performance of the image.
The research of image fusion includes not only the algorithm but also the fusion rules. Fusion rules now generally select regional (or windowed) fusion rules. Because the low frequency mainly reflects the energy information of the image, and the high frequency reflects the boundary information of the image, that is, the degree of change. Variance also reflects the overall change between image pixels. Therefore, in this paper, we choose the regional variance to choose the weighted average fusion method in the high frequency part.
2. Wavelet-Contourlet transform
1. Wavelet Transform
In 1989, Mallat introduced the idea of ​​multi-scale analysis in the field of computer vision to wavelet analysis inspired by Burt and Adelson's image decomposition and reconstruction pyramid algorithm (ie, Gauss-Laplace pyramid algorithm) The concept of resolution analysis gives Mallat fast algorithm.
2. Contourlet transform
Because wavelet transform can not well represent the direction information of the image. In 2002, Do and Vetterli proposed the Contourlet transform. Contourlet transform is a multi-resolution, local and directional image representation method. It can provide information in any direction and is a sparse representation of a two-dimensional image. Contourlet transform uses a dual-channel filter bank, which mainly processes images in two steps:
â‘ The Laplacian pyramid (LP) is used to decompose the input image. LP decomposition includes four steps: low-pass filtering, down-sampling, interpolation amplification and band-pass filtering. Continue to perform LP decomposition on the low-frequency sub-bands to obtain low-frequency and a series of high-frequency sub-bands on different scales.
â‘¡ Directivity analysis is performed on the high frequency obtained by LP decomposition using directional filter bank. 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 one coefficient.
The directional filter bank decomposes the image in a tree-like structure and decomposes the frequency domain into subbands, each of which is wedge-shaped. This method first uses the fan filter and the five sampling filters shown in Figure 1 to decompose the input image into horizontal and vertical subbands, and then introduces Shearing resampling operator bands.
3. Wavelet-Contourlet transform
The LP decomposition used in the first stage of the Contourlet transform is redundant, resulting in a 4/3 redundancy of the Contourlet transform. In addition, the decorrelation of LP decomposition is not as good as wavelet transform. To solve the above problems, Eslami R and Radha H proposed wavelet-Contourlet transform. The wavelet-Contourlet transform is composed of two stages of filter banks. The first stage uses wavelet transform to decompose to obtain high-frequency components of the image, thereby reducing the correlation of detailed information of each subspace. Obtain high-frequency subbands in all directions.
Third, select the average fusion algorithm based on variance
The steps of the fusion algorithm given in this paper are as follows:
â‘ Wavelet-Contourlet transform is performed on 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;
â‘¡ The low-frequency part adopts simple weighted average fusion rule.
After the image is transformed by wavelet-contourlet, the low-frequency coefficient mainly concentrates most of the energy of the original image, which determines the overview of the image. In this paper, the weighted average fusion rule is used for low-frequency subband coefficients.
â‘¢ The high frequency part adopts the fusion rule of variance selection weighted average.
After the image is transformed by wavelet-contourlet, the high-frequency coefficients mainly contain the detailed information and edge information of the image. Each high-frequency subband coefficient reflects the directional characteristics.
4. Conclusion
This paper proposes an improved algorithm using weighted average of regional variance selection for high frequency coefficients and weighted average processing for low frequencies. Experiments show that the algorithm in this paper can obtain the details and edge information of images more conveniently. According to the experimental data, the deviation and cross entropy of wavelet-Contourlet transform are lower than those of wavelet transform and Contourlet transform.
Therefore, under the same fusion rule, the image fusion algorithm based on wavelet-Contourlet transform regional variance selection weighted average can obtain more ideal results than wavelet transform and Contourlet transform fusion algorithm.
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