DIGITAL MONOPLOTTING AND PHOTO-UNWRAPPING
OF DEVELOPABLE SURFACES IN ARCHITECTURAL PHOTOGRAMMETRY
G. E. Karras, P. Patias*, E. Petsa
Department of Surveying, National Technical University of Athens, GR-15780 Athens, Greece
*Department of Surveying, The Aristotle University of Thessaloniki, GR-54006 Thessaloniki, Greece
Commission V, Working Group 4
KEY WORDS: Monoplotting, Digital Surface Development, Image Transformation, Mosaic, Architecture
ABSTRACT
It is to the interest of both the photogrammetrist and the non-expert user that image-based measuring techniques and
user-oriented packages applied to architectural and archaeological documentation be kept as simple as possible. In this
context, the potential of single-image techniques should be exhausted, confining stereoscopic procedures to irregularly-
shaped surfaces. This contribution discusses a monoscopic approach for regular 3D surfaces whose known analytical
expression provides the missing equation. Products may be in both vector and raster forms obtained via monoplotting
and orthoimaging, respectively. Further, in the cases of developable surfaces (e. g. circular cylinders) digital unwrapping
of the original images can also be performed. Finally, the basic concept is tested with six non-metric photographs fully
covering a small late-19"-centrury railway water-tower having the shape of a right circular cylinder. The unwinded plot of
the surface as well as the mosaic of the digitally unwrapped images are presented.
1. INTRODUCTION
Documentation and conservation of cultural heritage are
being increasingly seen as tasks of national — ultimately
international — priority. Due to the digital techniques, pho-
togrammetry now appears as more efficient and inexpen-
sive; today's user-oriented software is easier to handle by
non-experts, thus widening the potential spectrum of ap-
plication in architectural and archaeological recording.
Thanks to its simplicity, image rectification remains the
most popular method in this field for both photogramme-
trists and users. But when object anaglyph exceeds the
tolerances of planarity, stereo or multi-image configura-
tions need to be considered. Notwithstanding the merits of
commercial software packages for relatively simple work
in close-range, the use of more images at a time does not
appeal to non-expert users but also raises cost; besides,
the point-wise reduction schemes are basically adequate
only for objects consisting of planes (for instance, conti-
nuous non-straight lines such as the outlines of a curved
wall-stone cannot be mapped). Of course, complications
and requirements in instrumentation grow rapidly once
stereoviewing is introduced.
Thus, it is expedient to go beyond the limitation of near-
planarity (posed by rectification) by exhausting the poten-
tial of 'monoplotting'. Its application to irregularly shaped
surfaces requires a digital elevation model (DEM). Con-
trary to aerial mapping tasks where ground DEMs may al-
ready be at hand from previous work, in terrestrial ap-
plications DEMs have first to be created. But — 'halfway'
between flatness and irregular relief — smooth surfaces
which may be approximated analytically are often to be
met in close-range applications. Among these, quadrics
are most widely encountered: cylindrical, spherical, conic
or parabolic analytical surfaces are suitable for partly, or
fully, describing shape for a variety of ancient theatres or
tombs and also churches, monasteries, towers, rotundas,
domes, cupolas, vaults, ceilings, mills, lighthouses, facto-
ries, aqueducts, chimneys etc. (to which several industrial
objects may be added).
290
On the one hand, the need for geometric shape-fitting to
3D data is now situated within the context of the growing
use of CAD systems (Chandler & Cooper, 1991); on the
other, second order surface fitting to points sampled by
photogrammetry has been employed to establish theoreti-
cal shape and check discprepancies (Feltham, 1990; Fo-
tiou et al., 1991) as well as for mapping and orthophoto
production tasks (Restle & Stephani, 1988). Questions of
‘flattening’ non-developable surfaces, e.g. spherical, have
also been addressed (Vozikis, 1979).
In this contribution, the basic idea lies in the recognition
that known analytical surfaces provide the missing third
equation supplementing the collinearity condition, hence
permitting mapping from single images. Unlike conventio-
nal monoplotting, this procedure is direct (non-iterative).
However, certain questions regarding non-uniqeness of
solution have to be answered. In the case of a develop-
able surface, monoplotting can further result in unwinded
vector data. In fact, for such objects not only the genera-
tion of orthoimages is possible; digital 'unwrapping' of the
original imagery and subsequent mosaicking may also be
performed with simple means and suitable software. In
this manner, full all-around development retaining all the
wealth of the original raster data may be generated. Here,
the underlying concept is exemplified by the case of right
circular cylinders but may well be accordingly extended to
the other analytical surfaces.
2. ANALYTICAL SURFACE FITTING
The best-fitting analytic expression of a quadric surface is
determined either directly (in the simple cylindrical case a
perimeter suffices) or by fitting to redundant points mea-
sured geodetically or photogrammetrically. A distinction is
made between cases where surface type is given or ‘ob-
vious’ and its specific equation is to be found; and instan-
ces where the surface type is not assumed beforehand.
In this last case the full second order equation of nine in-
dependant unknowns is fitted to the 3D point set. General-
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
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