imoments.m

这是一个基于MATLAB的机器视觉工具箱,里面用很多非常有价值的的程序

%IMOMENTS	Compute image moments
%
%	[F,M] = IMOMENTS(image)
%
%	[F,M] = IMOMENTS(rows, cols)
%	[F,M] = IMOMENTS(rows, cols, w)
%
%	The first form computes the grey-scale moments of the image (non-zero 
%	elements) image.  The actual pixel values are used as pixel weights.
%	The return vector is F = [area xc yc a b theta] where:
%		area	 is the number of pixels (for a binary image)
%		(xc, yc) is the centroid with respect to top-left point which
%			 is (1,1)
%		(a, b)   are axis lengths of the "equivalent ellipse"
%		theta    the angle of the major ellipse axis to the 
%		         horizontal axis.
%
%	The raw moments can also be returned M = [m00 m10 m01 m20 m02 m11].
%
%	The second form is used when the coordinates of the non-zero elements 
%	are known.
%
% NOTE:	this function does not perform connectivity, if connected blobs
%	are required then the ILABEL function must be used first.
%
% SEE ALSO: ilabel
%
%	Copyright (c) Peter Corke, 1999  Machine Vision Toolbox for Matlab


% 1996 Peter Corke

function [F,M] = imoments(a1, a2, a3)
	if nargin == 1,
		[i,j] = find(a1)
		w = a1(find(a1 > 0))
	else
		i = a1;
		j = a2;
		if nargin == 3,
			w = a3;
		else
			w = ones(size(i));
		end
	end

	% compute basic moments
	m00 = sum(w);
	m10 = sum(j.*w);
	m01 = sum(i.*w);
	m20 = sum((j.^2).*w);
	m02 = sum((i.^2).*w);
	m11 = sum((i.*j).*w);

	% figure some central moments
	u20 = m20 - m10^2/m00;
	u02 = m02 - m01^2/m00;
	u11 = m11 - m10*m01/m00;

	% figure the equivalent axis lengths, function of the principal axis lengths
	e = eig([u20 u11; u11 u02]);
	a = 2*sqrt(max(e)/m00);
	b = 2*sqrt(min(e)/m00);
	th = 0.5*atan(2*u11/(u20-u02));

	F = [m00 m10/m00 m01/m00 a b th];
	if nargin > 1,
		M = [m00 m10 m01 m20 m02 m11];
	end