A noise reduction method for range images using local Gaussian observation model constrained to unit tangent vector equality

Abstract

We present a method for smoothing heavy noisy surfaces acquired by on-the-fly 3D imaging devices to obtain the stable curvature. The smoothing is performed in a way that finds centers of probability distributions which maximizes the likelihood of observed points with smooth constraints. The smooth constraints are derived from the unit tangent vector equality. This provides a way of obtaining smooth surfaces and stable curvatures. We achieve the smoothing by solving the regularized linear system. The unit tangent vector equality involves consideration of geometric symmetry and it minimizes the variation of differential values that are a factor of curvatures. The proposed algorithm has two apparent advantages. The first thing is that the surfaces in a scene with various signals to noise ratio are smoothed and then they can earn suitable curvatures. The second is that the proposed method works on heavy noisy surfaces, e.g., a stereo camera image. Experiments on range images demonstrate that the method yields the smooth surfaces from the input with various signals to noise ratio and the stable curvatures obtained from the smooth surfaces.