Quantification of smoothing requirement for 3D optic flow calculation of volumetric images

Complexities of dynamic volumetric imaging challenge the available computer vision techniques on a number of different fronts. This paper examines the relationship between the estimation accuracy and required amount of smoothness for a general solution from a robust statistics perspective. We show that a (surprisingly) small amount of local smoothing is required to satisfy both the necessary and sufficient conditions for accurate optic flow estimation. This notion is called "just enough" smoothing, and its proper implementation has a profound effect on the preservation of local information in processing 3D dynamic scans. To demonstrate the effect of "just enough" smoothing, a robust 3D optic flow method with quantized local smoothing is presented, and the effect of local smoothing on the accuracy of motion estimation in dynamic lung CT images is examined using both synthetic and real image sequences with ground truth.