(2)
'ents. So, we need
H about the image
pendent in general
)
[ie / 19: 9)
sform, Generalized
ytiev's morphology
the Bayesian EA-
|, hypothesis tested
rocedures that are
1-based techniques
3;
information.
> accumulation of
-based hypothesis.
the assumption of
reral is enough to
llel independent
| on a hierarchical
ormation is clear
coarsening of the
eneous image data
ical image sources
s. Let we have N
f data abstraction.
n of information
ation, dot pattern,
Let the complex
et of propositions
t the object must
at this proposition
f abstraction if the
Then a posterior probability (3) takes a form:
N TE
P(H / IM) - (PGI) x DLTTI POM! / H)}/
N L
HPCE) x [TIT PM! / 8) POT) x [CT TT POM! / H99).--44)
i=1 1-1 [5 I=1
So, the events-based image analysis provides a generic
framework for non-homogeneous information analysis.
3. 3D-MODEL TO IMAGE MATCHING FOR
HOUSE DETECTION.
The problem of automatic 3D-model to image matching is
discussed in many papers and publications. Let consider
two of them that present the most pure concepts of such
matching. While one presumes that the complete 3D wire
frame model of the house and full camera geometry are
known, the "prediction" of 2D-contours of the house image
can be build. Then it can be matched to the real contour
preparation on the observed image. It is not a trivial task
due to the weak correspondence between the ideal contours
and the production of real edge detectors. Such
sophisticated contour-based matching technique is
described in (Huertas, Bejanin and Nevatia, 1995). Its
robustness strongly depends on the quality of initial
contour preparation. In the paper (Mueller and Olson,
1995), the intensity-based correlation approach is
presented. In this way the 2D prediction is an intensity
image and so one can reduce "model-to-image matching"
problem to the well known "image-to-image matching"
problem. However, to predict the intensity values on the
model image authors had to make both the geometric and
the radiometric prediction. The latter problem is
sophisticated too because, even the 3D-model includes the
plane surfaces only, it requires to estimate the color and
the reflectivity of these planes as well as the sun luminance
characteristics. The results seem to be satisfactory enough,
but it is the rare case when the reflectivities of the model
facets are precisely known.
As shown above, the Pytiev morphology provides a way for
comparison of images by their "shape" but not immediately
by pixel intensities. The "shape" of the intensity image is
equivalent to 2D-area tessellation and can be described by
a set of homogeneous areas that cover the image and pair-
wise not intersected. The projection of 3D wire frame onto
the image plane determines the unique Pytiev's "shape".
Then the test patch of the real image must be "projected"
(in the Pytiev sense) onto this shape. This "morphological
projection” will be the required model approximation to be
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
compared with the real image patch. Thus, the Pytiev
technique allows to realize the intensity-based model-to-
image matching using only the geometric prediction
(without the any of radiometric knowledge).
Let consider the simple case of planar facets and Lambert's
reflection model. It means that the intensity of reflected
light is just proportional to the angle of the facet
inclination and, consequently, the intensity of any image
region corresponded to the facet must be constant. Under
these assumptions, the morphological projection can be
obtained in the most simple way, through the computation
of the average values of image intensity over the each
region of the "shape". As we understood, Mueller and
Olson used the analogous technique (to compare with their
approach) and found it unsatisfactory due to false
detections occurred. These results are correct if the
morphological projection is used as a prediction and
compared with image by the usual correlation way.
However, the real success of the intensity-based model-to-
image matching takes place only if two following facts are
proved:
l. The intensity over the each of facet 2D-projection
(region) is homogeneous enough;
2. The edges between different facets are expressed
enough.
Contour data and intensity data make up the non-
homogeneous information set. So, they can be fused in the
EA-manner as described before. To do this we need to
agree some probabilistic model of object. Let the intensity
of pixels on the each facet projection is described by a
Gaussian distribution. Let the probabilities of contour point
at the expected contour and out of the expected contour are
known a priory (from expert analysis). We think that the
assumption of independence of pixel events is an
appropriate coarsening of reality. These assumptions lead
the following algorithm of model-to-image matching:
1. Build the 2D-projection of the object's wire-frame
onto the image plane to define the model image
"shape". Project (in the Pytiev sense) the
registered image onto the model "shape". Estimate
the parameters of intensity distribution using the
mid-level approximation as a set of average
values.
2. Build the contour preparation of the image.
3. | Evaluate the non-homogeneous criterion P(H/Im)
(4) that characterizes the quality of model-to-
image matching.
This approach has some advantages in comparison with
the discussed predictive approach:
e À prior radiometric information is not required.
