125 Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 8 DOI: 10.4018/978-1-4666-3994-2.ch008 INTRODUCTION Techniques are developed to reconstruct objects/ surfaces in 3D space. These techniques use groups of images taken by cameras. Variations of the problem include 3D reconstruction from uncalibrated monocular image sequence (Aze- vedo, Tavares, & Vaz, 2009, Fitzgibbon, Cross, & Zisserman, 1998, Pollefeys, Koch, Vergauwen, & Gool, 1998); 3D reconstruction from calibrated monocular image sequence (Nguyen & Hanajik, 1995); and 3D reconstruction from stereo images. This later case includes pairs of images taken at the same time by two cameras or at two different instants by one camera provided that the scene is static. In many cases, the solution is divided into two steps (Zhang, 1995). These steps are: 1. Extracting and matching features between corresponding images; and 2. Determining structure from corresponding features. Rimon Elias German University in Cairo, Egypt Projective Geometry for 3D Modeling of Objects ABSTRACT This chapter surveys many fundamental aspects of projective geometry that have been used extensively in computer vision literature. In particular, it discusses the role of this branch of geometry in reconstructing basic entities (e.g., 3D points, 3D lines, and planes) in 3D space from multiple images. The chapter presents the notation of diferent elements. It investigates the geometrical relationships when one or two cameras are observing the scene creating single-view and two-view geometry. In other words, camera parameters in terms of locations and orientations, with respect to 3D space and with respect to other cameras, create relationships. This chapter discusses these relationships and expresses them mathematically. Finally, dif- ferent approaches to deal with the existence of noise or inaccuracy in general are presented.