Generalized Point Photogrammetry and Its Application

Point based co-linearity is an essential conception in Photogrammetry. But point in photogrammetry means only physical or visible points, such as dots, cross points and corner point etc. Especially in the stage of either analogue or analytical, even digital photogrammetry, the main primitive feature, which can be measured by human operator, is physical point. It can be referred to as Point Photogrammetry contrary to Line photogrammetry, which is proposed and used only in the past about 20 years. For a straight line a coplanar equation is used, where the line on the image lies on the plane, passing through corresponding spatial straight line and the photographing centre in line photogrammetry. All straight lines and curves are normally referred to linear feature rather than point feature in line photogrammetry. The co-planarity can be normally explain as Sa·(SP×SQ)=0, which means the image point a must lie on the plane composed by perspective centre S and two end point P and Q of the 3D line. However, in mathematics all lines or curves are consists of points, which is expressed as generalized point in this paper. Collinear equation could be used to linear features similar as the visible point, and all kinds of features existing in photogrammetry can be concentrated on “point” – called as Generalized Point Photogrammetry. According to this philosophy the adjustment form would be consistent, simpler and more convenient comparing with line photogrammetry. In the Generalized point photogrammetry the only difference between physical points and feature line point is that two collinear equations of both x and y are used for the physical point and only one collinear equation of x or y depending on the local direction of the line segment is used for feature line point. The collinear equation, used for feature line point, includes the parameters of feature line. For example, the coordinates of point in a straight line or circle can be expressed by their parameters, and be substituted to the collinear equation, and the parameters can be computed in the same time. Besides physical point and feature line point, the invisible point – infinity is also included in generalized point scope, and collinear equations are used for them too. After the theory of the generalized point photogrammetry is introduced, its applications are presented, including extraction of vanish points, determination of interior parameters of the image, and sheet-metal part inspection and measurement. Corresponding experiments and results are demonstrated with the conclusion. * Corresponding author.