Computer Vision Foundations · free preview
The Laplacian, Sharpening and Retinex
The Laplacian adds the two second derivatives into one rotationally invariant operator whose zero-crossings mark edges, its blurred form models early vision, and thresholding its gradient relatives factors an image into reflectance and illumination.
1. The sum of second derivatives
The sum of second derivatives
2. Edges as zero-crossings
Edges as zero-crossings
3. An early model of the visual system
An early model of the visual system
4. Retinex, seeing paint under light
Retinex, seeing paint under light
5. What the zero-crossing buys
Why did Marr and Hildreth propose Laplacian zero-crossings rather than large Laplacian values as the definition of an edge?
6. Separating paint from light
Retinex takes logarithms of an observed image made of reflectance times illumination. What property of the two factors does the threshold exploit after differentiation?
7. The Laplacian on a ramp
Apply the 1D Laplacian to the ramp 0 1 2 3 at the position of the value 2, meaning compute one times 1 minus two times 2 plus one times 3. Write the result.
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