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Über dieses Buch

Vision has to deal with uncertainty. The sensors are noisy, the prior knowledge is uncertain or inaccurate, and the problems of recovering scene information from images are often ill-posed or underconstrained. This research monograph, which is based on Richard Szeliski's Ph.D. dissertation at Carnegie Mellon University, presents a Bayesian model for representing and processing uncertainty in low­ level vision. Recently, probabilistic models have been proposed and used in vision. Sze­ liski's method has a few distinguishing features that make this monograph im­ portant and attractive. First, he presents a systematic Bayesian probabilistic estimation framework in which we can define and compute the prior model, the sensor model, and the posterior model. Second, his method represents and computes explicitly not only the best estimates but also the level of uncertainty of those estimates using second order statistics, i.e., the variance and covariance. Third, the algorithms developed are computationally tractable for dense fields, such as depth maps constructed from stereo or range finder data, rather than just sparse data sets. Finally, Szeliski demonstrates successful applications of the method to several real world problems, including the generation of fractal surfaces, motion estimation without correspondence using sparse range data, and incremental depth from motion.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
This book examines the application of Bayesian modeling to low-level vision. Bayesian modeling is a probabilistic estimation framework that consists of three separate models. The prior model describes the world or its properties which we are trying to estimate. The sensor model describes how any one instance of this world is related to the observations (such as images) which we make. The posterior model, which is obtained by combining the prior and sensor models using Bayes’ Rule, describes our current estimate of the world given the data which we have observed.
Richard Szeliski

Chapter 2. Representations for low-level vision

Abstract
Representations play a central role in the study of any visual processing system (Marr 1982). The representations and algorithms that describe a visual process are a particular instantiation of a general computational theory, and are constrained by the hardware that is available for their implementation. Representations make certain types of information explicit, while requiring that other information be computed when needed. For example, a depth map and an orientation map may represent the same visible surface, but complex computations may be required to convert from one representation to the other. The choice of representation becomes crucial when the information being represented is uncertain (McDermott 1980).
Richard Szeliski

Chapter 3. Bayesian models and Markov Random Fields

Abstract
In the early days of computer vision, Bayesian modeling was a popular technique for formulating estimation and pattern classification problems (Duda and Hart 1973). This probabilistic approach fell into disuse, however, as computer vision shifted its attention to the understanding of the physics of image formation and the solution of inverse problems. Bayesian modeling has had a recent resurgence, due in part to the increased sophistication available from Markov Random Field models, and due to a realization of the importance of sensor and error modeling. In this chapter, we will briefly review the general Bayesian modeling framework. This will be followed by an introduction to Markov Random Fields and their implementation. We will then discuss the utility of probabilistic models in later stages of vision and preview the use of Bayesian modeling in the remainder of the book.
Richard Szeliski

Chapter 4. Prior models

Abstract
As we have seen in the previous chapter, prior models play an essential role in the formulation of Bayesian estimators. A prior model can be as simple as the prior probabilities of different terrain types used in our remote sensing example of Section 3.1, or as complicated as the initial state (position, orientation and velocity) estimate of a satellite in a Kaiman filter on-line estimation system. When applied to low-level vision, prior models encode the smoothness or coherence of the two-dimensional fields that are being estimated from the image. In this chapter, we will examine the spectral characteristics of our prior models, develop algorithms for efficiently generating random samples, develop a relative representation using a frequency domain approach, and compare our probabilistic models to deterministic (mechanical) models. Let us start by previewing how these four ideas fit together.
Richard Szeliski

Chapter 5. Sensor models

Abstract
Modeling the error inherent in sensors and using these error models to improve performance are becoming increasingly important in computer vision (Matthies and Shafer 1987). In the context of the Bayesian estimation framework, sensor models form the second major component of our Bayesian model. In this chapter, we will examine a number of different sensor models which arise from both sparse (symbolic) and dense (iconic) measurements.
Richard Szeliski

Chapter 6. Posterior estimates

Abstract
In the previous two chapters, we have developed a prior model for visible surfaces and a variety of sensor models for the inputs to low-level vision algorithms. In this chapter, we will see how the prior and sensor models can be combined using Bayes’ Rule to obtain a posterior model. We will study how to compute optimal estimates of the visible surface from the posterior distribution. We will also show to calculate from this distribution the uncertainty inherent in a visible surface estimate, and discuss why such uncertainty modeling is important. Two novel algorithms which are based on the probabilistic posterior model will then be presented. The first algorithm estimates the regularization parameter λ from the sensed data using a maximum likelihood approach. The second algorithm estimates observer motion by matching sparse range data without using correspondence. These two algorithms illustrate the advantages of using a Bayesian approach to low-level vision.
Richard Szeliski

Chapter 7. Incremental algorithms for depth-from-motion

Abstract
The Bayesian models which we have developed in this book allow us to obtain optimal estimates of static visible surfaces, to integrate information from multiple viewpoints, and to analyze the uncertainty in our estimates. Many computer vision applications, however, deal with dynamic environments. This may involve tracking moving objects or updating the model of the environment as the observer moves around. Recent results by Aloimonos et al. (1987) suggest that taking an active role in vision (either through eye or observer movements) greatly simplifies the complexity of certain low-level vision problems. In this chapter, we will examine one such problem, namely the recovery of depth from motion sequences.
Richard Szeliski

Chapter 8. Conclusions

Abstract
In this book, we have developed a Bayesian model for the dense fields that arise in low-level vision, and shown how this model can be be applied to a number of low-level vision problems. We have used this model to analyze the assumptions inherent in existing vision algorithms, to improve the performance of these algorithms, and to devise novel algorithms for problems which have not previously been studied. In this chapter, we will summarize these important results and discuss how they can be extended in the future to other computer vision problems.
Richard Szeliski

Backmatter

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