I need to resize an image using bilinear interpolation and create an image pyramid. I will detect corners at the different levels of the pyramid and scale the pixel co-ordinates so that they are relative to the dimensions of the largest image.
If a corner of an object is detected as a corner/keypoint/feature in all the levels, after scaling the corresponding pixel coordinates from the different levels so that they fall on the largest image, ideally I would like them to have the same value. Thus when resizing the images, I am trying to be as accurate as possible.
Let's assume I am resizing an image L_n_minus_1
to create a smaller image L_n
.
My scale factor is ratio
( with ratio
> 1).
I can resize using the pseudocode below (which is what I generally find when I search online for resizing algorithms.)
I cannot use any library.
int offset = 0;
for (int i = 0; i < height_of_L_n; i++){
for (int j = 0; j < width_of_L_n; j++){
//********* This part will differ in the later version I provided below **********
//
int xSrcInt = (int)(ratio * j);
float xDiff = ratio * j - xSrcInt;
int ySrcInt = (int)(ratio * i);
float yDiff = ratio * i - ySrcInt;
//********** The above code will differ in the later version I provided below **********
index = (ySrcInt * width_of_L_n_minus_1 + xSrcInt);
//Get the 4 pixel values to interpolate
a = L_n_minus_1[index];
b = L_n_minus_1[index + 1];
c = L_n_minus_1[index + width_of_L_n_minus_1];
d = L_n_minus_1[index + width_of_L_n_minus_1 + 1];
//Calculate the coefficients for interpolation
float c0 = (1 - x_diff)*(1 - y_diff);
float c1 = (x_diff)*(1 - y_diff);
float c2 = (y_diff)*(1 - x_diff);
float c3 = (x_diff*y_diff);
//half is added for rounding the pixel intensity.
int intensity = (a*c0) + (b*c1) + (c*c2) + (d*c3) + 0.5;
if (intensity > 255)
intensity = 255;
L_n[offset++] = intensity;
}
}
Or I could use this modified piece of code below :
int offset = 0;
for (int i = 0; i < height_of_L_n; i++){
for (int j = 0; j < width_of_L_n; j++){
//********* Here the code differs from the first piece of code **********
// Assume pixel centers start from (0.5,0.5). The top left pixel has co-ordinate (0.5,0.5)
// 0.5 is added to go to the co-ordinates where top left pixel has co-ordinate (0.5,0.5)
// 0.5 is subtracted to go to the generally used co-ordinates where top left pixel has co-ordinate (0,0)
// or in other words map the new co-ordinates to array indices
int xSrcInt = int((ratio * (j + 0.5)) - 0.5);
float xDiff = (ratio * (j + 0.5)) - 0.5 - xSrcInt;
int ySrcInt = int((ratio * (i + 0.5)) - 0.5);
float yDiff = (ratio * (i + 0.5)) - 0.5 - ySrcInt;
//********** Difference with previous code ends here ************
index = (ySrcInt * width_of_L_n_minus_1 + xSrcInt);
//Get the 4 pixel values to interpolate
a = L_n_minus_1[index];
b = L_n_minus_1[index + 1];
c = L_n_minus_1[index + width_of_L_n_minus_1];
d = L_n_minus_1[index + width_of_L_n_minus_1 + 1];
//Calculate the coefficients for interpolation
float c0 = (1 - x_diff)*(1 - y_diff);
float c1 = (x_diff)*(1 - y_diff);
float c2 = (y_diff)*(1 - x_diff);
float c3 = (x_diff*y_diff);
//half is added for rounding the pixel intensity.
int intensity = (a*c0) + (b*c1) + (c*c2) + (d*c3) + 0.5;
if (intensity > 255)
intensity = 255;
L_n[offset++] = intensity;
}
}
The second piece of code was developed assuming pixel centers having co-ordinates like (0.5, 0.5) as they have in textures. This way the top left pixel will have co-ordinate (0.5, 0.5).
Let us assume a 2 by 2 pixel Destination Image is being resized from a 4 by 4 Source Image.
In the first piece of code, it is assumed that the first pixel has co-ordinates (0,0), thus for example my ratio is 2. Then
xSrcInt = (int)(0*2); // 0
ySrcInt = (int)(0*2); // 0
xDiff = (0*2) - 0; // 0
yDiff = (0*2) - 0; // 0
Thus effectively I will just be copying the first pixel value from the source, as c0
will be 1
and c1
,c2
and c3
will be 0
.
But in the second piece of code I will get
xSrcInt = (int)((0.5*2) - 0.5); // 0;
ySrcInt = (int)((0.5*2) - 0.5); // 0;
xDiff = ((0.5*2) - 0.5) - 0; // 0.5;
yDiff = ((0.5*2) - 0.5) - 0; // 0.5;
In this case c0,c1,c2 and c3 will all be equal to 0.25. Thus I will be using the 4 pixels at the top left.
There is any bug in my second piece of code. As far as visual results go they are working perfectly.
But yes I do seem to notice better alignment of keypoints with the second piece of code. But may be that's because I am judging with prejudice.