Machine vision is the study of how to build intelligent machines using vision. Traditional projective geometry does not necessarily provide useful tools in its original form to solve machine vision problems. In this book, the author reformulates the structure of projective geometry from a computational viewpoint. Thus, it can be applied to machine vision problems. Unlike other books, this book does not discuss most of the traditional optics such as image processing, feature extraction, etc. There is a very well-written book. Each chapter ends with a set of exercises. Answers to the exercises are given at the end of the book.
In Chapter 2, basic concepts of (2-D) projective geometry are reformulated in terms of N-vectors (unit vectors consisting of homogeneous coordinates), and relationship to 3-D interpretations of the scene are described. In Chapter 3, the author shows that orthogonality in 3-D scenes can be described in terms of projective geometry by introducing a special ``conic'' called the absolute conic. Two important machine vision applications, camera calibration and 3-D road reconstruction, are also discussed.
Translational motion and stereo are the subject of the fourth chapter. Introducing N-velocity, the author shows that the 3-D shape of a translating object can be reconstructed up to scale from two consecutive images. Geometric relationships concerning stereo are also described.
Chapter 5 deals with 3-D rotation. Two application problems are studied. One is orthogonality fitting, fitting three mutually orthogonal lines to three not necessarily orthogonal orientations. The other is orthogonal frame reconstruction reconstructing an orthonormal system of vectors from its projection.
Chapter 6 deals with general 3-D rigid motion, 3-D rigid motion of a planar surface and 3-D rigid motion of an object of general shape. Special emphasis is placed on the robustness of computation.
Chapter 7 is devoted to the study of the mathematical analysis of optical flow. In Chapter 8, properties of conics are reformulated as computational procedures, and the geometric meaning s of conic-related concepts such as poles, polars, and conjugate pairs are described from computational point of view.
Statistical analysis of geometric computations based on image data is the topic of the last two chapters. Chapter 9 is devoted to statistical analysis of errors involved in geometric computation. In Chapter 10, the techniques established in Chapter 9 are applied to some important machine vision problems. A bibliography of general references is given at the end of the book.