Low-Level MRF Models

In this chapter, we formulate various MAP-MRF models for low-Level vision following the procedure summarized in Section 1.3.4. We begin with the prototypical MAP-MRF models for image restoration. The presentation therein introduces the most important concepts in MRF modeling. After that, the formulations for the image restoration are extended to a closely related problem, surface reconstruction, in which the observation may be sparser. The MRF models for boundary detection, texture and optical flow will be described subsequently. How to impose the smoothness constraint while allowing discontinuities is an important issue in computer vision (Terzopoulos 1983b; Geman and Geman 1984; Blake and Zisserman 1987) that deserves a thorough investigation; it is the topic of Chapter 5. Another important issue, MRF parameter estimation in low-Level vision, will be discussed in Chapter 7.