Rectifizierung

Rectifizierung (rectification) is a term used in German-speaking contexts to denote the act of correcting, restoring accuracy, or converting something to a standard form. It is used in various disciplines, often to describe different kinds of “correction” processes.

In mathematics, rectification of a curve refers to the determination of its length, i.e., the arc length. The problem is to transform the curvilinear path into a straight line with the same length. For a plane curve y = y(x), the length is L = ∫ from a to b sqrt(1+(dy/dx)^2) dx; for parametric curves, L = ∫ sqrt((dx/dt)^2 + (dy/dt)^2) dt. Rectification is a classical topic in differential geometry and has historical links to the development of integral calculus.

In metrology, surveying, and data processing, rectification denotes correcting measurements or sensor data to remove systematic errors and align with reference standards. This can include calibrating instruments, adjusting coordinates, or transforming data sets to a common frame.

In cartography and photogrammetry, rectification can refer to the correction of imagery to remove geometric distortions caused by sensor geometry or terrain; orthorectification is a related process that yields a planimetrically correct image.

In legal and administrative contexts, rectification denotes the correction of official records, contracts, or registrations to fix inaccuracies or spelling errors. This usage corresponds to the general sense of berichtigung or berichtigung im Rechtswesen.