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3D rendering engine. Plus modeling. Expected glsl textures 3d and 2d rendering
%SNAKEMINIMIZE Minimizes the energy function of a snake
%
% SYNOPSIS:
% snake_out = snakeminimize(snake_in,Fext,alpha,beta,stepsz,kappa,iterations)
%
% PARAMETERS:
% snake_in : initial snake, object of type DIP_SNAKE
% Fext : external force field, 2D-2D vector image
% for example: gradient, gvf, vfc
% alpha : elasticity parameter (membrane)
% beta : rigidity parameter (thin plate)
% stepsz : step size
% kappa : balloon force (negative for inwards force)
% iterations : number of iterations performed
%
% DEFAULTS:
% alpha = 0.2
% beta = 0.4
% stepsz = 1
% kappa = 0
% iterations = 20
%
% EXAMPLE:
% a = noise(50+100*gaussf(rr>85,2),'gaussian',20)
% f = gradient(gradmag(a,5));
% f = f./max(norm(f));
% x = 100+30*cos(0:0.1:2*pi); y = 150+40*sin(0:0.1:2*pi);
% s = dip_snake([x',y'])
% s = snakeminimize(s,f,0.01,100,3,0.3,20)
% s = snakeminimize(s,f,0.01,100,3,0.3,20)
% s = snakeminimize(s,f,0.01,100,3,0.3,20)
% s = snakeminimize(s,f,0.01,100,3,0.3,20)
% s = snakeminimize(s,f,0.01,100,3,0.3,20)
%
% NOTE:
% This function requires at least MATLAB version 7.6!
%
% LITERATURE:
% M. Kass, A. Witkin, D. Terzopoulos, "Snakes: Active Contour Models",
% Int. J. of Computer Vision 4(1):321-331 (1988)
% L.D. Cohen, I. Cohen, "Finite-element methods for active contour models and
% balloons for 2-D and 3-D images", IEEE TPAMI 15(11):1131-1147 (1993)
%
% SEE ALSO: dip_snake
% (C) Copyright 2009-2010, All rights reserved.
% Cris Luengo, Uppsala, 18 September 2009.
%
% 4 March 2010: Edited for compatability with DIPimage releases after 2.1.
function s = snakeminimize(varargin)
if ( exist('matlabver_ge')==2 && ~matlabver_ge([7,6]) ) || ( exist('matlabversion')==2 && matlabversion<7.6 )
error('The dip_snake object is not supported on your version of MATLAB.')
end
d = struct('menu','Segmentation',...
'display','Minimize snake energy',...
'inparams',struct('name', {'snake_in', 'Fext', 'alpha', 'beta', 'stepsz', 'kappa', 'iterations'},...
'description',{'Input snake', 'External force', 'Elasticity','Rigidity','Step size','Balloon force','Iterations'},...
'type', {'snake', 'image', 'array', 'array', 'array', 'array', 'array'},...
'dim_check', {0, 2, 0, 0, 0, 0, 0},...
'range_check',{[], {'real','tensor'}, 'R+', 'R+', 'R+', 'R', 'N'},...
'required', {1, 1, 0, 0, 0, 0, 0},...
'default', {'dip_snake(x)','gradient(gradmag(a))',0.2, 0.4, 1, 1, 20}...
),...
'outparams',struct('name',{'snake_out'},...
'description',{'Output snake'},...
'type',{'snake'}...
)...
);
if nargin == 1
s = varargin{1};
if ischar(s) & strcmp(s,'DIP_GetParamList')
s = d;
return
end
end
try
[s,f,alpha,beta,stepsz,kappa,iterations] = getparams(d,varargin{:});
catch
if ~isempty(paramerror)
error(paramerror)
else
error(firsterr)
end
end
if prod(imarsize(f))~=2
error('The external force image must have 2D vectors ');
end
[maxx,maxy] = imsize(f);
if any(s.imsz > [maxx,maxy])
error('The snake is defined on an image larger than the given external force image.');
end
s.imsz = [maxx,maxy];
maxx = maxx-1;
maxy = maxy-1;
% Do the snake!
md = 1; % The average distance we want to keep between points.
s = resample(s,md);
%h = disp(s);
P = compute_matrix(length(s),alpha,beta,stepsz);
for ii = 1:iterations
%disp(['iteration ii=',num2str(ii),', snake length = ',num2str(length(s))])
% Do we need to resample the snake?
d = sqrt( diff(s.x).^2 + diff(s.y).^2 );
if any(dmd*3)
%disp('resampling snake')
s = resample(s,md);
P = compute_matrix(length(s),alpha,beta,stepsz);
end
% Calculate external force
coords = [s.x,s.y];
fex = get_subpixel(f{1},coords,'linear');
fey = get_subpixel(f{2},coords,'linear');
% Calculate balloon force
if kappa~=0
b = [coords(2:end,:);coords(1,:)] - [coords(end,:);coords(1:end-1,:)];
m = sqrt(sum(b.^2,2));
bx = b(:,2)./m;
by = -b(:,1)./m;
% Add balloon force to external force
fex = fex+kappa*bx;
fey = fey+kappa*by;
end
% Move control points
x = P*(s.x+stepsz*fex);
y = P*(s.y+stepsz*fey);
% Constrict points to image
x(x<0) = 0;
x(x>maxx) = maxx;
y(y<0) = 0;
y(y>maxy) = maxy;
% Update snake
s.x = x;
s.y = y;
%if mod(ii,10)
% disp(s,h);
% drawnow;
% pause(0.5);
%end
end
% The matrix P = (tau*A+I)^-1
function P = compute_matrix(N,alpha,beta,stepsz)
a = stepsz*(2*alpha+6*beta)+1;
b = stepsz*(-alpha-4*beta);
c = stepsz*beta;
P = diag(repmat(a,1,N));
P = P + diag(repmat(b,1,N-1), 1) + diag( b, -N+1);
P = P + diag(repmat(b,1,N-1),-1) + diag( b, N-1);
P = P + diag(repmat(c,1,N-2), 2) + diag([c,c],-N+2);
P = P + diag(repmat(c,1,N-2),-2) + diag([c,c], N-2);
P = inv(P);