GUARNIERI, ALBERTO
AN APPROACH TO ESTIMATE OF 2D-3D MOTION OF SURFACES:
THE FREQUENCY DOMAIN TECHNIQUE
G..M. Cortelazzo* A. Guarnieri* L. Lucchese** A.Vettore*
* C.LR. GEO, Interdept. Research Center of Cartography, Photogrammetyr,Remote Sensing and GIS,
University of Padua — Italy, , vettoan@ux 1 .unipd.it
** Dept. of Electrical and Computational Engineering , University of California, Santa Barbara, USA
Working Group V/5
KEY WORDS: Algorithms, Computer vision, Image registration, 3D Modeling
ABSTRACT
Phase correlation is one of the robustest methods for estimating planar translations: it is a global approach because it
operates in the frequency domain using the whole image information and not just a selected subset of the image as the
feature-based methods do. The good characteristics of phase correlation for estimating planar translations were found to
be a strong motivation for its extension to the estimation of planar rotations. An original algorithm for estimating planar
rotations inspired by phase correlation is presented in this work. Practical experimentation on real imagery confirm the
expected robustness of the method. Furthermore, a natural extension of the proposed algorithm will be also presented
for 3D shapes motion estimation. Free-form 3-D surfaces registration is a fundamental problem in 3-D imaging, tipi-
cally approached by extensions or variations of the ICP algorithm [2,10]. In this paper an alternative procedure for 3-D
motion estimation wiil be suggested, based on the Fourier transform of the 3-D intensity function, implicitly described
by the registered time-sequences of range data. As the proposed method is very suitable for 2D and 3D modeling of
cultural heritages, some examples and results of its application to Madonna of Donatello, located in the Basilica of St.
Anthony in Padua, will be also presented.
1. ESTIMATION OF PLANAR ROTATIONS BY MEANS OF PHASE CORRELATION
Phase correlation has been developed in order to estimate planar translations between images pairs and has been shown
to be one of the most robust methods for estimating planar translations [3,5]. This method relies upon the following
concept: let g(x), xc R?, be an image and g,(x) = g1(x-t), te R?, be a translated version of g1(x). Denote as G;(k) =
F19:()| k], k = [ky, ky]r, the 2-D cartesian Fourier transform of g;(x), i = 1, 2; then
G,(k) = Get ; (1)
differs from G;(k) only in a phase shift. Therefore from
CG. KK). ous
ok) = = Q)
IG; (K)G, (k))
and
q(x) - F"|Qao x] - 8, (xt) G)
one can estimate translational vector t as the coordinates of the peak of impulsive signal g(x). This work extends this
idea to the case of planar rotations; in this case let f(x) and f(x), xe R*, respectively denote an image and its version
rotated by an angle ¢, i.e., in cartesian coordinates
f(x) = £i(R(p) x) (4)
where
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 319
