Plot normal vector field 3D - matlab

Question

I am implementing the algorithm for Photometric Stereo where I have already calculated the normals from a set of images with different light directions.
How can I plot the normal vector field in matlab? I have a matrix of normals of size (N x 3).

Answer 1

I'm afraid you have left out a step. You need to retrieve the depth map from the surface normals, and then you can start plotting. To see how to do this, you can check out section 4 of the following paper:
http://www.wisdom.weizmann.ac.il/~vision/photostereo/Photometric%20Stereo%20with%20General%20Unknown%20Lighting%20-%20BasriJacobsKemelmacher_ijcv06.pdf
There are other resources on the web too; I don't know of any built-in function in any Matlab library, but I don't have the Computer Vision toolbox, so who knows?

Answer 2

I suspect you are looking for quiver3.

Answer 3

You need to present normals field, as an gradient field, then you can,use quiver function. And in gradient field previously normalized triple {pn,qn,rn}, the data is presented in such a way , as to rend the third component of it always equal to one (at least in theory). I mean with rn=1, or should I now say, that now : R=1, and you actually need only {P,Q} coomponents to present contents of gradient field with ordinary 2D quiver function. Thus, gradient vector is something quite different and distinct from normals field, because: P=pn/sqrt(pn^2+qn^2+rn^2) , and Q=qn/(pn^2+qn^2+rn^2) POINTWISELY saying.
However you don't bother with double for loops, run over X,Y directions, cause POINTWISELY, correctly rendered calculations for gradient field from normals, is the following: P=pn./(pn.^2 + qn.^2 + rn.^2).^(1/2);, and so on.
You can see as well: http://www.mathworks.com/matlabcentral/fileexchange/authors/126090/

Answer 4

You need to present normals field, as an gradient field, then you can use a Matlab's quiver function. And in gradient field, the previously normalized triple {pn,qn,rn}, of the data, is presented in such a way, as to rend the third component of it always equal to one (at least in theory).
I mean with rn = 1, or should I now say, that now with: some R=1, you actually need only {P,Q} coomponents to present contents of gradient field with ordinary 2D quiver function. Thus, gradient vector is something quite different and distinct from normals field, because:
P=pn/sqrt(pn^2+qn^2+rn^2) , and Q=qn/(pn^2+qn^2+rn^2) POINTWISELY saying.
However you don't bother with double for loops, which would be run over X, Y directions, cause POINTWISELY, correctly rendered calculations for gradient field from normals, are the following:
P=pn./(pn.^2 + qn.^2 + rn.^2).^(1/2); , and: Q=qn./(pn.^2 + qn.^2 + rn.^2);
You can see as well:
http://www.mathworks.com/matlabcentral/fileexchange/authors/126090/
Briefly saying, the gradient field always represents slopes on X, Y directions, while descending exactly one height unit alongside Z axis on the 3D surface retrieved with for instance Photometric Stereo algorithm. That is why the third component in quiver function visualization is always equal to one (i.e. R = 1), and practically irrelevant.
I have posted, last month, some codes, on THE simplest Photometric Stereo methods, on Mathworks Web pages, due to some span of time available to tide it all up, I mean my own so far produced codes in Matlab...