Computer Vision Foundations · free preview

Gradient-Domain Editing

Storing an image as its gradients, editing those gradients, and reintegrating with the pseudoinverse yields inpainting that fills holes with surrounding color and sharpening that boosts detail without inventing it.

1. Encode, edit, decode

Encode, edit, decode

2. Inpainting by forgetting gradients

Inpainting by forgetting gradients

3. Sharpening by subtraction

Sharpening by subtraction

4. The pattern to keep

The pattern to keep

5. Why zero gradients fill the hole

In gradient-domain inpainting, all gradients inside the masked word region are set to zero before reintegration. Why does the surrounding red color flood into the hole?

6. The arithmetic of unsharp masking

The sharpening filter is twice the identity minus a normalized blur. Why does the DC gain equal exactly one rather than two?

7. Running the sharpening arithmetic

A flat region holds value 10, and the normalized blur returns 8 there because of a nearby edge bleeding in. The sharpening filter computes twice the original minus the blurred copy. Write the output value.

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