Activity 13: Photometric Stereometry

🕑04:02, 13 Nov 2019

For this activity [1], we are given four px intensity maps with different lighting conditions, shown in Fig.&nbsp1. We can stack these intensity maps into one multidimensional array . The source matrix is provided and is defined as

We can then solve for by least squares approximation:

and then normalize to get the surface normal vectors

The surface elevation is expressed as

which are related to the surface normals by

The surface elevation at point is given by

Using the Frankot-Chellappa algorithm [2], we can numerically perform this integral using Fourier transforms:

where and are the Fourier transform and its inverse, respectively, and is an arbitrarily small constant that allows the formulation to remain valid at . The recovered surface and its contour projection is shown in Fig. 2.

References

1. M. N. Soriano, A13 - Photometric stereo (2019).

2. R.T. Frankot, and R. Chellappa, A method for enforcing integrability in shape from shading algorithms. IEEE Trans. on Pattern Analysis and Machine Intelligence 10(4) (1988).

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