Dense Urban Elevation Models from Stereo Images by an Affine Region Merging Approach

Javier Preciozzi

Master thesis from Universidad de la República, Facultad de Ingeniería - 2006

Advisor:

Research Group(s): Tratamiento de Imagenes (gti)

Department(s): (unspecified)

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## Abstract

The main subject of this thesis is the computation of Dense Disparity Maps from a pair of satelite or
aerial stereo images from an urban scene, taken from two different viewpoints. Several steps are needed
to obtain the ?nal disparity map from the pair of images. We focus here on one of these steps: how
to match the points in one image with the points in the other one. This matching process is closely
related to the computation of the altitudes of the objects present in the scene. Indeed, the precision
we can obtain in these altitude values is directly proportional to the precision in the matching process.
This precision in the altitude is also inversely proportional to the distance between both viewpoints
where the images are taken(baseline).
The matching process is a widely studied ?eld in the Computer Vision Community and several
methods and algorithms have been developed so far ([31, 27, 49]). Most of them consider a big base-
line con?guration, which increases the performance in the altitude and also simpli?es the matching
process. However, this assumption presents a major drawback with objects that are occluded in one
image but appear in the other one. The bigger the baseline is, the more objects are occluded in one
image and are not occluded in the other one.
Recently, a different approach in which the images are taken with a very small baseline started
to be analyzed ([19, 20]). This approach has the advantage of eliminating most of the ambiguities
presented when one object occluded in one image is not occluded in the other one. Indeed, if we
consider that we have a very small baseline, the occlusions presented in both images are almost the
same. Now, this con?guration obviously decreases the precision in the ?nal altitude. In order to
continue obtaining highly accurate altitude values, the precision in the matching process must be im-
proved. The methods developed so far which consider the small baseline approach, compute altitude
values with a high precision at some points, but leave the rest of them with no altitude values at all,
generating a non-dense disparity map. Based on the fact that piecewise-a?ne models are reasonable
for the elevation in urban areas, we propose a new method to interpolate and denoise those non-dense
disparity maps.
Under lambertian illumination hypothesis 1 , it is reasonable to assume that homogeneous regions
in the graylevel image, correspond to the same a?ne elevation model. In other words, the borders
between the piecewise a?ne elevation model are included to a large extent within contrasted graylevel
borders. Hence, it is reasonable to look for an piecewise a?ne ?t to the elevation model where the
borders between regions are taken from a graylevel segmenation of the image
We present a region-merging algorithm that starts with an over-segmentation of the gray-level im-
age. The disparity values at each region are approximated by an a?ne model, and a meaningfulness
measure of the ?t is assigned to each of them. Using this meaningfulness as a merging order, the
method iterates until no new merge is possible, according to a merging criterion which is also based
on the meaningfulness of each pair of neighboring regions. In the last step, the algorithm performs a
validation of the ?nal regions using again the meaningfulness of the ?t. The regions validated in this
last step are those for which the a?ne model is a good approximation.
The region-merging algorithm presented in this work can be seen as an attempt to incorporate a
semantical meaning to real scenes: we have developed a validation method to determine whether the
data within a region is well approximated by an a?ne model or not. Hence, we could analyze more
complex models, de?ning a suitable validation criterion for each of them. In this way, we can search
for the model that best explains a given data set in terms of its meaningfulness.

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