Image conversion from Cartesian coordinate to polar coordinate

Question

I was wondering if someone helps me understand how to convert the top image to the bottom image. The images are available in the following link.The top image is in Cartesian coordinate. The bottom image is the converted image in polar coordinate

Answer 1

This is a basic rectangular to polar coordinate transform. To do the conversion, scan across the output image and treat x and y as if they were r and theta. Then use them as r and theta to look up the corresponding pixel in the input image. So something like this:

int x, y;
for (y = 0; y < outputHeight; y++)
{
    Pixel* outputPixel = outputRowStart (y); // <- get a pointer to the start of the output row
    for (x = 0; x < outputWidth; x++)
    {
        float r = y;
        float theta = 2.0 * M_PI * x / outputWidth;
        float newX = r * cos (theta);
        float newY = r * sin (theta);
        *outputPixel = getInputPixel ( newX, newY ); // <- Should probably do at least bilinear resampling in this function
        outputPixel++;
    }
}

Note that you may want to handle wrapping depending on what you're trying to achieve. The theta value wraps at 2pi.