Firstly, the source image was decomposed by wavelet, the low-frequency component was weighted and averaged, the high-frequency component was segmented by fuzzy C-means clustering algorithm, and the regions were fused based on SSIM value. Finally, the fused image was obtained by inverse wavelet transform.
Wavelet refers to a wave whose energy is very concentrated in the time domain, its energy is limited, all concentrated near a point, and the value of the integral is zero, which means that it is an orthogonal wave like Fourier wave.
The Fourier transform of an image is the decomposition of the image signal into sinusoidal waves of various frequencies. Similarly, wavelet transform is to decompose the image signal into a group of wavelets after the original wavelet displacement and scaling. Wavelet is called image microscope in image processing because of its multi-resolution decomposition ability to decompose image information layer by layer. The stripping is done through low-pass and high-pass filters.
The wavelet transform can be understood in conjunction with the Fourier transform. The Fourier transform is a series of sines and cosines of different frequencies that decompose the original function, and the result is the coefficients of the original function at different frequencies of sines and cosines. Wavelet transform uses a series of wavelet of different scale to decompose the original function, and the coefficients of the original function under different scale wavelet are obtained after the transformation. Different wavelets are decomposed by translation and scaling. The translation is to get the time characteristic of the original function, and the scaling is to get the frequency characteristic of the original function.
Steps of wavelet transform:
1. Compare the wavelet w(t) with the beginning part of the original function F (t) and calculate the coefficient C. The coefficient C represents the similarity between the partial function and wavelet.
2. Move the wavelet to the right by k units to obtain the wavelet W (t-k), repeat 1. Repeat this step until the end of function f.
3. Expand wavelet w(t) to obtain wavelet w(t/2). Repeat step 1,2.
4. Expand wavelets, repeat 1,2,3.
Haar wavelet:
The Haar wavelet I use here, the scale function is [1 1] and the wavelet function is [1-1]. It’s the simplest wavelet.
Image two-dimensional discrete wavelet transform:
The two-dimensional discrete wavelet decomposition and reconstruction process of the image is shown in the figure below. The decomposition process can be described as follows: First, 1D-DWT is performed on each row of the image to obtain the low frequency component L and high frequency component H of the original image in the horizontal direction. Then 1D-DWT is performed on each column of the transformed data. The low-frequency components LL, LH, HL and HH of the original image in horizontal and vertical directions were obtained.
The reconstruction process can be described as follows: first, the inverse transform of discrete wavelet is carried out for each column of the transformation result, and then the inverse transform of one-dimensional discrete wavelet is carried out for each row of the data obtained by the transformation to obtain the reconstructed image. It can be seen from the above process that image wavelet decomposition is a process of separating signals according to low frequency and directed high frequency. During the decomposition process, further wavelet decomposition can be carried out for the LL component as required until the requirements are met.
For two-dimensional images, Haar transform is no longer filtered from one direction, but low-pass and high-pass filters are carried out from horizontal and vertical directions (horizontal and vertical directions are not affected successively), as shown in the figure: In the figure, A represents the original image, b represents the result of first-order wavelet transform, H1 represents the detail of horizontal reverse, V1 represents the detail of vertical direction, C1 represents the detail of diagonal direction, and B represents the image sampled in the next 2. Figure C shows the continuation of Haar wavelet transform. The actual effect of first-order Haar wavelet transform is shown in Figure 3
clear all; close all; clc; I1=imread('a.tif'); I1=rgb2gray(I1); I2=imread('b.tif'); I2=rgb2gray(I2); F=bbsd_fuse(I1,I2); figure(1) subplot(131) imshow(I1); Subplot (132) imshow(I2); Subplot (133) imshow(F); Title (' after fusion ')Copy the code
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