Lumigraphs and Manifolds

介绍和目标。基于图像的渲染（IBR）是一种相对较新的计算机图形技术，其中对场景的多个图像（计算机生成或照片）进行修改和组合以产生代表场景新视图的图像。最终得到的图像通常有很好的细节，但有时是不正确的，部分原因是缺乏潜在的几何模型。相比之下，传统图形使用几何和光照模型从任意视点生成场景的正确视图；但由于建模成本，它们往往缺乏细节。一个理想的几何模型应该既有物体的完整几何形状，又有表面上每个点的BRDF（双向反射分布函数），以描述光与物体的相互作用，允许在任何照明条件下计算物体的任何视图。这种理想的一个简单近似是一个单一颜色的几何模型；纹理映射通过将图像映射到几何上来改进这种近似。该项目旨在开发一种新的基于IBR的建模范式，通过在表面上的每个点添加BRDF的近似值来进一步扩展这一思想。这种新的建模范式通过将基于图像的渲染模型与几何模型信息相结合，提高了生成和存储基于图像的渲染模型的效率，从而弥合了两种方法之间的差距。其目的是构建视觉上复杂和几何上忠实的几何模型，但避免几何建模表面细节的开销。与开发底层模型同样重要的是使用真实世界的对象来创建模型的能力。当今许多复杂的几何模型都是通过激光扫描或3D数字化仪从实物中获取的。本研究的目标之一是建立一种类似的机制来捕捉和渲染具有复杂视觉特性的物体或场景。要合并的两个学科是基于图像的渲染和几何建模。该项目将使用IBR的lumigraph，部分原因是它已经包含了一个有限的几何模型，并将使用基于流形的几何组件模型。光图是捕捉光离开物体时的行为的一种非常通用的方法。基于流形的几何通过混合小表面块来支持任意拓扑表面的构造。将光线图与流形相结合的结果是一个几何模型，该模型具有光线如何从其发射的信息。使用这种结构，沿表面发射的光的任何局部常数都很容易识别，从而具有相当大的数据压缩优势。因此，除了有趣的几何模型之外，这种结构还允许IBR数据集的有效存储。同样的局部恒常性可以用来指导表面与被建模对象的实际几何形状的拟合度。这些操作中的每一个都需要底层几何的同质表示——其中所有的点都可以被平等地对待，而不是，例如，将点划分为多面体的顶点、边缘和面，或者b样条模型的相邻块。流形结构恰恰提供了这种同质性。许多基于图像的渲染方法使用一些几何知识，通常是深度。添加显式几何对象有两个潜在的好处；一种更丰富的建模类型，其中全局类lumigrapa数据附加到几何基础上，以及一种明确探索几何与从图像中收集的数据压缩之间关系的方法。由此产生的模型将在多种应用程序中有用，特别是那些高图像质量必不可少，但不可能进行显式建模的应用程序。这些包括特效制作和教育应用（例如，在线医疗模型），以及逆向工程和建筑照明模拟中的可能应用。

Introdurtion and Objectives. Image-based rendering (IBR) is a relatively new computer graphics technique in which multiple images (either computer-generated or photographs) of a scene are modified and combined to produce an image representing a novel view of the scene. The resulting images often have great detail but are sometimes incorrect, partly because of the lack of an underlying geometric model. Traditional graphics, by contrast, uses geometric and lighting models to generate correct views of a scene from an arbitrary view-point; but because of modeling costs, they often lack detail.An ideal geometric model would have both the complete geometry of the object plus a BRDF (bidirectional reflectance distribution function) at every point on the surface to describe how light interacts with the object, allowing computation of any view of the object under any lighting conditions. A simple approximation to this ideal is a geometric model with a single color; texture maps improve this approximation by mapping an image onto the geometry. This project is to devlop a new modeling paradigm, based on IBR, that extends this idea further by adding an approximation to the BRDF at every point on the surface.This new modeling paradigm improves upon the efficiency of generating and storing image-based rendering models by combining them with geometric model information, thus bridging the gap between the two methods. The intent is to construct geometric models which are visually complex and geometrically faithful, but avoid the overhead of geometrically modeled surface detail.Just as important as developing an underlying model is the ability to use real-world objects to create the models. Many of today's complicated geometric models were captured, using a laser scan or a 3D digitizer, from physical objects. One goal of this research is a similar mechanism for capturing and rendering objects or scenes with complex visual properties.Methods. The two disciplines to be merged are image-based rendering and geometric modeling. The project will use the lumigraph for IBR, partly because it already incorporates a limited geometric model, and will use a manifold-based models for the geometric component. The lumigraph is a very general method for capturing the behavior of light as it leaves an object. Manifold-based geometry supports construction of arbitrary-topology surfaces by blending small surface pieces. The result of combining a lumigraph with a manifold is a geometric model that has information about how light rays are emitted from it.With this structure, any local constancy in emitted light along the surface is easily recognized, leading to considerable data-compression advantages. Thus, in addition to an interesting geometric model, this structure allows for efficient storage of IBR datasets. This same local-constancy can be used as a guide to goodness-of-fit of the surface to the actual geometry of the object being modeled. Each of these operations requires a homogeneous representation of the underlying geometry - one in which all of the points can be treated equally, rather than, for example, the division of the points into the vertices, edges, and faces of polyhedra, or the abutting patches of B-spline models. The manifold structure provides exactly this homogeneity.Impact. Many image-based rendering approaches use some knowledge of geometry, usually depth. The addition of explicit geometry object has two potential benefits; a richer modeling type, in which global lumigraph-like data is attached to a geometric foundation, and a means for explicitly exploring the relationship between geometry and the compression of data gathered from images.The resulting models will be useful in multiple applications, particularly those in which high image quality is essential, but where explicit modeling is impossible. These include special-effects production and educational applications (e.g., on-line medical models), as well as possible applications in reverse engineering and architectural lighting simulation.