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DEFORMABLE MODELS AS A PHOTOGRAMMETRIC MEASUREMENT
TOOL - POTENTIAL AND PROBLEMS
Eberhard Gülch
Institute of Photogrammetry, University Bonn, D-53115 Bonn, Germany, e-mail: ebs@ipb.uni-bonn.de
on leave from: Department of Geodesy and Photogrammetry, KTH, S - 10044 Stockholm, Sweden
Commission III, Working Group 2
KEY WORDS: Cartography, automation, geometric feature extraction, active contour models, deformable surfaces
ABSTRACT
Deformable models or snakes are a shape extraction tool based on energy minimization functions. The contour or surface
extracted through an iteration process is a compromise between the external energies defined by image features and the internal
energies of the deformable model. During the last decade substantial research efforts have been reported on improvement and
extension of that method. We will describe several representative approaches on open and closed contours and surfaces and
analyse the encountered difficulties. We will add our own experience with 2D snakes. Snakes have been applied to all kinds of
images, from satellite to medical imagery, from mono-images to image sequences in 2D and 3D. The independence from sensor
type and application area makes them interesting for photogrammetry. The largest potential is currently in the usage as a
refinement tool for interactive measurements with simple models. Most applications are specific and require substantial user
guidance and validation. The lack of quality estimates, the quite huge number of parameters to be set by an operator and the
large computational efforts still hinder a usage on a broader basis as a generic photogrammetric measurement tool.
1. MOTIVATION
Deformable models or active contour models or deformable
surfaces are feature extraction tools based on energy
minimization functions (Kass et. al., 1987). External
energies can be image energies derived from grey values or
image features. Internal energies describe the behaviour, e.g.
rigidity of the deformable model. The contour or surface
extracted through an iteration process is a compromise
between the external energies and the internal energies of the
deformable model. The method was clearly designed for
interactive extraction of image contours, but has potential
for more automated surface reconstruction or motion tracking
as well. In this report we will examine how this method could
be or is used for photogrammetric applications or related
fields. We will discuss several representative approaches that
have improved the performance of the original method and
analyse and compare the encountered difficulties. We will add
own experience with 2D snakes in satellite, aerial and
medical imagery and discuss the potential and problems to
introduce deformable models on a broader basis in photo-
grammetric applications like e.g. topographic mapping.
2. DEFORMABLE MODELS
The published reports of the last years in photogrammetry
indicate intensified research on deformable models, which is
still very much dominated by the computer vision field.
Development started on contours and continued on surfaces.
2.1 Basic approach for deformable models
The basic approach is summarized here as presented by Kass
et al., 1987. The behaviour of an active contour model
(snake) is controlled by internal and external forces. The
energy of a deformable model depends on where it is placed
and how its shape changes locally in space. The active
contour can be described in parametric representation with
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
v(s) = (x(s),y(s)) s = arc length (1)
The snake attracts to features of an image structure by
minimizing an integral measure which represents the snake's
total energy. The energy functional is:
i 1
F make: he (2)
The total energy is a sum of single energies. During
minimization the snake is deforined to find an optimal
compromise between the constraints introduced by internal
forces (Ejnt) and external forces such as image forces (Eima)
and external constraint forces (Econ).
Internal forces open the possibility to introduce geometric
constraints on the shape of the contour. The internal energy
is composed of a first order term and a second order term
forcing the active contour to act like a membrane or a thin
plate, thus introducing material parameters:
Eint(s) = (as) Ivs(s)I2 + ß(s) Ivss(s)I? /2 (3)
The tension is controlled by a(s) and the rigidity by B(s).
Image forces attract the snake to salient features in the
image. The image energy Ejma is written as a combination of
different weighted energy terms. External constraint forces
are provided by higher level image interpretation or user-
interface. The user selects starting points and can apply
forces interactively on the snake during the minimization
process, like a spring or a repulsion force.
The energy minimization itself is done in four steps. A
variational integral is set up in the continuos space, a pair of
Euler equations is derived, the equations are discretized and
the position vectors are solved iteratively with a given step
size y until convergence is reached.
2.2 Major extensions of deformable models
Since the initialization by Terzopoulos et al. the work on
deformable models has expanded very much. Major
variations and extensions of the approach have been
reported. We can observe conceptual work like in Amini et
al., 1988, Fua and Leclerc, 1988, Cohen, 1991, Szeliski and
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