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1
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- Today’s Readings
- Trucco & Verri, 8.3 – 8.4 (skip 8.3.3, read only top half of p.
199)
- Numerical Recipes (Newton-Raphson), 9.4 (first four pages)
- http://www.library.cornell.edu/nr/bookcpdf/c9-4.pdf
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2
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- Lots of uses
- Track object behavior
- Correct for camera jitter (stabilization)
- Align images (mosaics)
- 3D shape reconstruction
- Special effects
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3
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4
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- How to estimate pixel motion from image H to image I?
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5
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- Let’s look at these constraints more closely
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6
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- Combining these two equations
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7
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- Q: how many unknowns and
equations per pixel?
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8
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9
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10
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- How to get more equations for a pixel?
- Basic idea: impose additional
constraints
- most common is to assume that the flow field is smooth locally
- one method: pretend the pixel’s
neighbors have the same (u,v)
- If we use a 5x5 window, that gives us 25 equations per pixel!
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11
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- Prob: we have more equations than
unknowns
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12
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- Optimal (u, v) satisfies Lucas-Kanade equation
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13
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- What are the potential causes of errors in this procedure?
- Suppose ATA is easily invertible
- Suppose there is not much noise in the image
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14
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- Recall our small motion assumption
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15
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16
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- Is this motion small enough?
- Probably not—it’s much larger than one pixel (2nd order
terms dominate)
- How might we solve this problem?
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17
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18
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19
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20
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21
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- Suppose we have more than two images
- How to track a point through all of the images?
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22
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- Feature tracking
- Find feature correspondence between consecutive H, I
- Chain these together to find long-range correspondences
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23
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Notes