Robust Depth Estimation from Optical Flow

Abstract

A robust method for obtaining dense depth-maps from a sequence of noisy intensity images (obtained by a moving camera is presented. Controlled camera motion is exploited to reduce the complexity of the optical flow solution to closed-form. It is well known that optical flow computations suffer from high noise sensitivity. Tensor-product smoothing splines are employed to construct a 3-D continuous approximation to the time-varying intensity data which serves to reduce the effects of noise and restore the properties of continuous optical flow. Spatial and temporal derivative estimates obtained from the 3-D spline approximation are used to compute the depth. Unreliable depth estimates are discarded based on the temporal rate of change of intensity. The effectiveness of the smoothing spline approximation coupled with the efficiency of tensor products and the closed form solution for depth leads to a robust method for obtaining dense depth maps with low computational cost. Experimental results are presented which demonstrate the robustness of the method applied to real image data. These experiments indicate an average relative error of 3.7 percent in the depth measurement is obtainable using a sequence of seven 8-bit quantized images. Suggestions for further improvements in the quality of the depth maps by adjusting the parameters of the smoothing spline are discussed.