% MAXLINEDEV - Find max deviation from a line in an edge contour.%% Function finds the point of maximum deviation from a line joining the% endpoints of an edge contour.%% Usage:   [maxdev, index, D, totaldev] = maxlinedev(x,y)%% Arguments:%          x, y   - arrays of x,y  (col,row) indicies of connected pixels %                   on the contour.% Returns:%          maxdev   - Maximum deviation of contour point from the line%                     joining the end points of the contour (pixels).%          index    - Index of the point having maxdev.%          D        - Distance between end points of the contour so that%                     one can calculate maxdev/D - the normalised error.%          totaldev - Sum of the distances of all the pixels from the%                     line joining the endpoints.%% See also:  EDGELINK, LINESEG%% Peter Kovesi  % School of Computer Science & Software Engineering% The University of Western Australia% pk at csse uwa edu au% http://www.csse.uwa.edu.au/~pk%% December 2000 - Original version% February 2003 - Added calculation of total deviation% August   2006 - Avoid degeneracy when endpoints are coincident% February 2007 - Corrected distance calculation when endpoints are%                 coincident.function [maxdev, index, D, totaldev] = maxlinedev(x,y)    Npts = length(x);        if Npts == 1	warning('Contour of length 1');	maxdev = 0; index = 1;	D = 1; totaldev = 0;	return;    elseif Npts == 0	error('Contour of length 0');    end    %    D = norm([x(1) y(1)] - [x(Npts) y(Npts)]);  % Distance between end points    D = sqrt((x(1)-x(Npts))^2 + (y(1)-y(Npts))^2); % This runs much faster    if D > eps    		% Eqn of line joining end pts (x1 y1) and (x2 y2) can be parameterised by	%    	%    x*(y1-y2) + y*(x2-x1) + y2*x1 - y1*x2 = 0	%	% (See Jain, Rangachar and Schunck, "Machine Vision", McGraw-Hill	% 1996. pp 194-196)		y1my2 = y(1)-y(Npts);                       % Pre-compute parameters	x2mx1 = x(Npts)-x(1);	C = y(Npts)*x(1) - y(1)*x(Npts);		% Calculate distance from line segment for each contour point	d = abs(x*y1my2 + y*x2mx1 + C)/D;          	    else    % End points are coincident, calculate distances from 1st point            d = sqrt((x - x(1)).^2 + (y - y(1)).^2);	D = 1;  % Now set D to 1 so that normalised error can be used	    end						    [maxdev, index] = max(d);    if nargout == 4	totaldev = sum(d.^2);    end