%基于PCA變換的圖像融合方法
up=imread（‘D:\MATLABprojects\plane.png‘）;
low=imread（‘D:\MATLABprojects\tree.png‘）;
[MNcolor]=size（up）;
RGB=low;
%把函數類型uint8轉換為double
[up_R]=double（up（::1））;
[up_G]=double（up（::2））;
[up_B]=double（up（::3））;
[low_R]=double（low（::1））;
[low_G]=double（low（::2））;
[low_B]=double（low（::3））;

up_Mx=0;
low_Mx=0;
for?i=1:M
????for?j=1:N
????????up_S=[up_R（ij）up_G（ij）up_B（ij）]‘;%生成由RGB組成的三維列向量
????????up_Mx=up_Mx+up_S;%疊加計算RGB各列向量的總和
????????low_S=[low_R（ij）low_G（ij）low_B（ij）]‘;
????????low_Mx=low_Mx+low_S;
????end
end
up_Mx=up_Mx/（M*N）;%計算三維列向量的平均值
low_Mx=low_Mx/（M*N）;

up_Cx=0;
low_Cx=0;
for?i=1:M
????for?j=1:N
????????up_S=[up_R（ij）up_G（ij）up_B（ij）]‘;%矩陣轉置
????????up_Cx=up_Cx+up_S*up_S‘;
????????low_S=[low_R（ij）low_G（ij）low_B（ij）]‘;
????????low_Cx=low_Cx+low_S*low_S‘;
????end
end
%計算協方差矩陣及特征值
up_Cx=up_Cx/（M*N）-up_Mx*up_Mx‘;%計算協方差矩陣
low_Cx=low_Cx/（M*N）-low_Mx*low_Mx‘;
[up_Aup_latent]=eigs（up_Cx）;%協方差矩陣的特征向量組成的矩陣
[low_Alow_latent]=eigs（low_Cx）;%即PCA變換的系數矩陣，特征值

for?i=1:M
????for?j=1:N
????????up_X=[up_R（ij）up_G（ij）up_B（ij）]‘;
????????up_Y=up_A‘*up_X;%對每個像素點進行PCA正變換
????????up_Y=up_Y‘;
????????up_R（ij）=up_Y（1）;%plane圖像的第三主成分
????????up_G（ij）=up_Y（2）;%plane圖像的第二主成分
????????up_B（ij）=up_Y（3）;%plane圖像的第一主成分
????????low_X=[low_R（ij）low_G（ij）low_B（ij）]‘;
????????low_Y=low_A‘*low_X;
????????low_Y=low_Y‘;
????????low_R（ij）=low_Y（1）;%tree圖像的第三主成分
????????low_G（ij）=low_Y（2）;%tree圖像的第二主成分
????????low_B（ij）=low_Y（3）;%tree圖像的第一主成分
?
????end
end
figure;
subplot（311）;imshow（uint8（up_R））;title（‘plane圖像的第三主成分‘）;
subplot（312）;imshow（uint8（up_G））;title（‘plane圖像的第二主成分‘）;
subplot（313）;imshow（uint8（up_B））;title（‘plane圖像的第一主成分‘）;
figure;
subplot（311）;imshow（uint8（low_R））;title（‘tree圖像的第三主成分‘）;
subplot（312）;imshow（uint8（low_G））;title（‘tree圖像的第二主成分‘）;
subplot（313）;imshow（uint8（low_B））;title（‘tree圖像的第一主成分‘）;

for?i=1:M
????for?j=1:N
????????up_Y=[up_R（ij）up_G（ij）up_B（ij）]‘;
????????up_X=up_A*up_Y;%對每個像素點進行PCA反變換
????????up_X=up_X‘;
????????up_r（ij）=up_X（1）;
????????up_g（ij）=up_X（2）;
????????up_b（ij）=up_X（3）;
????????low_Y=[low_R（ij）low_G（ij）up_B（ij）]‘;%用plane圖像的第一主成分替換
????????low_X=low_A*low_Y;
????????low_X=low_X‘;
????????low_r（ij）=low_X（1）;
????????low_g（ij）=low_X（2）;
????????low_b（ij）=low_X（3）;
?
????end
end
for?i=1:M
????for?j=1:N
????????RGB（ij1）=round（low_r（ij））;
????????RGB（ij2）=round（low_g（ij））;
????????RGB（ij3）=round（low_b（ij））;
????end
end

figure;
subplot（311）;imshow（up）;
subplot（312）;imshow（low）;
subplot（313）;imshow（uint8（RGB））;title（‘融合后圖像‘）;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2020-06-16?10:55??新建文件夾?（2）\images\
?????文件???????23329??2007-01-07?19:04??新建文件夾?（2）\images\clock1.bmp
?????文件???????26535??2007-01-07?19:04??新建文件夾?（2）\images\clock2.bmp
?????文件???????17263??2004-06-13?15:46??新建文件夾?（2）\images\high.jpg
?????文件???????12150??2004-06-13?15:47??新建文件夾?（2）\images\low.jpg
?????文件????????2887??2020-05-04?19:40??新建文件夾?（2）\PCA_2.m
?????文件????????2791??2020-05-04?18:13??新建文件夾?（2）\PCA_ronghe.m
?????文件???????83485??2020-05-04?16:13??新建文件夾?（2）\plane.png
?????文件????????2804??2020-05-04?19:17??新建文件夾?（2）\ronghe1.m
?????文件????????1117??2020-05-04?21:14??新建文件夾?（2）\ronghe2.m
?????文件??????670977??2020-05-04?15:58??新建文件夾?（2）\tree.png