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Thus, the aspect ratio of the ellipse at the center of the image plane is equal to cos a All ellipses along the same horizontal line in the image plane will have the same aspect ratio Now consider an ellipse with its center at (0, y') in the image plane The disc corresponding to this ellipse is at an angle with respect to the optical axis as shown in Figure 74(b) and (c), where tanB = y'/f The major diameter of the ellipse is now given by Equation 78 with a slight modification Since the disc is now located at a distance S away from the camera center, z must be replaced with S From Figure 74(b) and (c):

ive S implementation is the first step toward a successful Six Sigma integration It gets everyone on board and excited about change and solving problems in the organization from within

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Figure 74: (a) The three-dimensional representation of the camera system with slanted texture plane (b) The y-z view of (a) Note that the x axis is going into the paper (c) The x-z vew of (a) Note that the y axis is coming out of the paper

41 42 43 44 45 46 47 48 49 410

Figure 75: The image captured from the camera system in Figure 74 S-z tan a S= Therefore,

dmajor(O,y')

---------~~~"4848

51 52 53 54 55 61 62

(710) (711) (712)

(713)

The derivation of dminor(O, is a bit more involved First, from Figure y') 74(b), Z (714) S1 = 1- tan 01 tan a

63 64 65 66 67 68 69 610 611

(715) tan B tana 2 Now if we assume that the diameter of the disk d is very small so that it subtends a small angle at the camera center, we can approximate (716) Therefore, z (717) (718)

= 1-

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1 - tan B tan a'

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