Three-dimensional shape reconstruction using
photometric stereo
Goal:
The goal of this project is to introduce a basic method for reconstruction of a three-dimensional
surface using the concept of photometric stereo. We will see that it is possible to reconstruct the
underlying shape of an object using only shading information (brightness or intensities of an
image)
Description:
Image formation:
We will assume that the surface is Lambertian and that it is illuminated at each image by a given
single light source. Lambertian surface means that a surface point has the same apparent
brightness from any viewing angle. At image location (x,y) the intensity of a pixel I(x,y) is given
by
,
=
,
(, )
where:
(, ) is the albedo (the extent to which the surface reflects light) at each point (a scalar)
is a three-dimensional vector of a relatively distant light source (the same for the whole image).
( includes the direction and the intensity of the light source.)
(, ) is a three-dimensional vector representing the direction of the surface normal at each
point
3D reconstruction from 3 images
The input images are images of the same scene taken from the same camera view but under
different lighting conditions.
When we are interested in finding the three-dimensional shape of the imaged surface, we
basically would like to recover the surface normals
(, ) and integrate them to get the surface
,
(depth map). Since in our case the light will be given, we can recover
(, ) =
,
(, ) from as few as three images. For each pixel we have
1
(, )
2
(, )
3
(, )
=
(, )
1
2
3
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