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function [imout, thresh] = edge( im, method, thresh, param2 )
# EDGE: find image edges
# [imout, thresh] = edge( im, method, thresh, param2 )
#
# OUTPUT
# imout -> output image
# thresh -> output thresholds
#
# INPUT
# im -> input image (greyscale)
# thresh -> threshold value (value is estimated if not given)
#
# The following methods are based on high pass filtering the image in
# two directions, calculating a combined edge weight from and then thresholding
#
# method = 'roberts'
# filt1= [1 0 ; 0 -1]; filt2= rot90( filt1 )
# combine= sqrt( filt1^2 + filt2^2 )
# method = 'sobel'
# filt1= [1 2 1;0 0 0;-1 -2 -1]; filt2= rot90( filt1 )
# combine= sqrt( filt1^2 + filt2^2 )
# method = 'prewitt'
# filt1= [1 1 1;0 0 0;-1 -1 -1]; filt2= rot90( filt1 )
# combine= sqrt( filt1^2 + filt2^2 )
# method = 'kirsh'
# filt1= [1 2 1;0 0 0;-1 -2 -1]; filt2 .. filt8 are 45 degree rotations of filt1
# combine= max( filt1 ... filt8 )
#
# methods based on filtering the image and finding zero crossings
#
# method = 'log' -> Laplacian of Gaussians
# param2 is the standard deviation of the filter, default is 2
# method = 'zerocross' -> generic zero-crossing filter
# param2 is the user supplied filter
#
# method = 'andy' -> my idea
# A.Adler's idea (c) 1999. somewhat based on the canny method
# Step 1: Do a sobel edge detection and to generate an image at
# a high and low threshold
# Step 2: Edge extend all edges in the LT image by several pixels,
# in the vertical, horizontal, and 45degree directions.
# Combine these into edge extended (EE) image
# Step 3: Dilate the EE image by 1 step
# Step 4: Select all EE features that are connected to features in
# the HT image
#
# Parameters:
# param2(1)==0 or 4 or 8 -> perform x connected dilatation (step 3)
# param2(2) dilatation coeficient (threshold) in step 3
# param2(3) length of edge extention convolution (step 2)
# param2(4) coeficient of extention convolution in step 2
# defaults = [8 1 3 3]
# Copyright (C) 1999 Andy Adler
# This code has no warrany whatsoever.
# Do what you like with this code as long as you
# leave this copyright in place.
#
# $Id$
[n,m]= size(im);
xx= 2:m-1;
yy= 2:n-1;
if strcmp(method,'roberts') || strcmp(method,'sobel') || ...
strcmp(method,'prewitt')
if strcmp(method,'roberts')
filt= [1 0;0 -1]/4; tv= 6;
elseif strcmp(method,'sobel')
filt= [1 2 1;0 0 0; -1 -2 -1]/8; tv= 2;
elseif strcmp(method,'prewitt')
filt= [1 1 1;0 0 0; -1 -1 -1]/6; tv= 4;
end
imo= conv2(im, rot90(filt), 'same').^2 + conv2(im, filt, 'same').^2;
# check to see if the user supplied a threshold
# if not, calculate one in the same way as Matlab
if nargin<3
thresh= sqrt( tv* mean(mean( imo(yy,xx) )) );
end
# The filters are defined for sqrt(imo), but since we calculated imo, compare
# to thresh ^2
imout= ( imo >= thresh^2 );
# Thin the wide edges
xpeak= imo(yy,xx-1) <= imo(yy,xx) & imo(yy,xx) > imo(yy,xx+1) ;
ypeak= imo(yy-1,xx) <= imo(yy,xx) & imo(yy,xx) > imo(yy+1,xx) ;
imout(yy,xx)= imout(yy,xx) & ( xpeak | ypeak );
elseif strcmp(method,'kirsch')
filt1= [1 2 1;0 0 0;-1 -2 -1]; fim1= conv2(im,filt1,'same');
filt2= [2 1 0;1 0 -1;0 -1 -2]; fim2= conv2(im,filt2,'same');
filt3= [1 0 -1;2 0 -2;1 0 -1]; fim3= conv2(im,filt3,'same');
filt4= [0 1 2;-1 0 1;-2 -1 0]; fim4= conv2(im,filt4,'same');
imo= reshape(max([abs(fim1(:)) abs(fim2(:)) abs(fim3(:)) abs(fim4(:))]'),n,m);
if nargin<3
thresh= 2* mean(mean( imo(yy,xx) )) ;
end
imout= imo >= thresh ;
# Thin the wide edges
xpeak= imo(yy,xx-1) <= imo(yy,xx) & imo(yy,xx) > imo(yy,xx+1) ;
ypeak= imo(yy-1,xx) <= imo(yy,xx) & imo(yy,xx) > imo(yy+1,xx) ;
imout(yy,xx)= imout(yy,xx) & ( xpeak | ypeak );
elseif strcmp(method,'log') || strcmp(method,'zerocross')
if strcmp(method,'log')
if nargin >= 4; sd= param2;
else sd= 2;
end
sz= ceil(sd*3);
[x,y]= meshgrid( -sz:sz, -sz:sz );
filt = exp( -( x.^2 + y.^2 )/2/sd^2 ) .* ...
( x.^2 + y.^2 - 2*sd^2 ) / 2 / pi / sd^6 ;
else
filt = param2;
end
filt = filt - mean(filt(:));
imo= conv2(im, filt, 'same');
if nargin<3 || isempty( thresh )
thresh= 0.75* mean(mean( abs(imo(yy,xx)) )) ;
end
zcross= imo > 0;
yd_zc= diff( zcross );
xd_zc= diff( zcross' )';
yd_io= abs(diff( imo ) ) > thresh;
xd_io= abs(diff( imo')') > thresh;
# doing it this way puts the transition at the <=0 point
xl= zeros(1,m); yl= zeros(n,1);
imout= [ ( yd_zc == 1 ) & yd_io ; xl] | ...
[xl; ( yd_zc == -1 ) & yd_io ] | ...
[ ( xd_zc == 1 ) & xd_io , yl] | ...
[yl, ( xd_zc == -1 ) & xd_io ];
elseif strcmp(method,'canny')
error("method canny not implemented");
elseif strcmp(method,'andy')
filt= [1 2 1;0 0 0; -1 -2 -1]/8; tv= 2;
imo= conv2(im, rot90(filt), 'same').^2 + conv2(im, filt, 'same').^2;
if nargin<3 || thresh==[];
thresh= sqrt( tv* mean(mean( imo(yy,xx) )) );
end
# sum( imo(:)>thresh ) / prod(size(imo))
dilate= [1 1 1;1 1 1;1 1 1]; tt= 1; sz=3; dt=3;
if nargin>=4
# 0 or 4 or 8 connected dilation
if length(param2) > 0
if param2(1)==4 ; dilate= [0 1 0;1 1 1;0 1 0];
elseif param2(1)==0 ; dilate= 1;
end
end
# dilation threshold
if length(param2) > 2; tt= param2(2); end
# edge extention length
if length(param2) > 2; sz= param2(3); end
# edge extention threshold
if length(param2) > 3; dt= param2(4); end
end
fobliq= [0 0 0 0 1;0 0 0 .5 .5;0 0 0 1 0;0 0 .5 .5 0;0 0 1 0 0;
0 .5 .5 0 0;0 1 0 0 0;.5 .5 0 0 0;1 0 0 0 0];
fobliq= fobliq( 5-sz:5+sz, 3-ceil(sz/2):3+ceil(sz/2) );
xpeak= imo(yy,xx-1) <= imo(yy,xx) & imo(yy,xx) > imo(yy,xx+1) ;
ypeak= imo(yy-1,xx) <= imo(yy,xx) & imo(yy,xx) > imo(yy+1,xx) ;
imht= ( imo >= thresh^2 * 2); # high threshold image
imht(yy,xx)= imht(yy,xx) & ( xpeak | ypeak );
imht([1,n],:)=0; imht(:,[1,m])=0;
% imlt= ( imo >= thresh^2 / 2); # low threshold image
imlt= ( imo >= thresh^2 / 1); # low threshold image
imlt(yy,xx)= imlt(yy,xx) & ( xpeak | ypeak );
imlt([1,n],:)=0; imlt(:,[1,m])=0;
# now we edge extend the low thresh image in 4 directions
imee= ( conv2( imlt, ones(2*sz+1,1) , 'same') > tt ) | ...
( conv2( imlt, ones(1,2*sz+1) , 'same') > tt ) | ...
( conv2( imlt, eye(2*sz+1) , 'same') > tt ) | ...
( conv2( imlt, rot90(eye(2*sz+1)), 'same') > tt ) | ...
( conv2( imlt, fobliq , 'same') > tt ) | ...
( conv2( imlt, fobliq' , 'same') > tt ) | ...
( conv2( imlt, rot90(fobliq) , 'same') > tt ) | ...
( conv2( imlt, flipud(fobliq) , 'same') > tt );
# imee(yy,xx)= conv2(imee(yy,xx),ones(3),'same') & ( xpeak | ypeak );
imee= conv2(imee,dilate,'same') > dt; #
% ff= find( imht==1 );
% imout = bwselect( imee, rem(ff-1, n)+1, ceil(ff/n), 8);
imout = imee;
else
error (['Method ' method ' is not recognized']);
end
#
# $Log$
# Revision 1.1 2002/03/17 02:38:52 aadler
# fill and edge detection operators
#
# Revision 1.4 2000/11/20 17:13:07 aadler
# works?
#
# Revision 1.3 1999/06/09 17:29:36 aadler
# implemented 'andy' mode edge detection
#
# Revision 1.2 1999/06/08 14:26:50 aadler
# zero-cross and LoG filters work
#
# Revision 1.1 1999/06/07 21:01:38 aadler
# Initial revision
#
#
#