FFT卷积- 3x3核

Question

我编写了一些例程来使用3x3内核来锐化灰度图像，

-1 -1 -1 
-1  9 -1 
-1 -1 -1

以下代码在非FFT(空域)卷积的情况下工作良好，但不工作于基于FFT的(频域)卷积。。

输出图像似乎模糊了。

我有几个问题：

(1)此例程无法生成所需的结果。它还冻结了应用程序。

    public static Bitmap ApplyWithPadding(Bitmap image, Bitmap mask)
    {
        if(image.PixelFormat == PixelFormat.Format8bppIndexed)
        {
            Bitmap imageClone = (Bitmap)image.Clone();
            Bitmap maskClone = (Bitmap)mask.Clone();

            /////////////////////////////////////////////////////////////////
            Complex[,] cPaddedLena = ImageDataConverter.ToComplex(imageClone);
            Complex[,] cPaddedMask = ImageDataConverter.ToComplex(maskClone);

            Complex[,] cConvolved = Convolution.Convolve(cPaddedLena, cPaddedMask);

            return ImageDataConverter.ToBitmap(cConvolved);
        }
        else
        {
            throw new Exception("not a grascale");
        }
    }

(2)这个例程取得了很好的效果。但是，太慢了。

    public static Bitmap Apply(Bitmap sourceBitmap)
    {
        Sharpen filter = new Sharpen();

        BitmapData sourceData = sourceBitmap.LockBits(new Rectangle(0, 0,
                                 sourceBitmap.Width, sourceBitmap.Height),
                                 ImageLockMode.ReadOnly, PixelFormat.Format32bppArgb);

        byte[] pixelBuffer = new byte[sourceData.Stride * sourceData.Height];
        byte[] resultBuffer = new byte[sourceData.Stride * sourceData.Height];

        Marshal.Copy(sourceData.Scan0, pixelBuffer, 0, pixelBuffer.Length);

        sourceBitmap.UnlockBits(sourceData);

        double blue = 0.0;
        double green = 0.0;
        double red = 0.0;

        int filterWidth = filter.FilterMatrix.GetLength(1);
        int filterHeight = filter.FilterMatrix.GetLength(0);

        int filterOffset = (filterWidth - 1) / 2;
        int calcOffset = 0;

        int byteOffset = 0;

        for (int offsetY = filterOffset; offsetY < sourceBitmap.Height - filterOffset; offsetY++)
        {
            for (int offsetX = filterOffset; offsetX <
                sourceBitmap.Width - filterOffset; offsetX++)
            {
                blue = 0;
                green = 0;
                red = 0;

                byteOffset = offsetY *
                             sourceData.Stride +
                             offsetX * 4;

                for (int filterY = -filterOffset;
                    filterY <= filterOffset; filterY++)
                {
                    for (int filterX = -filterOffset;
                        filterX <= filterOffset; filterX++)
                    {

                        calcOffset = byteOffset +
                                     (filterX * 4) +
                                     (filterY * sourceData.Stride);

                        blue += (double)(pixelBuffer[calcOffset]) *
                                filter.FilterMatrix[filterY + filterOffset,
                                                    filterX + filterOffset];

                        green += (double)(pixelBuffer[calcOffset + 1]) *
                                 filter.FilterMatrix[filterY + filterOffset,
                                                    filterX + filterOffset];

                        red += (double)(pixelBuffer[calcOffset + 2]) *
                               filter.FilterMatrix[filterY + filterOffset,
                                                  filterX + filterOffset];
                    }
                }

                blue = filter.Factor * blue + filter.Bias;
                green = filter.Factor * green + filter.Bias;
                red = filter.Factor * red + filter.Bias;

                if (blue > 255)
                { blue = 255; }
                else if (blue < 0)
                { blue = 0; }

                if (green > 255)
                { green = 255; }
                else if (green < 0)
                { green = 0; }

                if (red > 255)
                { red = 255; }
                else if (red < 0)
                { red = 0; }

                resultBuffer[byteOffset] = (byte)(blue);
                resultBuffer[byteOffset + 1] = (byte)(green);
                resultBuffer[byteOffset + 2] = (byte)(red);
                resultBuffer[byteOffset + 3] = 255;
            }
        }

        Bitmap resultBitmap = new Bitmap(sourceBitmap.Width, sourceBitmap.Height);

        BitmapData resultData = resultBitmap.LockBits(new Rectangle(0, 0,
                                 resultBitmap.Width, resultBitmap.Height),
                                 ImageLockMode.WriteOnly, PixelFormat.Format32bppArgb);

        Marshal.Copy(resultBuffer, 0, resultData.Scan0, resultBuffer.Length);
        resultBitmap.UnlockBits(resultData);

        return resultBitmap;
    }

(3)下面是我的GUI代码。如果我使用图像作为掩码，SharpenFilter.ApplyWithPadding()就能正常工作。但是，如果我使用3x3内核，则无法工作。

    string path = @"E:\lena.png";
    string path2 = @"E:\mask.png";

    Bitmap _inputImage;
    Bitmap _maskImage;

    private void LoadImages_Click(object sender, EventArgs e)
    {
        _inputImage = Grayscale.ToGrayscale(Bitmap.FromFile(path) as Bitmap);

        /*
        _maskImage = Grayscale.ToGrayscale(Bitmap.FromFile(path2) as Bitmap);
        */

        SharpenFilter filter = new SharpenFilter();
        double[,] mask = new double[,]  { { -1, -1, -1, }, 
                                        { -1,  9, -1, }, 
                                        { -1, -1, -1, }, };
        _maskImage = ImageDataConverter.ToBitmap(mask);

        inputImagePictureBox.Image = _inputImage;
        maskPictureBox.Image = _maskImage;
    }

    Bitmap _paddedImage;
    Bitmap _paddedMask;
    private void padButton_Click(object sender, EventArgs e)
    {
        Bitmap lena = Grayscale.ToGrayscale(_inputImage);
        Bitmap mask = Grayscale.ToGrayscale(_maskImage);

        ////Not working...
        //int maxWidth = (int)Math.Max(lena.Width, mask.Width);
        //int maxHeight = (int)Math.Max(lena.Height, mask.Height);

        ////This is working correctly in case if I use a png image as a mask.
        int maxWidth = (int)Tools.ToNextPow2(Convert.ToUInt32(lena.Width + mask.Width));
        int maxHeight = (int)Tools.ToNextPow2(Convert.ToUInt32(lena.Height + mask.Height));

        _paddedImage = ImagePadder.Pad(lena, maxWidth, maxHeight);
        _paddedMask = ImagePadder.Pad(mask, maxWidth, maxHeight);

        paddedImagePictureBox.Image = _paddedImage;
        paddedMaskPictureBox.Image = _paddedMask;
    }

    private void filterButton_Click(object sender, EventArgs e)
    {
        // Not working properly.
        // Freezes the application. 
        Bitmap sharp = SharpenFilter.ApplyWithPadding(_paddedImage, _paddedMask);

        ////Works well. But, very slow.
        //Bitmap sharp = SharpenFilter.Apply(_paddedImage);

        filteredPictureBox.Image = sharp as Bitmap;
    }

输出：

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源代码:

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• 您可以从在这个链接中下载整个解决方案。

Answer 1

主要问题似乎是将内核解释为由无符号字节值组成的图像。因此，将-1值转换为255，有效地计算了与内核的卷积。

255 255 255
255  9  255
255 255 255

这可以立即从“卷积核”图像的白色区域观察到。因此，产生的核心是低通滤波器，产生相应的模糊效应.

可能是处理这一问题的最佳方法，即将内核读入有符号值的矩阵，而不是图像。

如果您仍然喜欢将内核作为映像处理，则需要将图像转换回有符号的值。我认为实现这一结果的最简单方法是创建一个修改过的ImageDataConverter.ToInteger(Bitmap)版本，将字节映射到有符号的值：

public static Complex[,] Unwrap(Bitmap bitmap)
{
  int Width = bitmap.Width;
  int Height = bitmap.Height;

  Complex[,] array2D = new Complex[bitmap.Width, bitmap.Height];
  ...

        else// If there is only one channel:
        {
          iii = (int)(*address);
          if (iii >= 128)
          {
            iii -= 256;
          }
        }
        Complex tempComp = new Complex((double)iii, 0.0);
        array2D[x, y] = tempComp;

然后，您就可以使用以下方法在SharpenFilter.ApplyWithPadding中转换您的图像：

Complex[,] cPaddedMask =  ImageDataConverter.Unwrap(maskClone);

然后，这将给出以下结果：

​

​

虽然这提高了图像的清晰度，但您应该立即注意到，图像比原始图像暗得多。这是由于Convolution.Rescale函数，它根据图像的最小值和最大值动态地重新调整图像的标度。这可以方便地显示图像的最大动态范围，但可能导致一个不同的整体缩放比标准卷积。要实现此标准缩放(基于FFT实现的缩放)，可以使用以下实现：

    //Rescale values between 0 and 255.
    private static void Rescale(Complex[,] convolve)
    {
        int imageWidth = convolve.GetLength(0);
        int imageHeight = convolve.GetLength(1);

        double scale = imageWidth * imageHeight;

        for (int j = 0; j < imageHeight; j++)
        {
            for (int i = 0; i < imageWidth; i++)
            {
                double re = Math.Max(0, Math.Min(convolve[i, j].Real * scale, 255.0));
                double im = Math.Max(0, Math.Min(convolve[i, j].Imaginary * scale, 255.0));
                convolve[i, j] = new Complex(re, im);
            }
        }
    }

这将为您提供一个亮度级别更合适的图像：

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最后，对于滤波操作，通常期望结果与原始图像大小相匹配(不像包含尾部的卷积)。在SharpenFilter.ApplyWithPadding中将结果裁剪为：

...
// -3 terms are due to kernel size
// +5 vertical offset term is due to vertical reflection & offset in SetPixel
Rectangle rect = new Rectangle((cPaddedLena.GetLength(0) / 2 - 3) / 2,
                               (cPaddedLena.GetLength(1) / 2 - 3) / 2 + 5, 
                               cPaddedLena.GetLength(0) / 2,
                               cPaddedLena.GetLength(1) / 2);
return ImageDataConverter.ToBitmap(cConvolved).Clone(rect, PixelFormat.Format8bppIndexed);

应该给你：

​

​

为了更容易地进行视觉比较，这里再次显示了原始图像：

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