We present a novel method for automatically geo-tagging photographs of man-made environments via detection and matching of repeated patterns. Highly repetitive environments introduce numerous correspondence ambiguities and are problematic for traditional wide-baseline matching methods. Our method exploits the highly repetitive nature of urban environments, detecting multiple perspectively distorted periodic 2D patterns in an image and matching them to a 3D database of textured facades by reasoning about the underlying canonical forms of each pattern. Multiple 2D-to-3D pattern correspondences enable robust recovery of camera orientation and location. We demonstrate the success of this method in a large urban environment.
Computer scientists have long believed that software is different from physical systems in one fundamental way: while the latter have continuous dynamics, the former do not. In this paper, we argue that notions of continuity from mathematical analysis are relevant and interesting even for software. First, we demonstrate that many everyday programs are continuous (i.e., arbitrarily small changes to their inputs only cause arbitrarily small changes to their outputs) or Lipschitz continuous (i.e., when their inputs change, their outputs change at most proportionally). Second, we give an mostly-automatic framework for verifying that a program is continuous or Lipschitz, showing that traditional, discrete approaches to proving programs correct can be extended to reason about these properties. An immediate application of our analysis is in reasoning about the robustness of programs that execute on uncertain inputs. In the longer run, it raises hopes for a toolkit for reasoning about programs that freely combines logical and analytical mathematics.
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