 Photometric
Stereo: Introduction
| Introduction | Advantages | Equations | Gradient & albedo | PS3
vs PS4 |
Photometric stereo (PS) gives us ability to estimate local surface
orientation by using several images of the same surface taken from
the same viewpoint but under illumination from different directions
(see figures below). It was first introduced by Woodham in 1980. The
light sources are ideally point sources some distance away in different
directions, so that in each case there is a well-defined light source
direction from which to measure surface orientation. Therefore, the
change of the intensities in the images depends on both local surface
orientation and illumination direction.
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| Photometric stereo geometry |
Photometric stereo example images |
The orientation of each surface facet is expressed in terms of the
derivatives of the surface at that point: p(x,y) and q(x,y). For a
given image, the appearance of an object varies with the derivatives
of the object's surface p(x,y) and q(x,y). If we hold the lighting
and viewing geometry constant we can express the intensity of a facet
as a function of its surface derivatives, using the Reflectance Map.
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A sphere
rendered with Lambert's law (left); intensity can be expressed
as a function of p and q using the reflectance map (right).
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We want to infer two quantities the surface derivatives, p and q,
from one measurement - intensity, i. This is an ill-posed problem -
the facet can appear equally bright for several different orientations.
In other words we can only identify a curve of possible solutions.
If we rotate the light source to a different azimuth, the reflectance
function also rotates. A particular facet's position on the reflectance
map doesn't change. Threfore it should lie at the intersection of the
two solution curves. For a surface that obeys Lambert's law three
images are required to resolve any possible ambiguities.
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A facet's
intensity only allows us to identify a curve of possible solutions.
However, if we light it from a different direction we can identify
the facet's orientation from the intersection of the solution
curves.
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| Introduction | Advantages | Equations | Gradient & albedo | PS3
vs PS4 |
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