Lanczos interpolation in C

Question

i need to implement the following formula in c-code: https://en.wikipedia.org/wiki/Lanczos_resampling Therefore i'm using the multidimensional interpolation approach:

where L(x-i) or L(y-i) is:

I'm using the ppm image format to get rgb values trough a small script. This is my actual lanczos approach now:

double _L(int param) {
    /*
    LANCZOS KERNEL
    */
    
    int a = 2; // factor "a" from formula
    if(param == 0) {
        
        return 1;
    }
    if(abs(param) > 0 && abs(param) < a) {
        
        return (a*sin(PI*param) * sin((PI*param)/a))/(PI*PI*param*param)
    }
    return 0;
}

void lanczos_interpolation(PPMImage *img) {

    if(img) {
        
        int start_i, start_j, limit_i, limit_j;
        int a = 2; // factor "a" from formula
        samples_ij = img->x*img->y; // "sij" from formula
    
        for(x = 0;x < img->x;x++) {
            
            for(y = 0;y = < img->y;y++) {
                
                start_i = floor(x)-a+1:
                limit_i = floor(x)+a;
                for(i = start_i;i <= limit_i;i++) {
                    
                    start_j = floor(y)-a+1:
                    limit_j = floor(y)+a;
                    for(i = start_i;i <= limit_i;i++) {
                        
                        img->data[x+(W*y)].red = (int)(samples_ij * _L(x-i) * _L(y-j)) // "_L" represents "L(x-i)" from formula
                        img->data[x+(W*y)].green = (int)(samples_ij * _L(x-i) * _L(y-j)) // "_L" represents "L(x-i)" from formula
                        img->data[x+(W*y)].blue = (int)(samples_ij * _L(x-i) * _L(y-j)) // "_L" represents "L(x-i)" from formula
                    }
                }
            }
        }
    }   
}

This part of the code confused me a lot:

img->data[x+(W*y)].red = (int)(samples_ij * _L(x-i) * _L(y-j)) // "_L" represents "L(x-i)" from formula
img->data[x+(W*y)].green = (int)(samples_ij * _L(x-i) * _L(y-j)) // "_L" represents "L(x-i)" from formula
img->data[x+(W*y)].blue = (int)(samples_ij * _L(x-i) * _L(y-j)) // "_L" represents "L(x-i)" from formula

Can someone help me to get along with this lanczos interpolation in c? Here is my complete C-File:

http://pastebin.com/wdUHVh6U

Thanks!

Answer 1

See you are not doing any kind of interpolation in your code.

The interpolation operation is like this:

[input pixels] => [Lanczos interpolation] => [output interpolated pixels]

                        |
                        |
                        V
        a sum operation in the neighbourhood 
            of the corresponding location
               in the input image

Your problems are the following:

1. You have not understood the Lanczos interpolation technique. In fact, it seems you don't know what is interpolation.
2. Your code does not have the input pixels and the output pixels.
3. There is no summation in your code. (You are just assigning the Lanczos co-efficient times s_ij to img pixels. Again s_ij's are actually the input pixel values in the formula, but you have assigned a fixed value of total number of pixels in the image to s_ij.)
4. You have unnecessarily used floor(*) functions.

My suggestion to you is:

1. Understand what is interpolation in an algorithmic way.
2. Write the algorithm /pseudo-code for whatever your purpose is.
3. Make sure you are correct in Steps 1 and 2.
4. Then only try to write the code.