Dense urban elevation models from stereo images by an affine region merging approach

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.