MATLAB Central Newsreader - Image Invariant Moment

Image Invariant Moment

Nan W. — Sat, 14 Jun 2008 14:15:04 -0400

Dear all,

I tried to implement the image invariant moment but it
seems like it doesn't work well. Would you please check
the code for me? The goal is just to find the second
moment of the image though but since it doesn't work I
also try the 3rd and 4th and still doesn't work out.

Noted thanks for the guideline code from Yuan-Liang Tang.

function [m2 m3 m4]=findmoment(im)

%im=im/max(max(im));
cx = immoment(im, 1, 0);
cy = immoment(im, 0, 1);

u20= immoment(im,2,0,cx,cy);
u02= immoment(im,0,2,cx,cy);
u11= immoment(im,1,1,cx,cy);

u30= immoment(im,3,0,cx,cy);
u03= immoment(im,0,3,cx,cy);
u12= immoment(im,1,2,cx,cy);
u21= immoment(im,2,1,cx,cy);

m2=sqrt((u20-u02).^2+4*u11.^2);

m3=(u30-3*u12).^2 + (3*u21-u03).^2;

m4=(u30+u12).^2 + (u21+u02).^2;

function m = immoment(im, p, q, cx, cy)
% Compute image moment
[y x v] = find(im);
if nargin == 5
  x = x - cx;
  y = y - cy;
  m = sum(x.^p .* y.^q .* v)/sum(v).^((p+q)/2+1);
end
    m = sum(x.^p .* y.^q .* v)/sum(v);
return

**** Thank you ****

Re: Image Invariant Moment

Nan W. — Sat, 14 Jun 2008 14:18:01 -0400

>
> m2=sqrt((u20-u02).^2+4*u11.^2);
>

is actually

> m2=((u20-u02).^2+4*u11.^2);

sorry I was trying various of versions though.

Please help I really stucked!
Thank you so much

Re: Image Invariant Moment

ImageAnalyst — Sat, 14 Jun 2008 14:29:14 -0400

On Jun 14, 10:18=A0am, "Nan W." <iiuu_c...@yahoo.co.jp> wrote:
> > m2=3Dsqrt((u20-u02).^2+4*u11.^2);
>
> is actually
>
> > m2=3D((u20-u02).^2+4*u11.^2);
>
> sorry I was trying various of versions though.
>
> Please help I really stucked!
> Thank you so much

------------------------------------
NaN:
Is your original image a uint8 (with values of 0-255)? If so the
squaring and summing operations may exceed its range and it will
either clip or wrap around (I don't know which), or maybe just give an
error or warning or NaN (I'm not sure). You might need to convert
your image to floating point with single() or double() before
computing the moments.

You need to detail more what "doesn't work out" actually means. Does
that mean there is an error message, warnings displayed in the command
window, or the results just don't seem like the correct results?
Regards,
ImageAnalyst

Re: Image Invariant Moment

Nan W. — Sat, 14 Jun 2008 23:19:02 -0400

I'm sorry for haven't posted the details.

My test image is in gray-scale and the thing that is
incorrect is the result (value) of the output 'm2 m3 m4'.

I set up the experiment as
1.Reference image
2.Translated and Rotated image

Then I cropped a part from Image1 and almost exactly portion
from Image2 with a circular mask to make it safe for some
unwanted details. Then only pixel in those masks are fed
into my above moment invariant code. But the result didn't
give the nearly the same moment value from both. Some are!
but some aren't! So I was wondering whether my code is wrong
or not.

Please guide me so. Thank you so much.

Re: Image Invariant Moment

ImageAnalyst — Sun, 15 Jun 2008 01:12:45 -0400

On Jun 14, 10:15=A0am, "Nan W." <iiuu_c...@yahoo.co.jp> wrote:
> Dear all,
>
> I tried to implement the image invariant moment but it
> seems like it doesn't work well. Would you please check
> the code for me? The goal is just to find the second
> moment of the image though but since it doesn't work I
> also try the 3rd and 4th and still doesn't work out.
>
> Noted thanks for the guideline code from Yuan-Liang Tang.
>
> function [m2 m3 m4]=3Dfindmoment(im)
>
> %im=3Dim/max(max(im));
> cx =3D immoment(im, 1, 0);
> cy =3D immoment(im, 0, 1);
>
> u20=3D immoment(im,2,0,cx,cy);
> u02=3D immoment(im,0,2,cx,cy);
> u11=3D immoment(im,1,1,cx,cy);
>
> u30=3D immoment(im,3,0,cx,cy);
> u03=3D immoment(im,0,3,cx,cy);
> u12=3D immoment(im,1,2,cx,cy);
> u21=3D immoment(im,2,1,cx,cy);
>
> m2=3Dsqrt((u20-u02).^2+4*u11.^2);
>
> m3=3D(u30-3*u12).^2 + (3*u21-u03).^2;
>
> m4=3D(u30+u12).^2 + (u21+u02).^2;
>
> function m =3D immoment(im, p, q, cx, cy)
> % Compute image moment
> [y x v] =3D find(im);
> if nargin =3D=3D 5
> =A0 x =3D x - cx;
> =A0 y =3D y - cy;
> =A0 m =3D sum(x.^p .* y.^q .* v)/sum(v).^((p+q)/2+1);
> end
> =A0 =A0 m =3D sum(x.^p .* y.^q .* v)/sum(v);
> return
>
> **** Thank you ****

---------------------------------------
Well you're passing in 5 arguments so you're getting into the if
statement and assigning m, yet right after that if statement, you're
setting m to some other value, so, in essence, the if statement was
useless. Is that what you want to do?
Regards,
ImageAnalyst