Photometric Stereo Reconstruction. Dr. Maria E. Angelopoulou. (1). Photometric Stereo (PS) Basics. Input images: same viewpoint / different illumination directions Varying albedo values → minimum of 3 illumination directions
Dr. Maria E. Angelopoulou
+ ability to operate on featureless objects
+ absence of feature matching errors
+ computational simplicity
controlled imaging conditions
inaccurate simplifying assumptions
need for off-line calibration sessions & exclusive access to the imaging system
Provide an autonomous, purely data-driven PS reconstruction system that is suitable for real-life applications.
Focus on: uncalibrated flatfielding & uncalibrated light estimation.
Diffuse light component as a degradation factor for intended directional lighting. Indicate up to which ratio of ambient to directional light component photometric stereo gives useful reconstruction outputs.
The variation in brightness for a given pixel is solely dependent on the angle between the illumination vector and the surface normal at the corresponding real-world surface facet.
Use a grey piece of card as calibrating device.
Photograph the card multiple times under the same illumination as the main imaging session.
Perform 2D 2nd order polynomial fitting on the flatfielding reference images to smooth out high frequency noise. This gives the illumination fields .
For every point of the image plane, the new pixel value is computed as
(c) uncalibrated flatfielding
- The relationship between surface gradients and brightness is captured by the reflectance map of the surface.
- A Lambertian sphere illuminated by a point source in direction
has a reflectance map of the form:
denote the global maximum of the kth
reflectance map. It is
- Thus the surface orientation that maximizes the Lambertian
reflection component is the one for which the normal vector
points to the illumination source!
- Let the gradient at surface patch o be .
- If patch o is projected at pixel ,
then the measured image intensity at that pixel is given by the
image irradiance equation as
- Due to equations
the global maximum of the Lambertian reflectance map
corresponds to the maximum intensity measurement , the
luminous dot. If the latter resides at and
is the projection of the real-world patch m then
- If a Lambertian sphere is photographed, the normal vector can
be recovered at any point and can be estimated once the
luminous dot is identified.