Translation of "Zur Ermittlung eines Objektes aus zwei Perspektiven mit innerer Orientierung" by Erwin Kruppa (1913)

TL;DR

Kruppa's 1913 paper introduces the first five-point algorithm for relative pose estimation from two calibrated images, significantly impacting computer vision and camera self-calibration research.

Contribution

The paper presents the pioneering five-point algorithm for determining relative pose from five point matches, a foundational method in geometric computer vision.

Findings

First five-point algorithm for pose estimation

Finite solutions for relative pose from five points

Influence on camera self-calibration research

Abstract

Erwin Kruppa's 1913 paper, Erwin Kruppa, "Zur Ermittlung eines Objektes aus zwei Perspektiven mit innerer Orientierung", Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Kaiserlichen Akademie der Wissenschaften, Vol. 122 (1913), pp. 1939-1948, which may be translated as "To determine a 3D object from two perspective views with known inner orientation", is a landmark paper in Computer Vision because it provides the first five-point algorithm for relative pose estimation. Kruppa showed that (a finite number of solutions for) the relative pose between two calibrated images of a rigid object can be computed from five point matches between the images. Kruppa's work also gained attention in the topic of camera self-calibration, as presented in (Maybank and Faugeras, 1992). Since the paper is still relevant today (more than a hundred citations within the last ten years) and the paper is not available online, we ordered a copy from the German National Library in Frankfurt and provide an English translation along with the German original. We also adapt the terminology to a modern jargon and provide some clarifications (highlighted in sans-serif font). For a historical review of geometric computer vision, the reader is referred to the recent survey paper (Sturm, 2011).