Optical flow estimation in the rainy scenes is challenging due to background degradation introduced by rain streaks and rain accumulation effects in the scene. Rain accumulation effect refers to poor visibility of remote objects due to the intense rainfall. Most existing optical flow methods are erroneous when applied to rain sequences because the conventional brightness constancy constraint (BCC) and gradient constancy constraint (GCC) generally break down in this situation. Based on the observation that the RGB color channels receive raindrop radiance equally, we introduce a residue channel as a new data constraint to reduce the effect of rain streaks. To handle rain accumulation, our method decomposes the image into a piecewise-smooth background layer and a high-frequency detail layer. It also enforces the BCC on the background layer only. Results on both synthetic dataset and real images show that our algorithm outperforms existing methods on different types of rain sequences. To our knowledge, this is the first optical flow method specifically dealing with rain.
 Virtually all variational methods for motion estimation regularize the gradient of the flow field, which introduces a bias towards piecewise constant motions in weakly textured areas. We propose a novel regularization approach, based on decorrelated second-order derivatives, that does not suffer from this shortcoming. We then derive an efficient numerical scheme to solve the new model using projected gradient descent. A comparison to a TV regularized model shows that the proposed second-order prior exhibits superior performance, in particular in low-textured areas (where the prior becomes important). Finally, we show that the proposed model yields state-of-the-art results on the Middlebury optical flow database. A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the gradient-projection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t--- 0o the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear to be state-of-the-art for very noisy images. The method is noninvasive, yielding sharp edges in the image. The technique could be interpreted as a first step of moving each level set of the image normal to itself with velocity equal to the curvature of the level set divided by the magnitude of the gradient of the image, and a second step which projects the image back onto the constraint set.