图像分割是图像分析的关键步骤，而水平集方法是图像分割的一项热门方法，它有着许多

function [phi] = evolve2D(phi, dx, dy, alpha, iterations, accuracy, is_signed_distance, normal_evolve, Vn, vector_evolve, u, v, kappa_evolve, b) % % function [phi] = evolve2D(phi, dx, dy, iterations, accuracy, ... % is_signed_distance, normal_evolve, Vn, vector_evolve, u, v, kappa_evolve, b) % % Calculates evolution for a 2D curve (3D level set function) phi. % phi is the input level set function. % % dx and dy are the resolution of the grid at x and y dimensions. % alpha is a constant for calculating the euler step (dt). Should % be between 0 and 1. 0.5 is quite safe whereas 0.9 can be risky. % iterations specifies the number of iterations before the function returns. % normal_evolve, vector_evolve, kappa_evolve should be either set to 0 and 1. This % indicates if these forces are present or not. If any of these are set to 1, % corresponding variables (e.g. Vn, u, v, b) should not be an empty array []. if % either normal_evolve or vector_evolve are set to 1, accuracy needs to be specified, % otherwise accuracy can be set to an empty array. Allowed values for accuracy are % 'ENO1', 'ENO2', 'ENO3', 'WENO'. These correspond to 1st, 2nd, 3rd and 5th order % accurate schemes for calculating the derivative of phi. if both normal_evolve and % vector_evolve are set to 1, then is_signed_distance needs to be specified. If phi is % approximately a signed distance function, set this variable to 1. If % is_signed_distance == 1, Godunov scheme will be used, otherwise Stencil Local % Lax-Friedrichs (SLLF) scheme will be used (See Osher&Fedkiw section 6.4). % % Other variables (these are either a scalar or of the same size as phi): % Vn: Force in the normal direction. % u: x component of the vector field % v: y component of the vector field % b: this specifies the weighting for the curvature (always positive everywhere). % % Author: Baris Sumengen sumengen@ece.ucsb.edu % http://vision.ece.ucsb.edu/~sumengen/ % tic if alpha <= 0 | alpha >= 1 error('alpha needs to be between 0 and 1!'); end % expand parameters if they are scalar if length(Vn) == 1 Vn = Vn.*ones(size(phi)); end if length(u) == 1 u = u.*ones(size(phi)); end if length(v) == 1 v = v.*ones(size(phi)); end if length(b) == 1 b = b.*ones(size(phi)); end % Understand what kind of evolution the user is interested in. if (normal_evolve == 1) & (vector_evolve == 1) & (kappa_evolve == 1) evolution_type = 'normal_vector_kappa'; if isempty(Vn) | isempty(u) | isempty(v) | isempty(b) error('Some of the variables should not be empty!') end switch(accuracy) case 'ENO1' init_normal = @init_normal_ENO1; init_vector = @init_vector_ENO1; if is_signed_distance == 1 evolve_normal_vector = @evolve_normal_vector_ENO1_SD; else evolve_normal_vector = @evolve_normal_vector_ENO1; end case 'ENO2' init_normal = @init_normal_ENO2; init_vector = @init_vector_ENO2; if is_signed_distance == 1 evolve_normal_vector = @evolve_normal_vector_ENO2_SD; else evolve_normal_vector = @evolve_normal_vector_ENO2; end case 'ENO3' init_normal = @init_normal_ENO3; init_vector = @init_vector_ENO3; if is_signed_distance == 1 evolve_normal_vector = @evolve_normal_vector_ENO3_SD; else evolve_normal_vector = @evolve_normal_vector_ENO3; end case 'WENO' init_normal = @init_normal_WENO; init_vector = @init_vector_WENO; if is_signed_distance == 1 evolve_normal_vector = @evolve_normal_vector_WENO_SD; else evolve_normal_vector = @evolve_normal_vector_WENO; end otherwise error('Desired type of the accuracy is not correctly specified!'); end elseif (normal_evolve == 1) & (vector_evolve == 1) & (kappa_evolve == 0) evolution_type = 'normal_vector'; if isempty(Vn) | isempty(u) | isempty(v) error('Some of the variables should not be empty!') end switch(accuracy) case 'ENO1' init_normal = @init_normal_ENO1; init_vector = @init_vector_ENO1; if is_signed_distance == 1 evolve_normal_vector = @evolve_normal_vector_ENO1_SD; else evolve_normal_vector = @evolve_normal_vector_ENO1; end case 'ENO2' init_normal = @init_normal_ENO2; init_vector = @init_vector_ENO2; if is_signed_distance == 1 evolve_normal_vector = @evolve_normal_vector_ENO2_SD; else evolve_normal_vector = @evolve_normal_vector_ENO2; end case 'ENO3' init_normal = @init_normal_ENO3; init_vector = @init_vector_ENO3; if is_signed_distance == 1 evolve_normal_vector = @evolve_normal_vector_ENO3_SD; else evolve_normal_vector = @evolve_normal_vector_ENO3; end case 'WENO' init_normal = @init_normal_WENO; init_vector = @init_vector_WENO; if is_signed_distance == 1 evolve_normal_vector = @evolve_normal_vector_WENO_SD; else evolve_normal_vector = @evolve_normal_vector_WENO; end otherwise error('Desired type of the accuracy is not correctly specified!'); end elseif (normal_evolve == 1) & (vector_evolve == 0) & (kappa_evolve == 1) evolution_type = 'normal_kappa'; if isempty(Vn) | isempty(b) error('Some of the variables should not be empty!') end switch(accuracy) case 'ENO1' init_normal = @init_normal_ENO1; evolve_normal = @evolve_normal_ENO1; case 'ENO2' init_normal = @init_normal_ENO2; evolve_normal = @evolve_normal_ENO2; case 'ENO3' init_normal = @init_normal_ENO3; evolve_normal = @evolve_normal_ENO3; case 'WENO' init_normal = @init_normal_WENO; evolve_normal = @evolve_normal_WENO; otherwise error('Desired type of the accuracy is not correctly specified!'); end elseif (normal_evolve == 1) & (vector_evolve == 0) & (kappa_evolve == 0) evolution_type = 'normal'; if isempty(Vn) error('Some of the variables should not be empty!') end switch(accuracy) case 'ENO1' init_normal = @init_normal_ENO1; evolve_normal = @evolve_normal_ENO1; case 'ENO2' init_normal = @init_normal_ENO2; evolve_normal = @evolve_normal_ENO2; case 'ENO3' init_normal = @init_normal_ENO3; evolve_normal = @evolve_normal_ENO3; case 'WENO' init_normal = @init_normal_WENO; evolve_normal = @evolve_normal_WENO; otherwise error('Desired type of the accuracy is not correctly specified!'); end elseif (normal_evolve == 0) & (vector_evolve == 1) & (kappa_evolve == 1) evolution_type = 'vector_kappa'; if isempty(u) | isempty(v) | isempty(b) error('Some of the variables should not be empty!') end switch(accuracy) case 'ENO1' init_vector = @init_vector_ENO1; evolve_vector = @evolve_vector_ENO1; case 'ENO2' init_vector = @init_vector_ENO2; evolve_vector = @evolve_vector_ENO2; case 'ENO3' init_vector = @init_vector_ENO3; evolve_vector = @evolve_vector_ENO3; case 'WENO' init_vector = @init_vector_WENO; evolve_vector = @evolve_vector_WENO; otherwise error('Desired type of the accuracy is not correctly specified!'); end elseif (normal_evolve == 0) & (vector_evolve == 1) & (kappa_evolve == 0) evolution_type = 'vector'; if isempty(u) | isempty(v) error('Some of the variables should not be empty!') end switch(accuracy) case 'ENO1' init_vector = @init_vector_ENO1; evolve_vector = @evolve_vector_ENO1; case 'ENO2' init_vector = @init_vector_ENO2; evolve_vector = @evolve_vector_ENO2; case 'ENO3' init_vector = @init_vector_ENO3; evolve_vector = @evolve_vector_ENO3; case 'WENO' init_vector = @init_vector_WENO; evolve_vector = @evolve_vector_WENO; otherwise error('Desired type of the accuracy is not correctly specified!'); end elseif (normal_evolve == 0) & (vector_evolve == 0) & (kappa_evolve == 1) evolution_type = 'kappa'; if isempty(b) error('Some of the variables should not be empty!') end else error('Incorrect input parameters! normal_evolve, vecto