Do you know the angle? You could rotate the image to align the edge with the grid and then project along one dimension:
%% example preparation
% create edge
img = zeros(100,100);
img(:, 50:100) = 1;
theta = 10; % deg
% create slanted edge
imgR = imrotate(img, theta, 'bilinear');
%% solution
% align slanted edge with grid
imgRR = imrotate(imgR, -theta, 'bilinear');
% project image data of both images
projectionR = sum(imgR, 1);
projectionRR = sum(imgRR, 1);
figure
subplot(1, 3, 1)
title('original image')
imagesc(imgR)
subplot(1, 3, 2)
title('rotated image')
imagesc(imgRR)
subplot(1, 3, 3)
hold on
plot(projectionR)
plot(projectionRR)
Bear in mind, that imrotate adds zeros to contain all the infomation in the rotated image. Adding zeros does of course not interfere with the summation, but you need to make sure that the alignment is correct.
