Evaluating certainties in image intensity differentation for optical flow

We use 3x3x3 Sobel operators to compute both spatio-temporal derivatives s ξ , S y and S t and their certainties (scalar number) in a number of image sequences and then use Lucas and Kanade's weighted least squares framework to compute optical flow (image velocity) in 5x5 image neighbourhoods, where the weights are the derivative certainties. We model the certainties in the derivatives as proposed by Spies [Vision Interface 2003] and analyze them quantitatively by evaluating the flow computed using them. For a number of synthetic image sequences with the correct answer known, we perform a quantitative analysis using either weights of 1.0 or weights computed from the derivative certainties (2 ways) and show that using a good estimation of the derivative quality in a optical flow calculation leads to better quality optical flow (both more dense and more accurate).