% This Matlab/C code performs level set image segmentation using
% (1) Several multiphase (or multiregion) methods, including a fast scheme which results
% in a significant reduction in the computational load (the complexity grows linearly
% as a function of the number of regions).
% (2) Several region-based image descriptions more complex than the standard piecewise
% constant Chan-Vese model, including
% - A Gamma description that is applicable to image data corrupted with a multiplicative
% noise, e.g., data of the type SAR (synthetic aperture radar) in remote sensing, and of
% the type ultrasound, in medical imaging.
% - A kernel-mapping description that is flexible enough to be applicable to a variety of
% real images and noise types, including medical, satellite and natural images.
% Before using this script, the user need to compile the C files by running compiler.m in Matlab
% These functions were tested on the following versions of MATLAB and C
% MATLAB version: 18.104.22.1681 (R2008b)
% C compiler: Lcc-win32 C 2.4.1
% This software can be used only for research purposes, and is provided "as is", without warranty
% of any kind. Please cite the papers and book mentioned below in any resulting publication.
% Formal and complete details on the implementations as well as on the derivation of the level set
% evolution equations for the various energy functional types used in the software can be found in
% the book "Variational and Level Set Methods in Image Segmentation"
% by Amar Mitiche and Ismail Ben Ayed 2010, Springer, 1st edition.
% The users need to enter the inputs here (a full description of the meaning of these inputs
% will follow)
% Description of the inputs
% a) input_image: the image to be segmented
% b) output_image: the segmentation result
% c) output_image: the segmentation result
% d) nb_regions: the number of segmentation regions
% e) nb_iterations: the number of iterations
% f) curvature: the weight of the curvature velocity (or smoothness term).
% The higher the weight, the smoother the segmentation boundaries. Noisy images (e.g., SAR data)
% often require a high smoothness weight, e.g., curvature='2000'.
% g) time_step: the gradient-descent time step of curve evolution. a large step yields faster
% evolution but lesser stability. Typical values of this parameter are in between 0.0001 and
% h) display_frequency: the frequency of display of the active curve during the evolution.
% For instance, when display_frequency='20', the active curve is superimposed on the image each
% 20 iterations.
% i) initialization: this option defines the initial curves which can be either circles centered
% about the middle of the image (initialization='1') or small circles all over the input
% image (initialization='1').
% j) segmentation_method: this variable defines the image model and/or the multiphase method.
% The following lists and explains the possible options for this variable:
% - segmentation method = 'gamma'
% This function implements level set image segmentation by minimizing a data term which measures
% the conformity of image data within each region to the Gamma model. It is usefull for image
% data corrupted with a multiplicative noise such as in radar and ultrasound data. Please cite
% the following paper in any resulting publication:
%  I. Ben Ayed, A. Mitiche, and Z. Belhadj, Multiregion level set partitioning on synthetic
% aperture radar images, IEEE Transactions on Pattern Analysis and Machine Intelligence,
% vol. 27, no. 5, pp. 793800, 2005.
% Note that this gamma segmentation function requires a small time step, e.g., time_step='0.0001'.
% - segmentation method = 'ker'
% This method implements a kernel function which maps implicitly the original image data into data
% of a higher dimension so that the piecewise constant model becomes applicable to images corrupted
% with various noise models. This leads to a flexible alternative to complex modeling of the image
% data. The function is applicable to a variety of real images such as medical, satellite and natural
% images. Please cite the following paper in any resulting publication:
%  M. Ben Salah, A. Mitiche and I. Ben Ayed, Effective Level Set Image Segmentation with a Kernel
% Induced Data Term, IEEE Transactions on Image processing, vol. 19, no 1, pp. 220-232, 2010.
% Note that this kernel segmentation function requires a small time step, e.g., time_step='0.0001'.
% - Segmentation method = 'mean'
% This function implements level set image segmentation by minimizing the classical Chan-Vese data
% term which measures the conformity of image data within each region to the piecewise constant model.
% - Segmentation method = 'Gaussian'
% This function implements a Gaussian generalization of the classical piecewise constant model.
% Note that the case of a number of regions more than 2 (the multiphase case) uses several curves which
% can intersect. Therefore, a two-region formulation cannot be generalized directly by assigning a region
% to the interior of each curve because region membership becomes ambiguous when the curves intersect.
% The following lists the possible options to evolve multiple curves so that, at convergence, the curves
% define a partition of the image domain:
% - Segmentation method = 'clust'
% This method embeds directly a simple partition constraint in the curve evolution equations.
% Starting from an arbitrary initial partition, the constraints implements the rule that if
% a point leaves a region, it is claimed by a single other region. The scheme is fast, and
% results in a significant reduction in the computational load (the complexity grows linearly
% as a function of the number of regions). Please cite the following papers in any resulting
%  I. Ben Ayed, A. Mitiche, and Z. Belhadj, Polarimetric image segmentation via maximum
% likelihood approximation and efficient multiphase level sets, IEEE Transactions on Pattern
% Analysis and Machine Intelligence, vol. 28, no. 9, pp. 14931500, 2006.
%  I. Ben Ayed and A. Mitiche: A Partition Constrained Minimization Scheme for Efficient
% Multiphase Level Set Image Segmentation. IEEE ICIP 2006, pp. 1641-1644
%  I. Ben Ayed and A. Mitiche, A region merging prior for variational level set image
% segmentation, IEEE Transactions on Image Processing, vol. 17, no. 12, pp. 23012313, 2008.
% - Segmentation method = 'part'
% This method implements a systematic general mapping between the segmentation regions and the
% regions defined by the curves and their intersections. The mapping guarantees, by definition,
% a partition at all times during curve evolution. Please cite the following paper in any resulting
%  A. Mansouri, A. Mitiche, and C. Vazquez, Multiregion competition: A level set extension of
% region competition to multiple region partioning, Computer Vision and Image Understanding, vol.
% 101, no. 3, pp. 137150, 2006.
% - Segmentation method = 'ker_part'
% This option implements the kernel method in  with the multiphase method in . Please cite these
% two papers in any resulting publication.
% Note that when Segmentation method = 'gamma', 'ker', 'mean' or 'gaussian' and when the number of regions is
% more than 2 (nb_regions> 2), the default multiphase method is the one described in the following papers:
%  C. Vazquez, A. Mitiche, Ismail Ben Ayed, Image segmentation as regularized clustering: a fully
% global curve evolution method, IEEE ICIP 2004, pp. 3467-3470.
% This multiphase method views image segmentation as spatially regularized image data clustering, leading to the
% simultaneous minimization of N ?1 functionals to segment an image into N regions, each minimization involving
% a single region and its complement. Please cite  in any resulting publication.
curvature = num2str(str2double(curvature) * str2double(time_step));