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# curvature_cortex

## (Toolbox/curvature_cortex.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

    [curvature_sigmoid,curvature]=curvature_cortex(arg1,arg2,arg3,arg4)

### Help Text

    CURVATURE_CORTEX - calculates cortex curvature
     function [curvature_sigmoid,curvature]=curvature_cortex(arg1,arg2,arg3,arg4)

     function [curvature_sigmoid,curvature]=curvature_cortex(FV,VertConn,sigmoid_const,show_sigmoid)
     FV is the Faces/Vertices structure used to calculate curvature
     VertConn is the vertices connectivity of FV
     sigmoid_const is the sigmoid coefficient (small values give smooth transition of convex to concave areas
     and vice versa). Use close to zero for linear transition.
     show_sigmoid chooses whether to show the sigmoid (1) or not (0)

     curvature returned is the surface curvature
     curvature_sigmoid returned is the curvature weighted by a sigmoid

     function [curvature_sigmoid]=curvature_cortex(curvature,sigmoid_const,show_sigmoid)
     Used to change the transition of positive and negative curvatures

     Remarks: Curvature_cortex uses an approximation of mean curvature. It calculates the mean angle between
     the surface normal of a vertex and the edges formed by the vertex and the neighbouring ones.

     See also VERTICES_CONNECTIVITY

### Cross-Reference Information

This function calls

    colnorm                            C:\BrainStorm_2001\Toolbox\colnorm.m

This function is called by

    bst_imaging_display                C:\BrainStorm_2001\Toolbox\bst_imaging_display.m
    manage_corticalscouts              C:\BrainStorm_2001\Toolbox\manage_corticalscouts.m

### Listing of function C:\BrainStorm_2001\Toolbox\curvature_cortex.m

    function [curvature_sigmoid,curvature]=curvature_cortex(arg1,arg2,arg3,arg4)
    %CURVATURE_CORTEX - calculates cortex curvature
    % function [curvature_sigmoid,curvature]=curvature_cortex(arg1,arg2,arg3,arg4)
    %
    % function [curvature_sigmoid,curvature]=curvature_cortex(FV,VertConn,sigmoid_const,show_sigmoid)
    % FV is the Faces/Vertices structure used to calculate curvature
    % VertConn is the vertices connectivity of FV
    % sigmoid_const is the sigmoid coefficient (small values give smooth transition of convex to concave areas
    % and vice versa). Use close to zero for linear transition.
    % show_sigmoid chooses whether to show the sigmoid (1) or not (0)
    %
    % curvature returned is the surface curvature
    % curvature_sigmoid returned is the curvature weighted by a sigmoid
    %
    % function [curvature_sigmoid]=curvature_cortex(curvature,sigmoid_const,show_sigmoid)
    % Used to change the transition of positive and negative curvatures
    %
    % Remarks: Curvature_cortex uses an approximation of mean curvature. It calculates the mean angle between
    % the surface normal of a vertex and the edges formed by the vertex and the neighbouring ones.
    %
    % See also VERTICES_CONNECTIVITY

    %<autobegin> ---------------------- 26-May-2004 11:29:55 -----------------------
    % --------- Automatically Generated Comments Block Using AUTO_COMMENTS ---------
    %
    % CATEGORY: Visualization
    %
    % Alphabetical list of external functions (non-Matlab):
    %   toolbox\colnorm.m
    %
    % At Check-in: $Author: Mosher $  $Revision: 8 $  $Date: 5/26/04 9:59a $
    %
    % This software is part of BrainStorm Toolbox Version 2.0 (Alpha) 24-May-2004
    %
    % Principal Investigators and Developers:
    % ** Richard M. Leahy, PhD, Signal & Image Processing Institute,
    %    University of Southern California, Los Angeles, CA
    % ** John C. Mosher, PhD, Biophysics Group,
    %    Los Alamos National Laboratory, Los Alamos, NM
    % ** Sylvain Baillet, PhD, Cognitive Neuroscience & Brain Imaging Laboratory,
    %    CNRS, Hopital de la Salpetriere, Paris, France
    %
    % See BrainStorm website at http://neuroimage.usc.edu for further information.
    %
    % Copyright (c) 2004 BrainStorm by the University of Southern California
    % This software distributed  under the terms of the GNU General Public License
    % as published by the Free Software Foundation. Further details on the GPL
    % license can be found at http://www.gnu.org/copyleft/gpl.html .
    %
    % FOR RESEARCH PURPOSES ONLY. THE SOFTWARE IS PROVIDED "AS IS," AND THE
    % UNIVERSITY OF SOUTHERN CALIFORNIA AND ITS COLLABORATORS DO NOT MAKE ANY
    % WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO WARRANTIES OF
    % MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, NOR DO THEY ASSUME ANY
    % LIABILITY OR RESPONSIBILITY FOR THE USE OF THIS SOFTWARE.
    %<autoend> ------------------------ 26-May-2004 11:29:55 -----------------------

    % Author: Dimitrios Pantazis, Ph.D.

    % ----------------------------- Script History ---------------------------------
    % DP 05-May-2002  Creation
    % JCM 19-May-2004 Commenting
    % ----------------------------- Script History ---------------------------------

    %choose whether to display bars
    if(~exist('VERBOSE','var')),
       VERBOSE = 1; % default non-silent running of waitbars
    end

    narg = nargin;
    if narg==4
        %assign inputs
        FV=arg1;
        VertConn=arg2;
        sigmoid_const=arg3;
        show_sigmoid=arg4;

        %ititialization
        nVertices=size(FV.vertices,1);

        %calculate normals and curvature of FV
        hf=figure('Visible','off');
        hp=patch(FV);
        normals=get(hp,'VertexNormals');
        close(hf);
        %Make the normals unit norm
        [nrm,normalsnrm]=colnorm(normals');

        if(VERBOSE)
            hwait = waitbar(0,sprintf('Calculating curvature...'));
            drawnow %flush the display
            step=round(nVertices/10);
        end
        %compute average angle on each vertex
        curvature=zeros(nVertices,1);
        curvature_sigmoid=zeros(nVertices,1);
        for i=1:nVertices %for all vertices
            if(VERBOSE)
                if(~rem(i,step)) % ten updates
                    waitbar(i/nVertices,hwait,sprintf('Calculating curvature...'));
                    drawnow %flush the display
                end
            end
            nNeighbours=length(VertConn{i}); %number of neighbours
            edgevector=FV.vertices(VertConn{i},:)-repmat(FV.vertices(i,:),nNeighbours,1); %vectors joining vertex with neighbours
            [nrm,edgevector]=colnorm(edgevector');
            curvature(i)=mean(acos(normalsnrm(:,i)'*edgevector))-pi/2;
            curvature_sigmoid(i)= 1./(1+exp(-curvature(i).*sigmoid_const))-0.5;
        end
        close(hwait);
    end

    if narg==3
        %assign inputs
        curvature=arg1;
        sigmoid_const=arg2;
        show_sigmoid=arg3;

        curvature_sigmoid=zeros(length(curvature),1);
        for i=1:length(curvature)
            curvature_sigmoid(i)= 1./(1+exp(-curvature(i).*sigmoid_const))-0.5;
        end
    end

    if(exist('show_sigmoid'))
        if(show_sigmoid)
            x=-pi/2:0.01:pi/2;
            y=1./(1+exp(-x*sigmoid_const))-0.5;
            figure;
            plot(x,y)
            grid on;
            title('Transition between negative and positive curvature');
        end
    end

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