我正在用 FFT 滤波器（内核大小 = 10）对图像（512*512）进行卷积，看起来不错。
但是当我将它与我以正常方式进行复杂处理的图像进行比较时，结果是可怕的。
PSNR 约为 35。
67,187/262,144 像素值相差 1 或更多（峰值约为 8）（最大像素值为 255）。
我的问题是，在频率空间中进行卷积时是否正常，或者我的卷积/变换函数可能存在问题？. 因为奇怪的是，当我使用 double 作为数据类型时，我应该得到更好的结果。但它完全一样。
当我将图像转换为频率空间时，不要对其进行卷积，然后将其转换回来就可以了，使用浮点数时 PSNR 约为 140。
此外，由于像素差异只有 1-10，我想我可以排除缩放错误
编辑：无聊感兴趣的人的更多详细信息
我使用开源的 KissFFT 库。使用真正的二维输入 (kiss_fftndr.h)
我的图像数据类型是 PixelMatrix。简单的 alpha、red、green 和 blue 值从 0.0 到 1.0 float 的矩阵
我的内核也是一个 PixelMatrix。
这是卷积函数的一些片段
使用的数据类型：
#define kiss_fft_scalar float
#define kiss_fft_cpx struct {
kiss_fft_scalar r;
kiss_fft_scalar i,
}
FFT的配置：
//parameters to kiss_fftndr_alloc:
//1st param = array with the size of the 2 dimensions (in my case dim={width, height})
//2nd param = count of the dimensions (in my case 2)
//3rd param = 0 or 1 (forward or inverse FFT)
//4th and 5th params are not relevant
kiss_fftndr_cfg stf = kiss_fftndr_alloc(dim, 2, 0, 0, 0);
kiss_fftndr_cfg sti = kiss_fftndr_alloc(dim, 2, 1, 0, 0);
填充和转换内核：
I make a new array:
kiss_fft_scalar kernel[width*height];
I fill it with 0 in a loop.
Then I fill the middle of this array with the kernel I want to use.
So if I would use a 2*2 kernel with values 1/4, 1/4, 1/4 and 1/4 it would look like
0 0 0 0 0 0
0 1/4 1/4 0
0 1/4 1/4 0
0 0 0 0 0 0
The zeros are padded until they reach the size of the image.
Then I swap the quadrants of the image diagonally. It looks like:
1/4 0 0 1/4
0 0 0 0
0 0 0 0
1/4 0 0 1/4
now I transform it: kiss_fftndr(stf, floatKernel, outkernel);
outkernel is declarated as
kiss_fft_cpx outkernel= new kiss_fft_cpx[width*height]
将颜色放入数组：
kiss_fft_scalar *red = new kiss_fft_scalar[width*height];
kiss_fft_scalar *green = new kiss_fft_scalar[width*height];
kiss_fft-scalar *blue = new kiss_fft_scalar[width*height];
for(int i=0; i<height; i++) {
for(int j=0; i<width; j++) {
red[i*height+j] = input.get(j,i).getRed(); //input is the input image pixel matrix
green[i*height+j] = input.get(j,i).getGreen();
blue{i*height+j] = input.get(j,i).getBlue();
}
}
Then I transform the arrays:
kiss_fftndr(stf, red, outred);
kiss_fftndr(stf, green, outgreen);
kiss_fftndr(stf, blue, outblue); //the out-arrays are type kiss_fft_cpx*
卷积：
我们现在拥有的：
- 3个来自kiss_fft_cpx类型的转换颜色数组*
- 1个来自kiss_fft_cpx类型的转换内核数组*
它们都是复杂的数组
现在是卷积：
for(int m=0; m<til; m++) {
for(int n=0; n<til; n++) {
kiss_fft_scalar real = outcolor[m*til+n].r; //I do that for all 3 arrys in my code!
kiss_fft_scalar imag = outcolor[m*til+n].i; //so I have realred, realgreen, realblue
kiss_fft_scalar realMask = outkernel[m*til+n].r; // and imagred, imaggreen, etc.
kiss_fft_scalar imagMask = outkernel[m*til+n].i;
outcolor[m*til+n].r = real * realMask - imag * imagMask; //Same thing here in my code i
outcolor[m*til+n].i = real * imagMask + imag * realMask; //do it with all 3 colors
}
}
现在我将它们转换回来：
kiss_fftndri(sti, outred, red);
kiss_fftndri(sti, outgreen, green);
kiss_fftndri(sti, outblue, blue);
and I create a new Pixel Matrix with the values from the color-arrays
PixelMatrix output;
for(int i=0; i<height; i++) {
for(int j=0; j<width; j++) {
Pixel p = new Pixel();
p.setRed( red[i*height+j] / (width*height) ); //I divide through (width*height) because of the scaling happening in the FFT;
p.setGreen( green[i*height+j] );
p.setBlue( blue[i*height+j] );
output.set(j , i , p);
}
}
笔记：
- 我已经提前注意图像的大小为 2 (256*256)、(512*512) 等的幂。
例子：
内核大小：10
输入：
输出：
正常卷积的输出：
我的控制台说：
142519 out of 262144 Pixels have a difference of 1 or more (maxRGB = 255)
PSNR: 32.006027221679688
MSE: 44.116752624511719
虽然在我看来它们看起来是一样的°.°
也许一个人很无聊，并通过代码。不是很紧急，但这是一种问题我只是想知道我到底做错了什么^^
最后但并非最不重要的一点是我的 PSNR 功能，虽然我并不认为这是问题所在：D
void calculateThePSNR(const PixelMatrix first, const PixelMatrix second, float* avgpsnr, float* avgmse) {
int height = first.getHeight();
int width = first.getWidth();
BMP firstOutput;
BMP secondOutput;
firstOutput.SetSize(width, height);
secondOutput.SetSize(width, height);
double rsum=0.0, gsum=0.0, bsum=0.0;
int count = 0;
int total = 0;
for(int i=0; i<height; i++) {
for(int j=0; j<width; j++) {
Pixel pixOne = first.get(j,i);
Pixel pixTwo = second.get(j,i);
double redOne = pixOne.getRed()*255;
double greenOne = pixOne.getGreen()*255;
double blueOne = pixOne.getBlue()*255;
double redTwo = pixTwo.getRed()*255;
double greenTwo = pixTwo.getGreen()*255;
double blueTwo = pixTwo.getBlue()*255;
firstOutput(j,i)->Red = redOne;
firstOutput(j,i)->Green = greenOne;
firstOutput(j,i)->Blue = blueOne;
secondOutput(j,i)->Red = redTwo;
secondOutput(j,i)->Green = greenTwo;
secondOutput(j,i)->Blue = blueTwo;
if((redOne-redTwo) > 1.0 || (redOne-redTwo) < -1.0) {
count++;
}
total++;
rsum += (redOne - redTwo) * (redOne - redTwo);
gsum += (greenOne - greenTwo) * (greenOne - greenTwo);
bsum += (blueOne - blueTwo) * (blueOne - blueTwo);
}
}
fprintf(stderr, "%d out of %d Pixels have a difference of 1 or more (maxRGB = 255)", count, total);
double rmse = rsum/(height*width);
double gmse = gsum/(height*width);
double bmse = bsum/(height*width);
double rpsnr = 20 * log10(255/sqrt(rmse));
double gpsnr = 20 * log10(255/sqrt(gmse));
double bpsnr = 20 * log10(255/sqrt(bmse));
firstOutput.WriteToFile("test.bmp");
secondOutput.WriteToFile("test2.bmp");
system("display test.bmp");
system("display test2.bmp");
*avgmse = (rmse + gmse + bmse)/3;
*avgpsnr = (rpsnr + gpsnr + bpsnr)/3;
}