Bernhard P. Wrobel

Photogrammetric Computer Vision

WG I/4 Terms of Reference Small satellites for Earth observation—complexity, reliability, and comparative costs Platform guidance, navigation and positioning, integration of GPS, and orientation systems Performance of high resolution and hyperspectral imaging systems for Earth system science Monitor and report developments of new sensors such as smart sensors, polarisation sensors, pollution monitors, laser altimeters, and precipitation radar

The Photogrammetric Reconstruction Task Solved by Bundle Adjustment Directly with Pixel Bundles

At present the reconstruction task of photogrammetry is performed mostly in several steps: one feature-based bundle solution followed by many dense image matchings and fusion of intermediate results. To increase the performance of reconstruction to a maximum a different definition is proposed, starting from the approach of strict digital image inversion and the correspondence condition of image grey values with the unknown function of object surface intensity (or brightness). This leads again to a bundle solution (similar to the classical solution), however, directly with the image grey values as measurements so that each pixel represents a ray and each image a high-density bundle of rays (pixel bundle). All images of a block are forced to generate optimally one function of object surface intensity together with the object surface and the orientation of the images (WROBEL, Proceedings SPIE 804, pp 325–334. In German language: Bildmessung und Luftbildwesen 1987). The diverse tasks of modern life need different methods of 3D reconstructions in diverging performance. Here, we concentrate on a high-fidelity approach of both the functional and stochastic model of image evaluation. The fundamental derivations are presented, main properties (e.g. its statistical potential) are discussed and highlighted in comparison to deficiencies of existing approaches. Topographical reconstructions demonstrate the validity of the results with respect to the surface and the standard deviations of its heights.ZusammenfassungDie Rekonstruktionsaufgabe der Photogrammetrie gelöst durch Bündelausgleichung direkt mit Pixelbündeln . Die Rekonstruktionsaufgabe der Photogrammetrie wird gegenwärtig meist schrittweise gelöst mit einer merkmalsbasierten Bündellösung gefolgt von vielen dichten Bildzuordnungen plus Fusion zum Endresultat. Um die Leistungen der Rekonstruktion zum Maximum zu erhöhen, wird für sie eine andere Definition gegeben. Sie startet vom strengen Ansatz der digitalen Bildinversion und der Korrespondenzbedingung von Bildgrauwerten mit der unbekannten Funktion der Objekthelligkeit. Dies führt wieder zu einer Bündellösung (ähnlich der klassischen), jedoch direkt mit den Bildgrauwerten als Messwerten, so dass jedes Pixel einen Abbildungsstrahl repräsentiert und jedes Bild ein Strahlenbündel sehr hoher Dichte (Pixelbündel). Alle Bilder eines Blocks werden der Bedingung unterworfen, eine einzige Funktion der Objekthelligkeit optimal zu erzeugen gemeinsam mit der Objektoberfläche und der Orientierung der Bilder (WROBEL, Proceedings SPIE 804, pp 325–334. In German language: Bildmessung und Luftbildwesen 1987). Die Aufgaben des modernen Lebens benötigen Methoden für 3D Rekonstruktionen in sehr unterschiedlicher Leistung. Wir konzentrieren uns hier auf einen Ansatz in hoher Treue für das stochastische wie auch für das funktionale Modell der Bildauswertung. In diesem Beitrag werden die fundamentalen Ableitungen des Ansatzes aufgezeigt, die Haupteigenschaften (z.B. ihr hohes statistisches Potential) diskutiert und hervorgehoben im Vergleich zu Unzulänglichkeiten von existierenden Ansätzen. Topographische Rekonstruktionen demonstrieren die Gültigkeit der Ergebnisse gleichermaßen für die Oberfläche und die Standardabweichungen ihrer Höhen.

Oriented Projective Geometry

While classical projective geometry in general does not distinguish between the two opposite directions of a line or the two sides of a plane, oriented projective geometry provides a framework that accounts for situations where it is very useful to take the orientation of entities into account.

Homogeneous Representations of Points, Lines and Planes

This chapter motivates and introduces homogeneous coordinates for representing geometric entities. We aim at exploiting the algebraic properties of the representations of geometric entities and at giving geometrically intuitive interpretations.

Reasoning with Uncertain Geometric Entities

This chapter discusses the representation of uncertain homogeneous. We introduce a representation of the uncertainty which is minimal, thus does not contain singular covariance matrices, and develop methods for the estimation of geometric elements and transformation parameters.

Geometry and Orientation of the Image Triplet

This chapter discusses the basic geometry and orientation of image triplets. The higher redundancy caused by observing the scene in three instead of only two images, as before, leads to a number of advantages, so it is useful to treat the image triplet in detail.

Probability Theory and Random Variables

This chapter collects the basic terms from probability theory and statistics. It motivates the axiomatic approach for the concept of probability, introduces the concept of a random variable, describes the key properties of the main distributions of random variables occurring when modelling observational uncertainties and testing hypotheses, and provides an introduction to stochastic processes.

Geometry and Orientation of the Single Image

A single image of a scene is useful in various applications, such as ego-motion determination or partial scene reconstruction. We discuss models for cameras, develop methods for determining their parameters and provide tools for inferring 3D information from a single image.

Geometry and Orientation of the Image Pair

A pair of perspective images taken from two positions such that they show the scene from different directions is sufficient to reconstruct it without having pre-knowledge about it. We provide algorithms for recovering the orientation of the image pair and for determining the 3D coordinates of scene points.