Implementing sobel edge detection algorithm

Question

New to progamming; trying to implement a sobel edge detection algorithm. I am doing this in a function called edges, as per the code snippet below.

void edges(int height, int width, RGBTRIPLE image[height][width])
{
    // define kernals
    int Gx[3][3];
    Gx[0][0] = -1;
    Gx[0][1] = 0;
    Gx[0][2] = 1;
    Gx[1][0] = -2;
    Gx[1][1] = 0;
    Gx[1][2] = 2;
    Gx[2][0] = -1;
    Gx[2][1] = 0;
    Gx[2][2] = 1;

    int Gy[3][3];
    Gy[0][0] = -1;
    Gy[0][1] = -2;
    Gy[0][2] = -1;
    Gy[1][0] = 0;
    Gy[1][1] = 0;
    Gy[1][2] = 0;
    Gy[2][0] = 1;
    Gy[2][1] = 2;
    Gy[2][2] = 1;

    // define variables
    int Gx_red, Gx_green, Gx_blue;
    int Gy_red, Gy_green, Gy_blue;

    // define temporary array
    RGBTRIPLE edge_image[height][width];

    // loop through columns
    for (int i = 0; i < height; i++)
    {
        // loop through rows
        for (int j = 0; j < width; j++)
        {
            // set/reset sobel values for each colour channel
            Gx_red = Gx_green = Gx_blue = 0;
            Gy_red = Gy_green = Gy_blue = 0;

            // 3x3 kernal around [i][j]
            for (int x = -1; x < 2; x++)
            {
                for (int y = -1; y < 2; y++)
                {
                    // 'pixels' outside of image array treated as black pixels
                    if (i + x > height || i + x < 0 || j + y > width || j + y < 0)
                    {
                        // Gx kernal
                        Gx_red += 0;
                        Gx_green += 0;
                        Gx_blue += 0;

                        // Gy kernal
                        Gy_red += 0;
                        Gy_green += 0;
                        Gy_blue += 0;
                    }

                    // Multiply each channel by corresponding value in convolutional array
                    else if (i + x < height && i + x > 0 && j + y < width && j + y > 0)
                    {
                        // Gx kernal
                        Gx_red += (image[i + x][j + y].rgbtRed * Gx[x][y]);
                        Gx_green += (image[i + x][j + y].rgbtGreen * Gx[x][y]);
                        Gx_blue += (image[i + x][j + y].rgbtBlue * Gx[x][y]);

                        // Gy kernal
                        Gy_red += (image[i + x][j + y].rgbtRed * Gy[x][y]);
                        Gy_green += (image[i + x][j + y].rgbtGreen * Gy[x][y]);
                        Gy_blue += (image[i + x][j + y].rgbtBlue * Gy[x][y]);
                    }
                }
            }
            // Perform sobel operatation and assign each colour channel value to new array
            edge_image[i][j].rgbtRed = sobel(Gx_red, Gy_red);
            edge_image[i][j].rgbtGreen = sobel(Gx_green, Gy_green);
           edge_image[i][j].rgbtBlue = sobel(Gx_blue, Gy_blue);
        }
    }
    // assign temp array to origional array for output
    for (int i = 0; i < height; i++)
        for (int j = 0; j < width; j++)
            image[i][j] = edge_image[i][j];
}

The edges function calls the sobel function, written as below.

// Calculate sobel value for each channel (capping at 255)
int sobel (int Gx, int Gy)
{
    int n = sqrt(Gx^2 + Gy^2);
    if (n > 255)
    {
        n = 255;
    }
    return n;
}

This is the Input image

This is the Output image

As you can see the output is extremely grainy and the edges are undefined. Clearly, I haven't implemented the sobel alorithm properly, but I am unsure what I have done wrong. Please could you give me some advice on how I could fix this?

*Please note I am aware I could convert the image to greyscale before implementing the sobel algorithm but i'm trying to preserve the colour channels as much as possible. Let me know if I can provide any more information.

You can clean up your initializations with int Gx[3][3] = { { -1, 0 ,1}, {-2, 0, 2}, {-1, 0 , 2}}; — William Pursell
– William Pursell, Commented Mar 3, 2021 at 14:52

orlp · Accepted Answer · 2021-03-03 14:31:04Z

3

First of all, this all does nothing:

// 'pixels' outside of image array treated as black pixels
if (i + x > height || i + x < 0 || j + y > width || j + y < 0)
{
    // Gx kernal
    Gx_red += 0;
    Gx_green += 0;
    Gx_blue += 0;

    // Gy kernal
    Gy_red += 0;
    Gy_green += 0;
    Gy_blue += 0;
}

Adding zero is a no-op. You can safely delete that.

Your first main issue is here:

// Gx kernal
Gx_red += (image[i + x][j + y].rgbtRed * Gx[x][y]);
Gx_green += (image[i + x][j + y].rgbtGreen * Gx[x][y]);
Gx_blue += (image[i + x][j + y].rgbtBlue * Gx[x][y]);

// Gy kernal
Gy_red += (image[i + x][j + y].rgbtRed * Gy[x][y]);
Gy_green += (image[i + x][j + y].rgbtGreen * Gy[x][y]);
Gy_blue += (image[i + x][j + y].rgbtBlue * Gy[x][y]);

You defined x, y to loop through -1, 0, 1, but defined Gx, Gy as int[3][3] arrays. So when x or y is -1 you are indexing out of bounds.

I would suggest defining

int kx = x + 1; // Kernel x.
int ky = y + 1; // Kernel y.

And then

// Gx kernel
Gx_red += (image[i + x][j + y].rgbtRed * Gx[kx][sy]);
Gx_green += (image[i + x][j + y].rgbtGreen * Gx[kx][sy]);
Gx_blue += (image[i + x][j + y].rgbtBlue * Gx[kx][sy]);

// Gy kernel
Gy_red += (image[i + x][j + y].rgbtRed * Gy[kx][sy]);
Gy_green += (image[i + x][j + y].rgbtGreen * Gy[kx][sy]);
Gy_blue += (image[i + x][j + y].rgbtBlue * Gy[kx][sy]);

Your second main issue is here:

int n = sqrt(Gx^2 + Gy^2);

In C and C++ (and many, but not all other programming languages) ^ means the bit-wise XOR operator, not exponentiation. You want:

int n = sqrt(Gx*Gx + Gy*Gy);

answered Mar 3, 2021 at 14:31

orlp

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2 Comments

Rory V.S. Over a year ago

Thanks for the response, everything you said makes a lot of sense. I've implemented those changes and everything seems to work. Thanks again and all the best.

orlp Over a year ago

@RoryV.S. If my answer helped you please consider upvoting and accepting it :)

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