Regression-based surface reconstruction: coping with noise, outliers, and discontinuities

The automated processing of range data is an important problem in many computer vision applications. Range sensors are being used to aid navigation, object recognition, inspection, and reverse engineering. These applications require range sensors be placed on the factory floor and on autonomous vehicles, creating scenarios well removed from controlled laboratory settings. Instead of recording measurements from a single isolated object with consistent surface properties, range sensors are now exposed to scenes composed of many objects, varying surface properties, and objects occupying different portions of the depth of field and field of view. Not only is the composition of a range scene more complicated but the sensing environment is less amenable to precise and accurate measurements. While a direct and dense measurement of depth is attractive to many applications, a range map by itself has little practical use. The data is corrupted by noise, randomly of setting each measurement from its true position. The amount of noise can vary across the scene as a function of surface properties, depth, orientation, and position in the field of view. Furthermore, the data contains outliers or completely erroneous measurements in regions of specularity and along discontinuities. Finally, the data is not segmented, so the mapping of measurements to particular object surfaces is not immediate. These problems become more and more difficult to address as scene complexity increases. Here, we study the statistical properties of range data and surface estimates, constructing statistical tools for simultaneously segmenting and reconstructing complicated range images. First, using order statistics, we construct a robust local surface estimator, called M scUSE, which tolerates a large percentage of outlying data, small scale discontinuities, and multiple surfaces in an image region. Second, using multivariate regression and prediction intervals, we devise statistical decision criteria to control a surface growing segmentation process. These criteria reduce the number of tuning parameters while increasing the sensitivity to small scale discontinuities. We analyze the expected performance of these techniques on synthetic data and include a segmentation comparison study on data from a laser range sensor.