sun vector
surface normal
Figure 5: Computing the consistency of inter-surface intensi-
ties and the shadow-ground transition
itself formed by attachment or extrusion. Finally, if building
hypotheses overlap in object space, the overlapping hypoth-
esis with the best score is kept, and the other overlapping
hypotheses are rejected.
Before proceeding to a performance analysis for PIVOT, it is
important to note that the qualitative shadow analysis and
illumination consistency tests, as well as the object space
overlap tests, require the use of a rigorous camera model.
The verification of 3D building hypotheses necessitates the
ability to accurately project points to object space from image
space and vice versa.
6 RESULTS AND ANALYSIS
PIVOT has been tested on 22 images to date, and ex-
perimentation continues on a growing body of test scenes.
In this section, results are presented for two of these im-
ages; the FLAT.L image used in previous sections, and the
RADT5WOB image, distributed under the RADIUS research
initiative. We use performance evaluation metrics which have
been thoroughly described elsewhere [McGlone and Shufelt,
1994]; before proceeding with the results, we first briefly de-
scribe this evaluation process.
First, ground-truth site models were compiled using the
SiteCity interactive modeling system [Hsieh, 1996], which
uses rigorous photogrammetric solutions and semi-automated
feature extraction techniques to aid in site model compila-
tion. These ground-truth models are then compared with the
PIVOT models in 2D (image space) and 3D (object space). In
2D, models are compared on a pixel-by-pixel basis; in 3D, on
a voxel-by-voxel basis (object space is subdivided into cubes
0.5m on a side for this evaluation). The ground truth is used
to label each pixel/voxel as building or background. Then, a
true positive (TP) pixel is one labeled as building by both the
ground-truth and PIVOT; a true negative (TN) is one labeled
as background by both. A false positive (FP) is labeled as
building by the ground-truth, but as background by PIVOT;
a false negative (FN) is the opposite of an FP.
78
Figure 6: PIVOT results on FLAT_L
evaluation building branch | miss | quality
detection % | factor | factor %
2D 67.6 0.56 0.48 49.0
3D 54.9 0.82 0.82 37.9
Table 7: Evaluation results for FLAT_L
The number of TP, FP, TN, and FN pixels/voxels are
counted, and then four metrics are computed:
Building detection percentage: 100 x TP/(TP + F'N)
Branching factor: FP/TP
Miss factor: FN/TP
Quality percentage: 100 x TP/(TP + FP + FN)
Figure 6 shows the final 3D object space building hypothe-
ses produced for FLAT_L, and Table 7 gives the performance
statistics for these results. PIVOT hypothesizes several struc-
tures where no buildings exist, due to false alignments of
edges along vanishing lines; this explains the relatively high
branching factors and low quality percentages. Many build-
ings are well modeled; the exceptions lie in the lower right
corner of the image, where edge fragmentation hindered prim-
itive generation. Only one building, the lightly colored peaked
roof structure, is completely missed by PIVOT; that building
is actually found but discarded because the median intensity
of its sunward roof facet is darker than the other facet.
Figure 8 shows the final 3D object space building hypothe-
ses produced for RADT5WOB, and Table 9 gives the per-
formance statistics for these results. PIVOT detects at least
some portion of every building in the scene, and the high
building detection percentage and low miss factor reflect this
good performance. The low branching factor and high quality
percentage indicate that PIVOT is generating low amounts
of false positives; only three of PIVOT's buildings lie entirely
on background pixels.
These examples are representative of PIVOT's performance
on other images; with the use of photogrammetric techniques,
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B6. Vienna 1996
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