Description
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Name: |
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that satisfies the Optical Flow |
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1. Smallest Optical Flow (4 pts): What velocity |
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Constraint Equation |
+ |
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+ = 0 has the smallest magnitude | |? Hint: This can be |
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solved geometrically as was outlined in class by considering the OFCE in , space.
v
(0,−
(− ,0)
u
2. Moving Gaussian Blob (6 (pts): , , A) Gaussian=1 blob is observed over2 time to have brightness
−2 2( 2−2( 1+ 2) +( 1+ 2) )
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What are , , and ? Hint: You should find that these derivatives have a simple form.
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The Optical Flow Constraint Equation is + + = 0. Write this out using the results of Part a. and simplify it as much as possible. For example, you should be able to cancel terms that occur in each of , , and .
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( , , ) = |
+ 1 |
[( − |
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+(− )2 |
] |
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3. Quadratic Optical Flow (8 pts : Suppose the image brightness is given by |
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0 |
2 |
1 |
2 |
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What are Ix, Iy, and It? Hint: You should find that these derivatives have a simple form.
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Express the Optical Flow Constraint Equation + + = 0 in the simplest terms possible for this image sequence.
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The equation from b. must hold for all x, y, and t. Find a constant solution for u and v that makes this true, that is, such that u and v do not depend on x, y, and t.
