Complanarity constraint

Complanarity condition is a term from photogrammetry , which ensures with the relative orientation that the rays of the pixels of two images intersect in a model.

Coordinate systems and terms in photogrammetry:

  X,Y,Z ...... Koordinaten des Landessystems
  x',y' ...... gemessene Bildkoordinaten, ohne jegliche Korrekturen
  x,y,c ...... Hauptpunktzentriertes, kalibriertes Bildkoordinatensystem
  u',v',w' ... Drehung Bild 1 in zum Landessystem achsparallelen System
  u",v",w" ... Drehung Bild 2 in zum Landessystem achsparallelen System
  u,v,w ...... aus Bild 1 und 2 abgeleitete Modellkoordinaten
  bx,by,bz ... Basiskomponenten

GH Schut has shown that when two homologous rays intersect, they are in a plane with base b . This fact alone is sufficient for establishing the relative orientation and is referred to as the complanarity condition .

With reference to the above coordinate systems, the following determinant applies:

{\ displaystyle \ Delta = {\ begin {vmatrix} 1 & u '& u' '\\ b_ {y} & v' & v '' \\ b_ {z} & w '& w' '\ end {vmatrix}} = 0}

Since (u ', v', w ') and (u ", v", w ") are functions of the image coordinates, either the rotation matrices or the control points in the location must be known. The complanarity condition is only fulfilled with a relative orientation possible through multiple iterations as part of an adjustment.

literature

R. Finsterwalder, W. Hofmann: Photogrammetrie. Berlin 1968
J. Albertz, W. Kreiling: Photogrammetric paperback. Karlsruhe 1980/3.
GH Schut: An analysis of methods and results in analytical aerial triangulation. Phia, 1957/58, pp. 16-32.
GH Schut: Remarks on the Theory of Analytical Aerial Triangulation. Phia, 1959/60, pp. 57-66.
Shineas Walcher & Salvatore Cona: Photogrammetric Thinking Solothurn 2011