Appendix B 

 Photogrammetry 



The technique of using video images to determine ground topography is 

 straightforward and has been described by Lippmann and Holman (1989) 1 and 

 Holland et al. (1997). A summary of this photogrammetric method is 

 presented here to demonstrate the use of video to measure subaerial beach 

 profiles (following Holman et al. 1991). This method is essentially the same as 

 that for the video measurement of swash oscillations, except in reversed order. 

 The fundamental problem is that since video is two-dimensional and ground 

 topography is three-dimensional, the transformation is underdetermined. If one 

 more piece of information is known, then the transformation from video to 

 ground coordinates can be resolved, assuming that the camera geometry is 

 known (i.e., camera position and view angles). For example, if one coordinate 

 of an object is known, such as its longshore position, then a solution exists for 

 cross-shore and vertical positions. Thus, if a line was made to cross the beach 

 at a known angle, as with a beam of light or a shadow, then the profile along 

 that line could be determined. 



The photogrammetry of oblique images and labeling conventions used in the 

 rectification process are illustrated in Figure Bl. Coordinates in the image 

 plane are denoted with lower case letters (x,y) and with upper case letters 

 (X,Y,Z) for ground coordinates. The camera is located at point O and height 

 Z c above the horizontal (X-Y) reference plane, assumed to be MSL in this 

 application. The camera nadir line passes through this reference plane at the 

 nadir point N. The camera's focal length f c is the distance between the point O 

 and the x-y focal plane. The camera's tilt t is measured as the angle between 

 the nadir and to principal point p, the point where the optical axis intersects the 

 center of the focal plane. The camera azimuthal angle <$> is relative to the 

 positive y-axis (longshore direction). A point on the ground at Q(X Q ,Y Q ,Z Q ) 

 and corresponding image coordinates q(x q ,y q ) will have the same angles (a and 

 y) to their respective principal lines (the line passing through principal point 

 and nadir). 



References cited in this appendix are located at the end of the main text. 

 Appendix B Photogrammetry B1 



