How to substitute p(x/a+x1,y/a+x2) to p(x,y),where p(x,y) is original image, x1 and x2 are the centroid of p(x,y),x1=​m10/m00,x2​=m01/m00,a​=sqrt(β/m0​0),β is a predetermined value. In fact, this is doing scale and translation normalization

How to substitute p(x/a+x1,y/a+x2) to p(x,y),where p(x,y) is original image, x1 and x2 are the centroid of p(x,y),x1=m10/m00,x2=m01/m00,a=sqrt(β/m00),β is a predetermined value. In fact, this is doing scale and translation normalization

[Rik]

What is the exact data you have? And what have you tried?

[Abul Abbas]

I have image data, and i want to do scale and translation normalization, I want to substitute p(x/a+x1,y/a+x2) to p(x,y), where p(x,y) is original image, x1 and x2 are the centroid of p(x,y), and 'a' is a constant

[Rik]

Sounds like you want interpolation. The easiest way to do that is to generate a coordinate grid (e.g. with meshgrid or ndgrid).

Again, what have you tried? That might make it a bit more clear what you actually mean and what your specific problem is. What step is giving you trouble?

[Abul Abbas]

I have realized translation invariance by transforming the image into a new one whose first order moments, m01 and m10, are both equal to zero. This is done by transforming the original f (x, y) image into another one which is

f (x+x', y+y') where x' and y' are the centroid location of the original image. In summary an image function f (x, y) can be normalized with respect to scale and translation by transforming it into g (x, y), where

g(x,y) = f(x/a+x', y/a+y')

Answer 1

[Bjorn Gustavsson]

You solve that with interp2:

xi = xC + [-dx:dx]*xScale;
yi = yC + [-dy:dy]*yScale;
[xi,yi] = meshgrid(xi,yi);
p_prime = interp2(1:size(p,2),1:size(p,1),p,xi,yi);

You have to check for xi and yi falling outside of the image-coordinates, and handle that afterwards. By default you'll get nan-values. Check the help and documentation for interp2 for details. You'll also easily translate your coordinate-transformation to the one above.

HTH

[Abul Abbas]

what are xC, xScale and p ?

[Rik]

The idea here is to form a coordinate grid. So you need an array of points that represent x/a+x1,y/a+x2. xi and yi are vectors describing the x and y coordinates you want to sample, so you can create them any way you like. When you have those vectors you can use meshgrid and interp2 to create your new image.

[Abul Abbas]

so [-dx:dx] signifies what, actually i didn't get [-dx:dx] ?

[Bjorn Gustavsson]

If you for example want a region centred around [123,231] with size of 25x25 in a resolution of 0.2 you'd do something like:

xC = 123;
yC = 231;
xScale = 0.2;
dx = 25/xScale;
dy = 25/xScale;
xi = xC + [-dx:dx]*xScale;
yi = yC + [-dy:dy]*yScale;
[xi,yi] = meshgrid(xi,yi);
p_prime = interp2(1:size(p,2),1:size(p,1),p,xi,yi);

[Abul Abbas]

what about yScale, actually my scaled cordinates are much bigger than the image cordinates

[Abul Abbas]

and after interpolation i am getting values NaN only

[Bjorn Gustavsson]

If you have an image you only have information about the image intensities between the first and last pixels of the image, if you try to extrapolate intensities outside the image support [1 - sy , 1 - sx] you are only guessing. Matlab will allow you to do that type of guess-work, check the help and documentation for extrapolation-methods. Don't expect anything that is all that much worth by extrapolating, there is allways place for Occams pink elephant just outside the field-of-view.