| The focus of this thesis is a particular form of spatial-domain filtering that has been popularized in recent years as gradient-domain filtering. Gradient-domain filters manipulate pixel differences (e.g., first order image-gradients) in addition to pixel values of an image. The primary motivation for filtering in the gradient domain is that gradients are low-level image features that can be manipulated with ease in order to exert control over high-level image features like object boundaries, scene lighting, temporal flicker and compression noise, to name a few.;The overarching goal of this thesis is to expand on the domain knowledge, power, and tools available to the gradient-domain image processing community. Towards this end, we introduce GradientShop, an optimization framework for image and video processing, which generalizes many of the key ideas in the gradient-domain community. The utility of this framework is demonstrated by developing several simple, elegant, and effective solutions for challenging image processing problems.;We present Fourier analysis of the screened Poisson equation, which is shown to be equivalent to gradient-domain problems involving a data term. Our analysis leads to a direct, exact, and efficient solver for the problem. The analysis also reveals the structure of spatial filters that solve the screened Poisson equation and shows gradient scaling to be a well-defined sharpen filter, thus further expanding the general understanding of gradient-domain filtering.;We introduce a gradient-domain technique called spacetime fusion that can be used to combine the temporal richness of low resolution videos with the spatial richness of photographs, thereby producing videos with the combined strengths of both data sources. Spacetime fusion is also shown to be a general technique for applying image filters to videos in a temporally coherently manner. The recurring approach taken to application development in this thesis has been to leverage gradient-domain techniques in making imperfect results produced by computer-vision algorithms like multi-view stereo and optical flow visually palatable to humans, thereby demonstrating gradient-domain filtering to be a valuable post-processing step for images manipulated by computer vision algorithms. We also present improvements to computer vision algorithms like multi-view stereo, optical flow, and edge detection. |
