The perpendicular projection of any 

 other point in space can be located similarly 

 on the ori enta tion line HJ to give some other 

 value say OQ,, . The algebraic subtraction of 

 OQ, from OO2 then will give the longitudinal 

 distance between the two points Q, and Q2- 



Perspective error 



The problem of eliminating perspective 

 error is solved by drawing a number of equally 

 spaced, parallel lines (called grid lines) on the 

 base plane. Figure 7 (I) shows such a plane 

 with grid lines 1.5 centimeters apart. Two ob- 

 jects, A and B, of equal length have been placed 

 on this plane, and a camera has been positioned 

 to take a picture of them . 



The term "perspective", as used here, 

 is defined as "natural objects as they appear to 

 the eye represented on a plane, such as a pic- 

 ture" . Figure 5 illustrates the error caused 

 by perspective; that is, the jumping salmon 

 appears lar^^f^r than does the fishing vessel 

 since the salmon was much closer to the cam- 

 era than was the vessel when the picture was 

 taken. Similarly, if two objects of the same 

 size, such as objects A and B (fig. 6), are 

 placed on a flat board or base plane in such a 

 manner that one is at a greater distance from 

 the camera than is the other, they will not ap- 

 pear to be the same size in a picture taken of 

 them . 



In the preceding section, we developed 

 equation 10 for eliminating parallax error. 

 This equation was based upon the stipulation 

 that the various projections involved would be 

 free from all other errors. We now see that 

 owing to perspective, this stipulation is not met 

 and that a suitable correction will have to be 

 made for the perspective error as well. 



To the camera, all objects appear to be 

 lying in one plane regardless of the actual posi- 

 tion of them in space. Hence, for simplicity 

 in the following discussion, we will assume that 

 all of the objects are lying on one plane --the 

 base plane- -since that is the one on which they 

 will appear to lie in the photograph. 



,^^ 



The diagram of the resulting photograph 

 shown in figure 7 (II) illustrates that the grid 

 lines appear to become progressively closer to- 

 gether. Similarly, object A appears to be larger 

 than object B, since object A was closer to the 

 camera than object B was. From our knowledge 

 however, that the distance between the grid 

 lines is actually 1 .5 centimeters, we can deter- 

 mine that both objects A and B are 3.0 centimeters 

 long despite the perspective error. 



If one end of the object falls between two 

 of the grid lines, as illustrated in figure 8, we 

 must determine the proportionality factor for 

 the distance between the particular lines involved 

 and apply this factor to the measurement of the 

 object in the picture. If, for example, the actual 

 distance between lines 4 and 5 in figure 8 was 

 1 .5 centimeters and the measurement between 

 them, in the picture, was 0.5 centimeters, then 

 the proportionality factor would be 1.5 = 3.0. 



Now, if the measurement of A, in the picture 

 was 0.27 centimeters, its actual length would 

 be 0.27 X 3.0 = 0.81 centimeters. 



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