带通滤波器的旋转角度不能超过90度 [英] Band-pass filter can't rotate more than 90 degrees

问题描述

我正在尝试实现以下FFT过滤器内核:

I was trying to implement the following FFT filter kernel:

^{该公式在sqrt下缺少两个正方形.}

源代码

Source code

public partial class Form1 : Form
{
    public Form1()
    {
        InitializeComponent();

        Bitmap image = DataConverter2d.ReadGray(StandardImage.LenaGray);
        Array2d<double> dImage = DataConverter2d.ToDouble(image);            

        int newWidth = Tools.ToNextPowerOfTwo(dImage.Width) * 2;
        int newHeight = Tools.ToNextPowerOfTwo(dImage.Height) * 2;

        double n = 6;
        double f0 = 0.5;
        double theta = 60;
        double a = 0.4;

        Array2d<Complex> kernel2d = CustomFft(newWidth, newHeight, n, f0, theta, a);

        dImage.PadTo(newWidth, newHeight);
        Array2d<Complex> cImage = DataConverter2d.ToComplex(dImage);
        Array2d<Complex> fImage = FourierTransform.ForwardFft(cImage);

        // FFT convolution .................................................
        Array2d<Complex> fOutput = new Array2d<Complex>(newWidth, newHeight);
        for (int x = 0; x < newWidth; x++)
        {
            for (int y = 0; y < newHeight; y++)
            {
                fOutput[x, y] = fImage[x, y] * kernel2d[x, y];
            }
        }

        Array2d<Complex> cOutput = FourierTransform.InverseFft(fOutput);
        Array2d<double> dOutput = Rescale2d.Rescale(DataConverter2d.ToDouble(cOutput));

        dOutput.CropBy((newWidth - image.Width) / 2, (newHeight - image.Height) / 2);

        Bitmap output = DataConverter2d.ToBitmap(dOutput, image.PixelFormat);

        Array2d<Complex> cKernel = FourierTransform.InverseFft(kernel2d);
        cKernel = FourierTransform.RemoveFFTShift(cKernel);
        Array2d<double> dKernel = DataConverter2d.ToDouble(cKernel);
        Array2d<double> dLimitedKernel = Rescale2d.Limit(dKernel);

        Bitmap kernel = DataConverter2d.ToBitmap(dLimitedKernel, image.PixelFormat);

        pictureBox1.Image = image;
        pictureBox2.Image = kernel;
        pictureBox3.Image = output;
    }

    private double Basic(double u, double v, double n, double f0, double rad, double a, double b)
    {
        double ua = u + f0 * Math.Cos(rad);
        double va = v + f0 * Math.Sin(rad);

        double ut = ua * Math.Cos(rad) + va * Math.Sin(rad);
        double vt = (-1) * ua * Math.Sin(rad) + va * Math.Cos(rad);

        double p = ut/a;
        double q = vt/b;

        double sqrt = Math.Sqrt(p*p + q*q);

        return 1.0 / (1.0+ 0.414 * Math.Pow(sqrt, 2*n));
    }

    private double Custom(double u, double v, double n, double f0, double theta, double a)
    {
        double rad1 = (Math.PI / 180) * (90-theta);
        double rad2 = rad1 + Math.PI;
        double b = (a / 5.0) / (2*n);

        double ka = Basic(u, v, n, f0, rad1, a, b);
        double kb = Basic(u, v, n, f0, rad2, a, b);

        return Math.Max(ka, kb);
    }

    private Array2d<Complex> CustomFft(double sizeX, double sizeY, double n, double f0, double theta, double a)
    {
        double halfX = sizeX / 2;
        double halfY = sizeY / 2;

        Array2d<Complex> kernel = new Array2d<Complex>((int)sizeX, (int)sizeY);

        for (double y = 0; y < sizeY; y++)
        {
            double v = y / sizeY;

            for (double x = 0; x < sizeX; x++)
            {
                double u = x / sizeX;

                double kw = Custom(u, v, n, f0, theta, a);

                kernel[(int)x, (int)y] = new Complex(kw, 0);
            }
        }

        return kernel;
    }
}

^{这时仅关注算法和公式.}

输出

Output

此滤镜的问题在于，它只能在0-90度之间旋转，并且不能在该范围之外工作.

The problem with this filter is, it can only rotate between 0-90 degrees, and doesn't work outside that range.

如何使其旋转0-360度之间的任意角度?

推荐答案

使用无损变换旋转90、180和270，然后将其用于其余的旋转.

Rotate 90, 180, and 270 using lossless transforms and then use this for the remainder of the rotate.

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