Dynamic Geometric Structure Based Modeling And Editing Of Visual Media

Vision is the most important way that human apperceive the world. The media thatcontains visual information is called visual media, including image, video, digital geom-etry, etc. Our world is full of geometric structures; since visual media is the projectionof the real world, geometric structures also exist widely in visual media. Most geometricstructures are dynamic, which means they can move under certain constraints. Dynam-ic geometric structures are essential to the modeling and editing process of visual media.Understanding what constraints that dynamic geometric structures should satisfy and howthey can move under these constraints, is important to visual media modeling; analysinghow dynamic geometric structures’ move afect visual media’s appearance, is also usefulto visual media editing.This paper focuses on studying the invariant properties of dynamic geometric struc-tures in visual media, particular in the following problems: pop-up structure modeling,cage-based image deformation, and edge-aware image filtering. The contribution of thispaper includes:It studied the geometric structure of L-style pop-ups, and proposed sufcient con-ditions for the foldability and stability of an L-style pop-up. Based on these condi-tions, an automatic algorithm was proposed to generate an L-style pop-up accord-ing to a given3d model.It studied the geometric structure of V-style pop-ups, and proposed sufcient con-ditions for the foldability and stability of a V-style pop-up, as well as closed-formcriteria for intersection-free and enclosing properties of a V-style pop-up. Based onthese conditions and criteria, it proposed an interactive system for V-style pop-upmodeling in real-time.It studied barycentric coordinates for cage-based image deformation. It generalizedthe classical mean value coordinates in two ways: it proposed the novel Poissoncoordinates which are pseudo-harmonic, and proposed the novel cubic mean valuecoordinates that interpolate both function values and gradients, which can be usedfor cage-network based image deformation with C1smoothness.It proposed a novel method for edge-aware image filtering in mixed-domain. Thismethod considers a bank of local filters in sub-windows, and merges the outputs of these local filters using a multi-scale optimization-based framework, to get anoverall output. This method is fast and robust, and is able to reduce halo and edge-reversal artifacts.