Corners

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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STOP
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STOP
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STOP
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STOP
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STOP
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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners

• Why are they important?

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Corners contain more edges than lines.

• A point on a line is hard to match.

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Corners contain more edges than lines.

• A corner is easier

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Edge Detectors Tend to Fail at Corners
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Matlab
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Finding Corners

• Intuition
• Right at corner, gradient is ill defined.
• Near corner, gradient has two different values.

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Formula for Finding Corners
We look at matrix
Gradient with respect to x, times gradient with
respect to y
Sum over a small region, the hypothetical corner
WHY THIS?
Matrix is symmetric
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First, consider case where

• This means all gradients in neighborhood are
• (k,0) or (0, c) or (0, 0) (or
  off-diagonals cancel).
• What is region like if
• l1 0?
• l2 0?
• l1 0 and l2 0?
• l1 gt 0 and l2 gt 0?

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General Case
From Linear Algebra we havent talked about it
follows that since C is symmetric
where R is a rotation matrix. So every case is
like one on last slide.
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So, to detect corners

• Filter image.
• Compute magnitude of the gradient everywhere.
• We construct C in a window.
• Use Linear Algebra to find l1 and l2.
• If they are both big, we have a corner.