Can anyone explain why the empty or black holes (or squares) disappear as I add more products (of the weighting function-Wx and pixels values - Nx) in the Y(i,j) sum ?

Hello,

I do need your help! Here's the source code that does the bilinear interpolation:

_I = imread('LENNA128.bmp');

[originheight, originwidth] = size(I);

ratio = 2;

H = ratio * originheight;

W = ratio * originwidth;

Y = zeros(H,W);

hscale = originheight/H;

wscale = originwidth/W;

for i = 1:H;

y = hscale*i;

for j = 1:W;

x = wscale*j;

if(floor(x)==0||floor(y)==0||floor(x)==originwidth floor(y)==originheight)

Y(i,j) = I(ceil(y),ceil(x));

else

x1=floor(x);

x2=x1+1;

y2=floor(y);

y1=y2+1;

N1=I(y2,x1);

N2=I(y2,x2);

N3=I(y1,x2);

N4=I(y1,x1);

W4 = (y-y2)*(x2-x);

W3 = (y-y2)*(x-x1);

W1 = (y1-y)*(x2-x);

W2 = (y1-y)*(x-x1);

Y(i,j) = N1*W1 + N2*W2 + N3*W3 + N4*W4;

end

end

end

Y = uint8(Y);

imshow(Y)

My questions are: When I modify the (second) Y(i,j) sum to Y(i,j) = N1 * W1, I obtain an incompletely interpolated image with many empty holes as shown in Figure(W1), crossing each other. Again, when I change Y(i,j) again and make it like this Y(i,j) = N1 * W1 + N2 * W2, I obtain an incompletely interpolated image, this time, with only empty straight lines. The first situation seems to repeat when I add N3 * W3 to Y(i,j) = N1 * W1 + N2 * W2. Finally, I obtain a completely interpolated image when I add N4 * W4 to Y(i,j) = N1 * W1 + N2 * W2 + N3 * W3.

Can anyone explain (with a drawing or diagram, if possible) why? Also, why, Y(i,j) = N1, the output image looks like an image interpolated using the Nearest Neighbor Algorithm ?

Many thanks and I would appreciate very much your replies at your earliest convenience.