In this paper, we proposed a novel motion model with Helmholtz decomposition for complex fluid flows in a filtering-based optical flow framework, where the optimization of the regularization term is treated as a filtering process, and different motion patterns can be captured by finding appropriate filter kernels based on the designed filters. In this framework, we introduce a novel optical flow method with a joint spatial filter, which is based on the Helmholtz decomposition theorem that assumes a local motion field is composed of a curl field and a divergence field. By adjusting the scale of the weights in the filter kernels and combining a curl filter with a divergence filter in a certain ratio, it can simulate different motion patterns. In addition, if the correlation between the horizontal and vertical components of the optical flow field in the filter kernel is eliminated, it will be transformed into a linear motion model. Based on this linear motion model, we also develop a novel optical flow method with an adaptive guided filter. By finding an adaptive filter kernel driven by both the input image and the guided motion field for the designed filter, it can successfully capture different motion patterns, and yield an edge-preserving smoothing optical flow field. Most importantly, the proposed optical flow model provides a new way to design the regularizers for capturing different motion patterns in complex fluid flow. In particular, the designed optical flow method with an adaptive guided filter significantly outperforms the current state-of-the-art optical flow methods in predicting complex fluid flows.

Optical flow computation for video under the dynamic illumination is a challenging issue in video multimedia applications. In this paper, we solve this issue by introducing an illumination-invariant framework for variational optical flow estimation. It consists of an illumination-invariance model that handles complex illumination changes and a data enhancement model that guarantees highly accurate optical flow estimation. In this framework, we design a log-correlation descriptor for the data term, which handles complex illumination changes by eliminating the common parameters shared by the neighboring pixels in the corresponding illumination change model while improving the accuracy of optical flow estimation by enhancing the discriminability of the data term matching. We also introduce a novel optical flow model with$L_{0}$norm regularization, which reconstructs optical flow field by a sparse flow gradient counting scheme. Different from other edge-preserving regularizers, it does not depend on local motion features, but locates important flow edges globally. Therefore, it will not cause edge blurriness due to avoiding local filtering or average operation. It is particularly effective for enhancing major flow edges while eliminating a manageable degree of low-amplitude motion structures to control smoothing and reduce oversegmentation artifacts. Even small-scale motion structures with high contrast can be preserved remarkably well. The experimental results show our method significantly outperforms previous illumination-robust optical flow methods in handling complex illumination changes, and achieves competitive evaluation results on the challenging MPI-Sintel and Kitti datasets.