Abstract: We present an optimization framework for exploring gradient-domain solutions for image and video processing. The proposed framework unifies many of the key ideas in the gradient-domain literature under a single optimization formulation. Our hope is that this generalized framework will allow the reader to quickly gain a general understanding of the field and contribute new ideas of their own. We propose a novel metric for measuring local gradient saliency that identifies salient gradients that give rise to long, coherent edges, even when the individual gradients are faint. We present a general weighting scheme for gradient constraints that improves the visual appearance of results. We also provide a solution for applying gradient-domain filters to videos and video streams in a coherent manner. Finally, we demonstrate the utility of our formulation in creating effective yet simple to implement solutions for various image-processing tasks. To exercise our formulation we have created a new saliency-based sharpen filter and a pseudo image-relighting application. We also revisit and improve upon previously defined filters such as nonphotorealistic rendering, image deblocking, and sparse data interpolation over images (e.g., colorization using optimization).