I = imread('myimage') ; % give your image
[y,x] = find(I==0) ; % white pixel value;
idx = boundary(x,y) ;
bnd = [x(idx) y(idx)] ; % boundary points data
Now you have boundary data points in hand. Make your line for which you want to get the intersection points with boundary. And then use https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections
Also there are other ways to get the intersection points without using the above. Read about knnsearch.
