This book presents a statistical learning framework for inferring geometric structures from images. The proposed framework computes dense range maps of locations in the environment using only intensity images and very limited amount of range data as an input. This is achieved by integrating and analyzing the statistical relationships between the visual data and the available depth on terms of small patches. The scientific issue is to represent this correlation such that it can be used to recover range data where missing. Markov Random Fields are used as a model to capture the local statistics of the intensity and range. Experiments on real-world data are conducted under different configurations to demonstrate the feasibility of the method. In particular, the application is in mobile robotics, where inferring the 3D layout of indoor environments is a critical problem for achieving exploration and navigation tasks. Additionally, the proposed method is used in the color correction and augmentation problem with the specific application to underwater images.

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