ABSTRACT
This chapter introduces the projective geometry, which provides the representations and transformations of geometric primitives in projective space. Multiple-view geometry provides a versatile tool to describe and analyze the geometric information based on the projected camera views at several poses. For visual control tasks, since the task and system feedback are both expressed in image space, multiple-view geometry is used to map the high-dimensional and redundant image information to the low-dimensional and compact geometric information. The single-view geometry is the fundamental model to describe the geometric relationship between 2D image space and 3D Euclidean space. Traditional two-view geometric models include the homography and epipolar geometry. In the applications of vision-based control, multiple-view geometry is generally estimated by the images captured by the camera at different poses. The homography is well defined and can be uniquely determined in various camera poses.
