%function to calculate the normalised line integral around a circular contour
%A polygon of large number of sides approximates a circle and hence is used
%here to calculate the line integral by summation
%INPUTS:
%1.I:Image to be processed
%2.C(x,y):Centre coordinates of the circumcircle
%Coordinate system :
%origin of coordinates is at the top left corner
%positive x axis points vertically down
%and positive y axis horizontally and to the right
%3.n:number of sides
%4.r:radius of circumcircle
%5.part:To indicate wheter search is for iris or pupil
%if the search is for the pupil,the function uses the entire circle(polygon) for computing L
%for the iris only the lateral portions are used to mitigate the effect of occlusions 
%that might occur at the top and/or at the bottom
%OUTPUT:
%L:the line integral divided by circumference

function [L]=lineint(I,C,r,n,part)
theta=(2*pi)/n;% angle subtended at the centre by the sides
%orient one of the radii to lie along the y axis
%positive angle is ccw
%Author:Anirudh S.K.
%Department of Computer Science and Engineering
%Indian Institute of Techology,Madras
rows=size(I,1);
cols=size(I,2);
angle=theta:theta:2*pi;
x=C(1)-r*sin(angle);
y=C(2)+r*cos(angle);
if (any(x>=rows)|any(y>=cols)|any(x<=1)|any(y<=1))
    L=0;
    return
    %This process returns L=0 for any circle that does not fit inside the image
end
%lines 34 to 42 compute the whole line integral
if (strcmp(part,'pupil')==1)
          s=0;
          for i=1:n
          val=I(round(x(i)),round(y(i)));
          s=s+val;
          end
          
          L=s/n;
      end
%lines 44 onwards compute the lateral line integral(to prevent occlusion affecting the results,the pixel average is taken only along the lateral portions)
if(strcmp(part,'iris')==1)
          s=0;
          for i=1:round((n/8))
          val=I(round(x(i)),round(y(i)));
          s=s+val;
          end
          
          for i=(round(3*n/8))+1:round((5*n/8))
          val=I(round(x(i)),round(y(i)));
          s=s+val;
          end
          
          for i=round((7*n/8))+1:(n)
          val=I(round(x(i)),round(y(i)));
          s=s+val;
          end
          
          L=(2*s)/n;
end