Okabe, Takahiro

EPrint Series of Department of Mathematics, Hokkaido University

Generalization of Photometric Stereo
Takahiro Okabe
Institute of Industrial Science
The University of Tokyo
Recovering the geometric structure of a scene is one of the fundamental
problems in computer vision. Photometric stereo is a technique for esti-
mating surface normals from a set of images of a stationary object taken
from a xed viewpoint and under dierent illumination conditions. Directly
acquiring surface normals is of critical importance for applications such as
image synthesis, because the appearance of an object is usually sensitive
to surface normals. Since Woodham rst addressed photometric stereo un-
der the assumptions of the Lambert model and calibrated light sources, its
generalization has extensively been studied.
In the rst half of this talk, we review recent progress of photometric
stereo: one direction of study is generalization to the case of unknown re-
ectance properties, and the other is generalization to the case of unknown
light source directions. The former direction of study makes use of general
properties of reectance such as isotropy, bilateral symmetry, and symme-
tries with respect to half-way vector, and therefore does not assume specic
reectance models. The latter direction resolves the ambiguity of shape re-
covery inherent in uncalibrated photometric stereo based on specularities,
interreections, nearby light sources, and priors on albedo.
In the last half of this talk, we present a novel technique, termed at-
tached shadow coding, for estimating surface normals from shadows when
both reectance properties and illumination conditions are unknown. Our
key idea is encoding surface points via attached shadows observed under
dierent light source directions and then estimating surface normals on the
basis of the similarity of the attached shadow codes. We theoretically show
that the distance between the codes at two surface points is equal to the
angle between the corresponding surface normals under the assumption of
uniform lighting and a convex object. Therefore, our method embeds high-
dimensional codes into a 3D surface normal space so that the inter-code
distances are preserved. Moreover, we extend the method in order to alle-
viate the eects of nonuniform lighting, and experimentally investigate the
eects of cast shadows.


Generalization of photometric stereo

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EPrint Series of Department of Mathematics, Hokkaido University