Photogrammetric Computer Vision: Statistics, Geometry, Orientation and Reconstruction

reviewed by: Charles Toth, Research Professor, The Ohio State University, Columbus, Ohio and Stewart Walker, San Diego, California. Photogrammetric Computer Vision represents a milestone publication in modern photogrammetry. Long years of intense labor by two legendary authors, eminent professors of geomatics from Bonn and Darmstadt, and a talented team of assistants, have produced a true magnum opus, a rare masterpiece, providing the most comprehensive description of the underlying theory at the intersection of photogrammetry and computer vision. The significance of the book is in a way mirrored by its huge weight and size (286 x 216 mm; 11.2 x 8.5 inches), with over 800 pages in small fonts. The book opens with a short introduction, which immediately defines both photogrammetry and computer vision and thus explains their joint treatment in the book. While the authors are firm that they will not cover hardware, they say enough in a few pages to indicate the scope of photogrammetric applications and allow readers to link this book to more traditional texts. Importantly, the focus on probabilistic and statistical reasoning is succinctly justified. They include useful suggestions on how the book can be used for courses at different levels. These confirm that the contents far exceed anything that can be reasonably included in a single course. Part I, “Statistics” and “Estimation” lays the critical ground work in three intense chapters. Chapter 2, “Probability Theory and Random Variables” is followed by the short Chapter 3 on “Testing”. These set the tone for the book – an advanced level of discourse, reinforced by mathematical rigor and innumerable equations. The reader must therefore concentrate and expect slow progress, but will be amply repaid, especially by the key Chapter 4, “Estimation”, well over a hundred pages covering models and estimation, i.e. it includes what most of us were brought up to call “least-squares adjustment”. One of your reviewers experimented by revising the topic of variance components: the concise exposition on pages 91-93 is exemplary. Part II, “Geometry”, is a little longer and covers the elements that will be used in the photogrammetric processes themselves in Part III. As we were led to expect in Part I, the treatment is detailed and demanding. Chapters 5-10 cover “Homogenous Representations of Points, Lines and Planes”, “Transformations”, “Geometric Operations”, “Rotations”, “Oriented Projective Geometry” and “Reasoning with Uncertain Geometric Entities”. With 440 pages under our belts, we are ready for the entrée, Part III, “Orientation and Reconstruction”. This brings the mathematical groundwork to bear on topics we all know: Chapter 11, “Overview”, is a useful outline of the material to come in the next five chapters, “Geometry and Orientation of the Single Image”, “Geometry and Orientation of the Image Pair”, “Geometry and Orientation of the Image Triplet”, “Bundle Adjustment” and “Surface Reconstruction”. In Chapter 11, too, the authors present a taxonomy of cameras and explain their emphasis on “central” cameras, i.e. with a single viewpoint. Perhaps some readers will be disappointed that the “non-central” camera, i.e. no single viewpoint, enjoys less coverage, since it includes the pushbroom design used to acquire most satellite imagery; a special case. We are in familiar territory in Part III, the substance of photogrammetry, but the rigorous mathematical approach and the widespread use of techniques and nomenclature from computer vision provide a freshness. In Chapter 12, for example, well known concepts related to the single photo are presented and the collinearity equations are given in their standard form, but the reader is reminded that the image coordinates therein are inhomogenous, i.e. concepts from photogrammetry and computer vision