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SHAPE FROM SHADINGS UNDER PERSPECTIVE PROJECTION
AND TURNTABLE MOTION
Miaomiao Liu and Kwan-Yee K. Wong
Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong
Keywords:
Two-frame-theory, Shape recovery, Turntable motion.
Abstract:
Two-Frame-Theory is a recently proposed method for 3D shape recovery. It estimates shape by solving a first
order quasi-linear partial differential equation through the method of characteristics. One major drawback of
this method is that it assumes an orthographic camera which limits its application. This paper re-examines the
basic idea of the Two-Frame-Theory under the assumption of a perspective camera, and derives a first order
quasi-linear partial differential equation for shape recovery under turntable motion. Dynamic programming is
used here to provide the Dirichlet boundary condition. The proposed method is tested against synthetic and
real data. Experimental results show that perspective projection can be used in the framework of Two-Frame-
Theory, and competitive results can be achieved.
1 INTRODUCTION
Shape recovery is a classical problem in computer
vision. Many constructive methods have been pro-
posed in the literature. They can generally be classi-
fied into two categories, namely multiple-view meth-
ods and single-view methods. Multiple-view meth-
ods such as structure from motion (Tomasi, 1992)
mainly rely on finding point correspondences in dif-
ferent views, whereas single-view methods such as
photometric stereo use shading information to recover
the model.
Multiple-view methods can be further divided into
point-based methods and silhouette-based methods.
Point-based methods are the oldest technique for 3D
reconstruction (Pollefeys et al., 2001). Once feature
points across different views are matched, the shape
of the object can be recovered. The major draw-
back of such methods is that they depend on find-
ing point correspondences between views. This is
the well-known correspondence problem which itself
is a very tough task. Moreover, point-based meth-
ods do not work for featureless object. On the other
hand, silhouette-based methods are a good choice for
shape recovery of featureless object. Silhouettes are
a prominent feature in an image, and they can be ex-
tracted reliably even when no knowledge about the
surface is available. Silhouettes can provide rich in-
formation for both the shape and motion of an object
(Wong and Cipolla, 2001; Liang and Wong, 2005).
Nonetheless, only sparse 3D points or a very coarse
visual hull can be recovered if the number of images
used for reconstruction is comparatively small. Pho-
tometric stereo, which is a single-view method, uses
images taken from one fixed viewpoint under at least
three different illumination conditions. No image cor-
respondences are needed. If the albedo of the ob-
ject and the lighting directions are known, the surface
orientations of the object can be determined and the
shape of the object can be recovered via integration
(Woodham, 1980). However, most of the photometric
stereo methods consider orthographicprojection. Few
works are related to perspective shape reconstruction
(Tankus and Kiryati, 2005). If the albedo of the ob-
ject is unknown, photometric stereo may not be feasi-
ble. Very few studies in the literature use both shading
and motion cues under a general framework. In (Jin
et al., 2008), the 3D reconstruction problem is formu-
lated by combining the lighting and motion cues in
a variational framework. No point correspondences
is needed in the algorithm. However, the method in
(Jin et al., 2008) is based on optimization and requires
piecewise constant albedo to guarantee convergence
to a local minimum. In (Zhang et al., 2003), Zhang
et al. unified multi-view stereo, photometric stereo
and structure from motion in one framework, and
achieved good reconstruction results. Their method
has a general setting of one fixed light source and one
camera, but with the assumption of an orthographic
camera model.
28
Liu M. and K. Wong K. (2010).
SHAPE FROM SHADINGS UNDER PERSPECTIVE PROJECTION AND TURNTABLE MOTION.
In Proceedings of the International Conference on Computer Vision Theory and Applications, pages 28-35
DOI: 10.5220/0002821300280035
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