A Geometrical Treatment for Establishment of Panoramic Perspective from Successive Photographs.

Abstract

The main objective of this study is to introduce some new methods to make a panorama with a regular camera. These methods, mathematical and graphical, are developed using central projection and based mainly on projective geometry and homogenous coordinates in order to make a panoramic perspective from successive photographs.

First, we introduce an extended review of the previous work concerning the mathematical and graphical methods used to make a panoramic photograph with a regular camera.Jhen, we give a survey on the background principles about the characteristics of projective geometry, coordinate systems and the equations of transformation needed for the mathematical approach.

Second, an algebraic solution of the problem was introduced. This solution is based mainly on projective geometry and the homogenous coordinates.

Third, a graphical representation of this algebraic solution based on the principles of perspective projection and collineation was given.

Finally, we introduce an analysis of errors and how to treat these errors using the method of least squares.