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Convolution of Bitmaps

, 29 Mar 2006
Article discussing how to convolve images, specificially the convolution of bitmaps.
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Introduction

Image convolution, plays an important role in computer graphics applications. Convolution of images allows for image alterations that enable the creation of new images from old ones. Convolution also allows for important features, such as edge detection, with many widespread uses. The convolution of an image is a simple process by which the pixel of an image is multiplied by a kernel or masked to create a new pixel value. Convolution is commonly referred to as filtering.

Details

First, for a given pixel (x,y), we give a weight to each of the surrounding pixels. It may be thought of as giving a number telling how important the pixel is to us. The number may be any integer or floating point number, though I usually stick to floating point since floats will accept integers as well. The kernel or mask, that contains the filter may actually be any size (3x3, 5x5, 7x7), however 3x3 is very common. Since the process for each is the same, I will concentrate only on the 3x3 kernels.

Second, the actual process of convolution involves getting each pixel near a given pixel (x,y), and multiplying each of the pixel's channels by the weighted kernel value. This means that for a 3x3 kernel, we would multiply the pixels like so:

(x-1,y-1)       *       kernel_value[row0][col0] (x  ,y-1)       *       kernel_value[row0][col1] (x+1,y-1)       *       kernel_value[row0][col2] (x-1,y  )       *       kernel_value[row1][col0] (x  ,y  )       *       kernel_value[row1][col1] (x+1,y  )       *       kernel_value[row1][col2] (x-1,y+1)       *       kernel_value[row2][col0] (x  ,y+1)       *       kernel_value[row2][col1] (x+1,y+1)       *       kernel_value[row2][col2]

The process is repeated for each channel of the image. This means that the red, green and blue color channels (if working in RGB colorspace) must each be multiplied by the kernel values. The kernel position is related to the pixel position it is multiplied by. Simply put, the kernel is allocated in kernel[rows][cols] which would be kernel[3][3] in this case. The 3x3 (5x5 or 7x7 if using a larger kernel) area around pixel (x,y) is then multiplied by the kernel to get the total sum. If we were working with a 100x100 image, allocated as image[100][100], and we wanted the value for pixel (10,10), the process for each channel would look like:

float fTotalSum = Pixel(10-1,10-1)       *       kernel_value[row0][col0] + Pixel(10  ,10-1)       *       kernel_value[row0][col1] + Pixel(10+1,10-1)       *       kernel_value[row0][col2] + Pixel(10-1,10  )       *       kernel_value[row1][col0] + Pixel(10  ,10  )       *       kernel_value[row1][col1] + Pixel(10+1,10  )       *       kernel_value[row1][col2] + Pixel(10-1,10+1)       *       kernel_value[row2][col0] + Pixel(10  ,10+1)       *       kernel_value[row2][col1] + Pixel(10+1,10+1)       *       kernel_value[row2][col2] +

Finally, each value is added to the total sum, which is then divided by the total weight of the kernel. The kernel's weight is given by adding each value contained in the kernel. If the value is zero or less, then a weight of 1 is given to avoid a division by zero.

The actual code to convolve an image is:

for (int i=0; i <= 2; i++)//loop through rows {     for (int j=0; j <= 2; j++)//loop through columns     {         //get pixel near source pixel         /*         if x,y is source pixel then we loop through and         get pixels at coordinates:         x-1,y-1         x-1,y         x-1,y+1         x,y-1         x,y         x,y+1         x+1,y-1         x+1,y         x+1,y+1         */         COLORREF tmpPixel = pDC->GetPixel(sourcex+(i-(2>>1)),                                               sourcey+(j-(2>>1)));         //get kernel value         float fKernel = kernel[i][j];         //multiply each channel by kernel value, and add to sum         //notice how each channel is treated separately         rSum += (GetRValue(tmpPixel)*fKernel);         gSum += (GetGValue(tmpPixel)*fKernel);         bSum += (GetBValue(tmpPixel)*fKernel);         //add the kernel value to the kernel sum         kSum += fKernel;     } } //if kernel sum is less than 0, reset to 1 to avoid divide by zero if (kSum <= 0)     kSum = 1; //divide each channel by kernel sum rSum/=kSum; gSum/=kSum; bSum/=kSum;

The source code included performs some common image convolutions. Also included is a Convolve Image menu option that allows users to enter their own kernel. Common 3x3 kernels include:

gaussianBlur[3][3] = {0.045, 0.122, 0.045, 0.122,    0.332, 0.122, 0.045, 0.122, 0.045}; gaussianBlur2[3][3] = {1, 2, 1, 2, 4, 2, 1, 2, 1}; gaussianBlur3[3][3] = {0, 1, 0, 1, 1, 1, 0, 1, 0}; unsharpen[3][3] = {-1, -1, -1, -1, 9, -1, -1, -1, -1}; sharpness[3][3] = {0,-1,0,-1,5,-1,0,-1,0}; sharpen[3][3] = {-1, -1, -1, -1, 16, -1, -1, -1, -1}; edgeDetect[3][3] = {-0.125, -0.125, -0.125, -0.125,    1, -0.125, -0.125, -0.125, -0.125}; edgeDetect2[3][3] = {-1, -1, -1, -1, 8, -1, -1, -1, -1}; edgeDetect3[3][3] = {-5, 0, 0, 0, 0, 0, 0, 0, 5}; edgeDetect4[3][3] = {-1, -1, -1, 0, 0, 0, 1, 1, 1}; edgeDetect5[3][3] = {-1, -1, -1, 2, 2, 2, -1, -1, -1}; edgeDetect6[3][3] = {-5, -5, -5, -5, 39, -5, -5, -5, -5}; sobelHorizontal[3][3] = {1, 2, 1, 0, 0, 0, -1, -2, -1 }; sobelVertical[3][3] = {1, 0, -1, 2, 0, -2, 1, 0, -1 }; previtHorizontal[3][3] = {1, 1, 1, 0, 0, 0, -1, -1, -1 }; previtVertical[3][3] = {1, 0, -1, 1, 0, -1, 1, 0, -1}; boxBlur[3][3] = {0.111f, 0.111f, 0.111f, 0.111f,    0.111f, 0.111f, 0.111f, 0.111f, 0.111f}; triangleBlur[3][3] = { 0.0625, 0.125, 0.0625,    0.125, 0.25, 0.125, 0.0625, 0.125, 0.0625};

Last but not least is the ability to show a convoluted image as a grayscale result. In order to display a filtered image as grayscale, we just add a couple lines to the bottom of the Convolve function:

//return new pixel value     if (bGrayscale)     {         int grayscale=0.299*rSum + 0.587*gSum + 0.114*bSum;         rSum=grayscale;         gSum=grayscale;         bSum=grayscale;     }      clrReturn = RGB(rSum,gSum,bSum);

This means that the entire Convolve function now looks like:

COLORREF CImageConvolutionView::Convolve(CDC* pDC, int sourcex,      int sourcey, float kernel[3][3], int nBias,BOOL bGrayscale) {     float rSum = 0, gSum = 0, bSum = 0, kSum = 0;     COLORREF clrReturn = RGB(0,0,0);     for (int i=0; i <= 2; i++)//loop through rows     {         for (int j=0; j <= 2; j++)//loop through columns         {             //get pixel near source pixel             /*             if x,y is source pixel then we loop              through and get pixels at coordinates:             x-1,y-1             x-1,y             x-1,y+1             x,y-1             x,y             x,y+1             x+1,y-1             x+1,y             x+1,y+1             */             COLORREF tmpPixel = pDC->GetPixel(sourcex+(i-(2>>1)),                 sourcey+(j-(2>>1)));             //get kernel value             float fKernel = kernel[i][j];             //multiply each channel by kernel value, and add to sum             //notice how each channel is treated separately             rSum += (GetRValue(tmpPixel)*fKernel);             gSum += (GetGValue(tmpPixel)*fKernel);             bSum += (GetBValue(tmpPixel)*fKernel);             //add the kernel value to the kernel sum             kSum += fKernel;         }     }     //if kernel sum is less than 0, reset to 1 to avoid divide by zero     if (kSum <= 0)         kSum = 1;     //divide each channel by kernel sum     rSum/=kSum;     gSum/=kSum;     bSum/=kSum;     //add bias if desired     rSum += nBias;     gSum += nBias;     bSum += nBias;     //prevent channel overflow by clamping to 0..255     if (rSum > 255)         rSum = 255;     else if (rSum < 0)         rSum = 0;     if (gSum > 255)         gSum = 255;     else if (gSum < 0)         gSum = 0;     if (bSum > 255)         bSum = 255;     else if (bSum < 0)         bSum = 0;     //return new pixel value     if (bGrayscale)     {         int grayscale=0.299*rSum + 0.587*gSum + 0.114*bSum;         rSum=grayscale;         gSum=grayscale;         bSum=grayscale;     }      clrReturn = RGB(rSum,gSum,bSum);     return clrReturn; }

Last but not least I did a little tweaking to get the program to load a default image from a resource (IDB_BITMAP1). Then I added the ability to convolve this default image. The program will still load image from a file, the only difference is that it will now show a default image at startup.

Please note that this article is by no means, an example of fast processing of pixels. It is merely meant to show how convolution CAN be done on images. If you would like a more advanced image processor, then feel free to email me with the subject "WANT CODE:ImageEdit Please". That is an unreleased image processor I have done, though parts are not implemented yet due to lack of time, that contains much more functionality using CxImage library as its basis for reading and saving images.

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