基于动态几何结构的可视媒体的建模与编辑
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摘要
视觉是人类获取外部信息的最主要途径，承载视觉信息的媒体统称为可视媒体，具体包括图像、视频、数字几何等主要形式。真实的三维世界中充满着几何结构；可视媒体是外在世界的缩影，几何结构也普遍存在于可视媒体之中。可视媒体中的几何结构具有动态性，通常能在一定的约束条件下自由变化。动态几何结构对可视媒体的建模与编辑至关重要。研究几何结构必须满足的约束条件及其变化规律，有利于合理的可视媒体建模；分析可视媒体的内容如何随着几何结构的动态变化而改变，是进行可视媒体编辑的常用方法。
本文围绕可视媒体中的动态几何结构，从动态几何结构的变化规律与变化过程中的不变性质入手，具体研究了立体纸雕结构的建模、基于Cage结构的图像变形、边缘结构敏感的图像滤波这三个可视媒体建模与编辑中的关键问题。论文的工作与创新点包括：
研究了L型立体纸雕这一动态几何结构，提出了能够保证其可动性和稳定性的充分条件；基于这一条件，进而提出了一个自动算法，能够通过任意给定输入模型生成与之相符的L型立体纸雕结构。
研究了V型立体纸雕这一动态几何结构，除了给出其可动性和稳定性的充分条件外，还提出了其不自交性和可封装性的闭式判定准则；基于这些充分条件和判定准则，进而实现了一个交互式的V型立体纸雕结构建模系统，支持实时的V型立体纸雕设计。
针对基于Cage的图像动态变形中的不变量—重心坐标进行了研究，对经典的均值坐标提出了两种扩展：具有伪调和性的泊松坐标和能够进行高阶插值的三次均值坐标，并提出了基于Cage网络的图像变形方法，能够保证图像变形的C1连续性。
提出了边缘结构敏感的混合域图像滤波方法。该方法通过对图像的子窗口内的局部滤波进行保持图像边缘结构的动态变换，结合一个多尺度优化框架将局部滤波的输出结果进行融合，获得全局的滤波输出。该方法快速鲁棒，能有效避免光环和边反转现象。
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.
本文围绕可视媒体中的动态几何结构，从动态几何结构的变化规律与变化过程中的不变性质入手，具体研究了立体纸雕结构的建模、基于Cage结构的图像变形、边缘结构敏感的图像滤波这三个可视媒体建模与编辑中的关键问题。论文的工作与创新点包括：
研究了L型立体纸雕这一动态几何结构，提出了能够保证其可动性和稳定性的充分条件；基于这一条件，进而提出了一个自动算法，能够通过任意给定输入模型生成与之相符的L型立体纸雕结构。
研究了V型立体纸雕这一动态几何结构，除了给出其可动性和稳定性的充分条件外，还提出了其不自交性和可封装性的闭式判定准则；基于这些充分条件和判定准则，进而实现了一个交互式的V型立体纸雕结构建模系统，支持实时的V型立体纸雕设计。
针对基于Cage的图像动态变形中的不变量—重心坐标进行了研究，对经典的均值坐标提出了两种扩展：具有伪调和性的泊松坐标和能够进行高阶插值的三次均值坐标，并提出了基于Cage网络的图像变形方法，能够保证图像变形的C1连续性。
提出了边缘结构敏感的混合域图像滤波方法。该方法通过对图像的子窗口内的局部滤波进行保持图像边缘结构的动态变换，结合一个多尺度优化框架将局部滤波的输出结果进行融合，获得全局的滤波输出。该方法快速鲁棒，能有效避免光环和边反转现象。
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.
引文
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