- Read Images
Since Matlab cant handle tga files, I convert TGA files into BMP files
on the fly using ImageMagick's convert commandline tool.
code will need linux machine with "convert" command available.
For calibrating the direction of the light using the chrome ball, I
- Determined the center of the ball by averaging all pixels in mask with value=255, say [xc yc]
- Similarly determined the center of the bright spot, say [xl yl]
- Determined the radius by averaging the distance between points with value in mask greater than 0 but less than 255(boundary points). Say r.
- N = [xl-xc yl-yc sqrt(r^2 - (xl-xc)^2 - (yl-yc)^2)] normalized to norm=1. R=[0 0 -1]
- L = 2*N*R' - R
For detemining the normals, I
- For each pixel in ever image, combine the values for each
- Try to minimize the objective function, (w*I - w*L*g) where w =
- I even attempted using the hat function as the weight just like
the one used in HDR, but that had almost no impact on the output.
- N = (1/norm(g))*g. k = norm(g).
- Color Albedo
For obtaining the color albedo, I used the equation I.J/J.J as given
on the project page. This seems to work well.
- Least Square Fitting
For solving this problem, I
- Created an index of pixel co-ordinates where mask value is
- Created two sparse matrices A and b
- A and b contain rows corresponding to gradient in each direction as
per the equations on the project page. Since every row in A has only
two non-zero entries, the matrix is very sparse.
- A has one row to fix one pixel to a height > 0 so that the entire
surface appears to be above 0.
There were multiple small changes that I attempted.
- Used a hat weighing function for the normal computation. Causes
some peaks - look at the eyes.
- Used no weighing function for the normal computation. Still doesn't get rid off the peaks.
- Used a hat weighing function for surface estimation. So every
row in the matrix A and b was scaled by the intensity. Creates wierd
peaks in the image.
- Used the intensity itself as the weighing function. This also
creates peaks in the image.
- To reduce the peaks in the surface, I added another
minimization term to minimize the difference between the adjacent
points i.e. minimize the sum of squared differences between
neighbouring pixels. This still keeps A sparse.
This works well to
reduce noise. This is what I have used in all the output images.
- I used MATLAB's builtin "pcg" function to solve the surface
estimation equation with A'Az = A'b.
The result was not very
different from the output given by \.
NOTE: They both use the
squared difference terms mentioned in the previous point. Also PCG
with 100 iterations gave a very noisy answer, so I used 1000
| With \
|| With pcg (1000 iterations)
- Sometimes, the Z-values gradually increase to high
values. Hence, I tried adding a constraint to minimize the norm of
the Z values similar to HDR.
But this doesn't help much because I
was raising the entire surface. Also without that condition, even if
the norm is small, 10^-3 would appear as a peak if all values are
10^-3. The norm in this case would still be low.
- How to Run
Copy the psmImages folder into the directory that contains
Make sure convert is a valid command or add /usr/bin/
1. stereo e.g. stereo buddha
2. Various parameters that can be changed from stereo.m
- usePCG - Use PCG for solving surface estimation.
- useSquaredDiff - Use the squared differences between adjacent
- useWeightsSurf - Use weights for estimating the surface in computeZ.m
- useWeightsNormal - Use weights for estimating the normal in getNormals.m
RGB-encoded Normals(absolute values)
1. Woodham, Optical Engineering, 1980, Photometric Stereo.