Dense Depth Maps from Epipolar Images
Recovering three-dimensional information from two-dimensional images is the fundamental goal of stereo techniques. The problem of recovering depth (three-dimensional information) from a set of images is essentially the correspondence problem: Given a point in one image, find the corresponding point in each of the other images. Finding potential correspondences usually involves matching some image property. If the images are from nearby positions, they will vary only slightly, simplifying the matching process. Once a correspondence is known, solving for the depth is simply a matter of geometry. Real images are composed of noisy, discrete samples, therefore the calculated depth will contain error. This error is a function of the baseline or distance between the images. Longer baselines result in more precise depths. This leads to a conflict: short baselines simplify the matching process, but produce imprecise results; long baselines produce precise results, but complicate the matching process. In this paper, we present a method for generating dense depth maps from large sets (1000's) of images taken from arbitrary positions. Long baseline images improve the accuracy. Short baseline images and the large number of images greatly simplifies the correspondence problem, removing nearly all ambiguity. The algorithm presented is completely local and for each pixel generates an evidence versus depth and surface normal distribution. In many cases, the distribution contains a clear and distinct global maximum. The location of this peak determines the depth and its shape can be used to estimate the error. The distribution can also be used to perform a maximum likelihood fit of models directly to the images. We anticipate that the ability to perform maximum likelihood estimation from purely local calculations will prove extremely useful in constructing three dimensional models from large sets of images.