Lumigraphs and Manifolds

引言和目标。基于图像的绘制(IBR)是一种相对较新的计算机图形学技术，其中场景的多个图像(计算机生成的或照片的)被修改和组合以产生表示场景的新视图的图像。生成的图像通常非常详细，但有时不正确，部分原因是缺乏基本的几何模型。相比之下，传统的图形学使用几何和照明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。理想的几何模型应该包括对象的完整几何加上表面上每个点的双向反射比分布函数(BRDF)来描述光线如何与对象交互，从而允许计算任何照明条件下对象的任何视图。这一理想的一个简单近似是具有单一颜色的几何模型；纹理贴图通过将图像映射到几何体来改进这种近似。该项目旨在开发一种新的基于IBR的建模范式，通过在曲面上的每个点添加对BRDF的近似值来进一步扩展这一思想，该新的建模范式通过将基于图像的绘制模型与几何模型信息相结合来提高基于图像的绘制模型的生成和存储的效率，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且几何上逼真的几何模型，但避免几何建模表面细节的开销。与开发底层模型一样重要的是使用真实世界对象创建模型的能力。今天的许多复杂几何模型都是使用激光扫描或3D数字化仪从物理对象中捕捉到的。这项研究的一个目标是建立一种类似的机制，用于捕获和渲染具有复杂视觉属性的对象或场景。要合并的两个学科是基于图像的绘制和几何建模。该项目将使用IBR的照相机，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模型的几何组件。照相是一种非常通用的方法，用于捕捉光线离开对象时的行为。基于流形的几何体支持通过混合小的曲面片来构建任意拓扑的曲面。将光照度计与流形相结合的结果是一个几何模型，它具有关于光线是如何从流形发射出来的信息。使用这种结构，可以很容易地识别出沿表面发射的光的任何局部不变性，从而产生相当大的数据压缩优势。因此，除了有趣的几何模型外，这种结构还允许高效存储IBR数据集。此相同的局部恒定性可用作曲面与正在建模的对象的实际几何体的适配度的指南。这些操作中的每一个都需要底层几何体的同质表示-其中所有点都可以被平等处理，而不是例如将点划分为多面体的顶点、边和面，或B样条线模型的邻接面片。流形结构恰恰提供了这种同质性。许多基于图像的绘制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，其中全局光照度数据被附加到几何基础上，以及一种显式探索几何与从图像中收集的数据的压缩之间的关系的方法。所得到的模型将在多种应用中有用，特别是在那些高图像质量必不可少但不可能显式建模的应用中。这些应用包括特效制作和教育应用(例如，在线医学模型)，以及可能在逆向工程和建筑照明模拟中的应用。

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.