Computer Vision Foundations · free preview

Steerable Filters

A filter rotated to any angle responds as a fixed linear combination of a few basis responses, the steering theorem, which turns orientation from a bank dimension into arithmetic and cleans up oriented energy at junctions.

1. Rotations for free

Rotations for free

2. The theorem and the count

The theorem and the count

3. Oriented energy

Oriented energy

4. Junctions and their cleanup

Junctions and their cleanup

5. What steering buys

What does the steering theorem save compared to a dense bank of rotated filters?

6. The junction artifact

At a junction of two edges, raw oriented energy shows extra lobes beyond the two true orientations. What produces them and what removes them?

7. Steering weights

First-order steering uses g_theta = cos(theta) g_x + sin(theta) g_y. With cos(theta) = 0.6, write the coefficient multiplying g_y if sin(theta) = 0.8.

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