Computer Vision Foundations · free preview
Gaussian Derivatives and Scale
Differencing noisy pixels doubles the noise, so differentiation rides with a Gaussian blur, producing a family of derivative filters indexed by scale.
1. Differentiation amplifies noise
Differentiation amplifies noise
2. Blur and derivative commute
Blur and derivative commute
3. Scale as a parameter of vision
Scale as a parameter of vision
4. The multiscale preview
The multiscale preview
5. Why blur before differencing
Why does convolving with the derivative of a Gaussian behave better than applying a raw difference kernel to a noisy image?
6. Choosing a scale for a task
A program must find the outline of a zebra against grass. Which derivative scale is the better tool and why?
7. Doubling the noise
Two neighboring pixels each carry independent noise of variance 9. Write the variance of the noise in their difference.
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