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Figure 4: Automated shadow-based vertical extrusion of the
triangular prism from Figure 3
ing, due to edge fragmentation along the roof ridge caused
by shadow-casting protusions on the roof. However, the tri-
angular faces of the prisms are in close proximity at each
vertex, and PIVOT generates a third hypothesis by removing
the intermediate points and fitting the new hypothesis to an
idealized prism model in object space.
In this case, the rectangular volume supporting the prism does
not have enough visible edges to generate a 2-corner, and so
PIVOT's first hypothesis generation phase is unable to gen-
erate this volume. However, PIVOT looks for visible verticals
at corner points of prisms to estimate the height of a possible
peaked roof building [McGlone and Shufelt, 1994]; it also uses
object-space shadow mensuration to estimate building height.
The basic method is reminiscent of earlier work [Irvin and
McKeown, 1989], but the approach described here operates
in object space rather than image space. PIVOT iteratively
extrudes the prism from the ground plane in object space,
each time computing the unoccluded cast shadow boundary
in object space and projecting it back to image space. This
iteration halts when the projected shadow boundary has a
good match with the image gradient, with the proper dark-
to-light transition. Figure 4 shows the shadow boundaries
77
produced at each iteration; the best match with the image is
highlighted.
The building hypothesis mechanisms in PIVOT make heavy
use of the photogrammetric camera model, which allows
the system to generate geometrically consistent hypotheses,
merge partial volumes, extrude triangular prisms by mea-
suring verticals, and use date/time acquisition information
in conjunction with the camera model to perform rigorous
shadow mensuration. The use of photogrammetric analysis
leads to robust performance in difficult image analysis situ-
ations where traditional image space vision techniques fail,
while still utilizing only a single image.
5 3D BUILDING HYPOTHESIS VERIFICATION
The previous section closed by discussing the use of solar az-
imuth and elevation information in conjunction with a pho-
togrammetric camera model to perform shadow mensura-
tion of peaked roof building heights. This information is
used again, in the hypothesis verification stage of PIVOT,
to evaluate the consistency of photometric effects; namely,
the expected shadow-to-ground dark-to-light transition, and
the change in intensity across faces of buildings with respect
to the sun vector.
PIVOT tests shadow-to-ground consistency by computing the
median intensities inside two regions of the image, the shadow
region and the ground region. The shadow region is created
by projecting all building points to the ground along the sun
vector, and then computing the enclosing polygon of these
ground points. This polygon is then projected back to image
space, and the building boundary polygon is subtracted from
the shadow polygon, leaving the shadow region. A fixed-
width distance transform is then run on the shadow region,
and the building boundary region is subtracted again, leaving
a ground region which is adjacent to the shadow region. If
the median intensity of the ground region is less than that of
the shadow region, the building hypothesis is rejected. Figure
5 illustrates these regions, as well as the key features of the
next topic, inter-surface illumination consistency.
Qualitatively, we expect that surfaces which face the sun
should be brighter than those which face further away. We
implement this idea with a simple illumination model from
computer graphics, I = a + ß cos, where / is the surface
intensity, 0 is the angle between the surface normal and the
sun vector (we consider only surfaces with 0 « 7/2), and a
and B are constants which depend on surface material prop-
erties. For each surface, / (the median surface intensity)
and cosÓÜ are known; a and 3 are unknowns. Thus, for two
or more surfaces, a least-squares line fit solves for a and ß.
Then, if 3 < 0, we reject the building hypothesis, since its
surfaces appear brighter as they face further away from the
sun. PIVOT tests the consistency of roof and wall surfaces
separately, since roofs are frequently composed of a different
surface material than walls.
After rejecting photometrically inconsistent hypotheses,
PIVOT computes a sum of scores which measure the good-
ness of fit to image gradient, the intensity homogeneity of
each surface, and the magnitude of the shadow-to-ground
transition. All hypotheses are then sorted by score, and
PIVOT traverses the sorted list, each time selecting the hy-
pothesis H in the list with the highest score and removing any
other hypotheses in the list which were formed by attachment
or extrusion of H, or which form components of H if H was
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B6. Vienna 1996
