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The Kinect system is arguably the most popular 3-D camera technology currently on the market. Its application domain is vast and has been deployed in scenarios where accurate geometric measurements are needed. Regarding the PrimeSense technology, a limited amount of work has been devoted to calibrating the Kinect, especially the depth data. The Kinect is, however, inevitably prone to distortions, as independently confirmed by numerous users. An effective method for improving the quality of the Kinect system is by modeling the sensor's systematic errors using bundle adjustment. In this paper, a method for modeling the intrinsic and extrinsic parameters of the infrared and colour cameras, and more importantly the distortions in the depth image, is presented. Through an integrated marker-and feature-based self-calibration, two Kinects were calibrated. A novel approach for modeling the depth systematic errors as a function of lens distortion and relative orientation parameters is shown to be effective. The results show improvements in geometric accuracy up to 53% compared with uncalibrated point clouds captured using the popular software RGBDemo. Systematic depth discontinuities were also reduced and in the check-plane analysis the noise of the Kinect point cloud was reduced by 17%.