IMPROVING AUTONOMOUS ESTIMATES OF DEM UNCERTAINTIES BY EXPLOITING COMPUTER MATCHING ASYMMETRIES Andr´ es Corrada-Emmanuel, Brian Pinette, Andrey Ostapchenko, Howard Schultz Departments of Computer Science, Physics at the University of Massachusetts at Amherst acorrada@physics.umass.edu, {pinette, ostrapchenko, schultz}@cs.umass.edu KEY WORDS: DEM, vertical uncertainty, computer matches ABSTRACT: We consider the problem of estimating the vertical uncertainty in Digital Elevation Models when results from asymmetric computer matches are used. The use of asymmetric matches doubles the height estimates available for creating a fused DEM. But if the asym- metric matches are perfectly correlated the variance would not drop by a factor of 1/ √ 2 as they would for uncorrelated measurements. We present an error model that uses the observed height estimates to measure the average correlation between the asymmetric matches absent any knowledge of the true heights in the DEM. It requires at least three photographs to autonomously estimate the correlation between asymmetric pairs. Experimental results with a specific set of aerial photographs show that the correlation coefficient varies from 0.5 to 0.9. This demonstrates that for any algorithm used to fuse DEMs from multiple photographs a better result would be obtained by employing the extra information in asymmetric pairs. 1 INTRODUCTION The process of creating accurate geographically registered maps is very time consuming, involving expensive data collection and highly technical information extraction procedures. Advances in sensor technology and the growing availability of unmanned air vehicles (UAVs) have the potential to create a real-time mapping appliance. Suppose such a device is trying to build a Digital Elevation Model (DEM) of a terrain autonomously, i.e. without ground truth. By this we mean more precisely that all that is known to the sensor is its own position and orientation relative to a local datum. It does not know the ‘true’ value of Z(x, y) for any location {x, y}. The user of the mapping appliance is most inter- ested in specifying a vertical uncertainty δdesiredand some vague promise that this means that the DEM satisfies Ztrue ≈ Zestimated + δdesired. To plan its mission it would have to answer three questions about the quality of the DEM: are the elevation postings reasonable? what is the vertical uncertainty in the estimated elevations? what is the spatial decorrelation length of the elevation postings? A technique for eliminating elevation blunders and increase the re- liability of postings is described in Schultz et al(Schultz et al., 2002). They show how asymmetries in image matching can be exploited to filter out elevation blunders. This gives an autonomous method for answering the first DEM quality question. In this pa- per we show how to improve the vertical uncertainty of DEMs produced in an automatic aerotriangulation system by using the correlation in asymmetric computer matches. The horizontal decor- relation length autonomous estimate will be treated in a subse- quent paper. 2 COMPUTER MATCHING ASYMMETRIES Consider an automatic DEM estimation process like the one used in the UMass Terrest system (Schultz, 1995). A pair of spatially overlapping images, call them A and B, go through an epipolar rectification process followed by an image matching procedure in which a disparity map DAB is found. DAB defines a set of matches between the reference image A and the target image B such that the pixel {i, j } in A and the pixel {i + DAB(i, j ),j } in B are projections of the same 3D world point. In the final step, the DEM estimator computes a digital elevation model ZAB from DAB and the camera orientation information. But image matching algorithms are not commutative. As a con- sequence, the DEM ZAB created with image A as the reference and image B as the target image is not identical to the DEM ZBA created when the image roles are reversed. This asymmetry in image matching is well-known in computer vision; for example, it is used by some occlusion detectors(Brown et al., 2003). The problems associated with errors in computer matching for the purposes of aerotriangulation is discussed by Jung et al. (Jung et al., 2002). The existence of this asymmetry is generally dis- regarded by photogrammetric systems. It seems to be treated as a ‘redundant’ or ‘defect’ measurement and therefore both mem- bers of the asymmetric pair should not be incorporated in a final computation of the DEM. It is our point of view that both asymmetric matches should be used. Their information is correlated, but not perfectly. The use- fulness of looking at both matches for the purposes of blunder removal has already been demonstrated by Schultz et al. (Schultz et al., 2002). They generalized the concept of self-consistency developed by Leclerc et al. (Leclerc et al., 2000) for process- ing multiple stereo image pairs to a single image pair. Values of |ZAB - ZBA| that are too high (by whatever criterion one chooses) can then be culled out. This dramatically improved the accuracy of a DEM that fused the information from multiple pairs as tested with a ”pseudo-ground” truth check that relied on ray tracing(Schultz et al., 2002). This paper will show that combining the asymmetric matches also improves the final DEM. The existence of two height estimates from two images means that p(p - 1) estimates are available whenever p photographs overlap in a DEM posting location. This contrasts with the usual use of 1/2p(p - 1) estimates. The reduc- tion in the variance of a height estimate obtained with a function