Remote sensing image fusion

^{[16]}^{[17]} is a multi-level and multi-layer processing process for multiple sensor images to improve image resolution, enhance target features, and improve classification accuracy. It is an important means to improve the applicability of remote sensing images. This dataset uses the Nearest Neighbor Diffusion pan-sharpening method to complete the fusion of full-color and multi-spectral data of GF-1 and GF-2 satellite images. Compared with Brovey Transform, Brovey, Principal Component Analysis, Gram-Schmidt and other methods, the PanSharpening method can better preserve color, texture and spectral characteristics of multi-spectral images and by reflecting the mean, standard deviation, average gradient, and carry out quantitative evaluation of image quality by reflecting the mean value, standard deviation, average gradient, spectral quality deviation index, correlation coefficient and cross entropy of image information.

(1) Mean value (*μ*)

The arithmetic mean value of all the image pixel gradation reflects the average reflectivity of the features in the image. Where *F(i,j)* is the gray-scale value of the fused image F at the pixel point (*i*,*j*), and *M* and *N* are the sizes of the image F. The higher the average, the higher the overall brightness of the image.

*μ* =\(\frac{1}{M×N}\sum _{i=1}^{M}\sum _{j=1}^{N}F\left(i,j\right)\) (5)

(2) Standard deviation (*std*)

The standard deviation is obtained indirectly from the mean value, which indicates the dispersion degree the image gray-scale pixel value and the average value. Where *F(i,j)* is the gray-scale value of the fused image F at the pixel point (*i*,*j*), and *M* and *N* are the sizes of the image F; \(\mu \mathrm{i}\mathrm{s}\mathrm{ }\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{ }\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{y}-\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{ }\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\). The larger the standard deviation , the farther the gradation dispersion, the larger the contrast of the image, and the better the visual effect.

*std* =\(\sqrt{\frac{1}{M×N}\sum _{i=1}^{M}\sum _{j=1}^{N}\left(F\left(i,j\right)-\mu }\right)\) (6)

(3) Average gradient (*g*)

The average gradient reflects the average grayscale change rate of the image, i.e. the sharpness. *F(i,j)* is the gray-scale value of the fused image F at the pixel *(i,j)*, and M and N are the sizes of the image F; their values represent the small detail contrast and the texture change feature in the fused image. In the fused image, the larger the average gradient, the higher the image sharpness.

*g=*\(\frac{1}{M×N}\sum _{i=1}^{M}\sum _{j=1}^{N}\sqrt{\frac{\left(\left(\frac{\partial F\left(i,j\right)}{\partial i}\right)²+\left(\frac{\partial F\left(i,j\right)}{\partial j}\right)²\right)}{2}}\) (7)

(4) Deviation index (*dc*)

The spectral distortion directly reflects the degree of distortion of the fused image to the original spectral image. The value indicates the difference and matching degree of pixel gray value between the fused image and the original multi-spectral image. Where *F(i,j)* is the gray-scale value of the fused image F at the pixel point *(i,j)*, and M and N are the sizes of the image F; *A(i,j)* represents the gray-scale value of the original multi-spectral image at the pixel point; the larger the deviation index, the more the image distortion.

*dc=*\(\frac{1}{M×N}\sum _{i=1}^{M}\sum _{j=1}^{N}\frac{|F\left(i,j\right)-\mathrm{A}\left(i,j\right)|}{\mathrm{A}\left(i,j\right)}\) (8)

(5) Correlation coefficient (*cc*)

The correlation coefficient reflects the correlation degree of the spectral features between the fused image and the source image, and the ability to maintain the spectral information of the fused image. Where *F(i,j)* is the gray-scale value of the fused image F at the pixel point *(i,j)*, and M and N are the sizes of the image F; *A(i,j)* represents the gray-scale value of the original multi-spectral image at the pixel point as well as the gray-scale values that represent the fused image and the source image respectively. \(\mu F\mu A\) The larger the correlation coefficient, the more information the fused image gets from the source image, and the better the fusion effect.

*cc=*\(\frac{\sum _{i=1}^{M}\sum _{j=1}^{N}\left(F\left(i,j\right)-\mu F\right)\left(A\left(i,j\right)-\mu A\right)}{\sum _{i=1}^{M}\sum _{j=1}^{N}\left(F\left(i,j\right)-\mu F\right)²\left(A\left(i,j\right)-\mu A\right)²}\) (9)

(6) Image information volume

* ()*The entropy value of the image reflects the richness of the image information. The cross entropy (

*ce*) is used to measure the difference in the gray distribution of the two images A and F. For a single image, the gray-scale value of each pixel is independent of each other, then the image gray distribution

*P*=｛

*P*_{0}*,P*_{1}*,…P*_{i}*,…P*_{n} ｝;

*P*_{i} represents the probability that the image pixel gray value

*i*, i.e. the ratio of the pixel with the gray value

* i* to the total pixel of the image.

*l* is the total gray level of the image, and

,

indicates the probability that the gray level of the two image pixels is

*i*. The smaller the cross entropy, the smaller the difference between the gray-scale distribution of the fused image and the source image, that is, the more source image information the fused image contains, the better the fusion effect.

(10)