midterm_solution

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Computer Science

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Jun 4, 2024

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Midterm Solutions Duo Lu <duolu@asu.edu>, Yezhou Yang <yz.yang@asu.edu>
Question 1 In which of the following scenarios can you use a weak perspective camera model for the target object? (a) A Squirrel passing quickly in front of you. (b) An airplane flying at a very high attitude. (c) The Eiffel tower when you are taking a photo of it. (d) A car beside you when you are driving. The best option is (b). Since the distance of the object is far away (an airplane typically flying at around 30,000 feet or 10,000 meters), the relative size of the object on the ground in the direction of depth is not significant ( Z Δ Z ). Hence, a weak perspective camera model can approximate the actual perspective camera model with negligible error.
2D-1D Weak Perspective Projection Weak Perspective Projection Perspective Projection X Δ Z x C orthographic projection scaling z -axis
Perspective Projection vs. Orthographic Projection C f x F x y z X f = ∞ x X Camera center at a finite point. Camera center at infinite and focal length is infinite. perspective camera weak perspective camera (affine camera)
Perspective Projection vs. Orthographic Projection perspective camera x = X / Z y = Y / Z x = X y = Y Scaling factor is the depth. Scaling factor is arbitrary. weak perspective camera (affine camera)
Image Courtesy: Richard Hartley and Andrew Zisserman
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