one.empty3.feature.snakes.SnakeMinimization Maven / Gradle / Ivy
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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.
*/
/*DipSnake snake_in : initial snake, object of type DIP_SNAKE
M 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
function s = snakeminimize(varargin)
*/
/* int N = (int) snake_in.size();
double a = gamma * (2 * alpha + 6 * beta) + 1;
double b = gamma * (-alpha - 4 * beta);
double c = gamma * beta;
M P = M.diag(M.repmat(new double[][]{{a}}, 1, N));
P = P.plus(M.diag(M.repmat(new double[][]{{b}}, 1, N - 1), 1)).plus(M.diag(new double[][]{{b}}, -N + 1));
P = P.plus(M.diag(M.repmat(new double[][]{{b}}, 1, N - 1), -1)).plus(M.diag(new double[][]{{b}}, N - 1));
P = P.plus(M.diag(M.repmat(new double[][]{{c}}, 1, N - 2), 2)).plus(M.diag(new double[][]{{c, c}}, -N + 2));
P = P.plus(M.diag(M.repmat(new double[][]{{c}}, 1, N - 2), -2)).plus(M.diag(new double[][]{{c, c}}, N - 2));
P = P.inverse();/*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_M(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(d < md / 3) || any(d > md * 3)
% disp('resampling snake')
s = resample(s, md);
P = compute_M(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 M P = (tau * A + I) ^ -1
function P = compute_M(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);
}¨*/