Vector components along another one

this is my situation: I have a 30x30 image and I want to calculate the radial and tangent component of the gradient of each point (pixel) along the straight line passing through the centre of the image (15,15) and the same (i,j) point.

[dx, dy] = gradient(img);

for i=1:30
    for j=1:30
        pt = [dx(i, j), dy(i,j)];
        line = [i-15, j-15];
        costh = dot(line, pt)/(norm(line)*norm(pt));
        par(i,j) = norm(costh*line);
        tang(i,j) = norm(sin(acos(costh))*line);
    end
end

is this code correct?

Answer 1

[Roger Stafford]

In the line

   par(i,j) = norm(costh*line);

it should be

   par(i,j) = costh*norm(line);

to allow the inward and outward radial components to be distinguished.

In the line

   tang(i,j) = norm(sin(acos(costh))*line);

you will be unable to distinguish between clockwise and counterclockwise tangential components. To correct this you need to compute something other than the cosine of the angle between the two vectors. The sine of acos will always be positive. I would recommend this for both 'par' and 'tang':

   line = line/norm(line);
   tang(i,j) = line(1)*pt(2)-line(2)*pt(1);
   par(i,j)  = line(1)*pt(1)+line(2)*pt(2);

instead of computing 'costh'.