On smoothness of vector field with discrete wavelet transform

The analysis of image sequences is one of the most actively areas studied in computer vision and image processing. A fundamental problem in the process of image sequences is the computation of the velocity vector field of apparent motion of brightness patterns usually referred as optical flow. Optical flow is usually adopted in many applications ranging from passive scene interpretation to autonomous active exploration. It has been used, quite successfully, as an intermediate step, in problem of 3D object reconstruction and 3D scene analysis for computing informnation such as depth and surface orientation. Numerous methods have been used to determine measurements of optical jlow and most of them perform relatively poorly generating many vectors with an inconsistent direction or magnitude. Hence a smoothness on optical flow is often needed to enhance the signal-to-noise ratio. In this paper discrete wavelet transform has been adopted to reduce noise in optical flow rendering it clean enough to be of pratical value. The algorithm adopied as flow estimator is the well-known Horn and Schunck's method which relates the spatio-temporal derivatives of the image intensity at each point to the optical flow field in a linear fashion. Experiments with compactly supported orthonormal wavelets have been reported by varing the number of vanishing moments and decomposition levels. Various experiments have been presented by removing small values of the discrete wavelet transform and by opportunely treating the spaces of the low and high frequencies. Interesting results have been obtained by substracting high level components in the wavelet expansion and by composing the low frequencies magnified M times using pixels replication where M is the wavelet multiplicity.