Corners Why are they important?.

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Feature extraction: Corners

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Presentation transcript:

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

STOP

STOP

STOP

STOP

STOP

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners Why are they important?

Corners contain more edges than lines. A point on a line is hard to match.

Corners contain more edges than lines. A corner is easier

Edge Detectors Tend to Fail at Corners

Matlab

Finding Corners Intuition: Right at corner, gradient is ill defined. Near corner, gradient has two different values.

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

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 > 0 and l2 > 0?

General Case: From Linear Algebra we haven’t talked about it follows that since C is symmetric: where R is a rotation matrix. So every case is like one on last slide.

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.