Sharpening kernel filter in 3D-CodePudding

A 3x3 sharpening kernel (2D) looks like this:

 0  -1   0
-1   5  -1
 0  -1   0

Then what are the values of a 3x3x3 sharpening kernel (3D)?

CodePudding user response：

That sharpening kernel is formed by subtracting a smoothing kernel from the identity kernel. You can sharpen an image by subtracting (with appropriate weight) a blurred image, and then scaling the result so you don’t loose brightness. Not loosing brightness means that the kernel must sum to 1. In pseudo-math notation we have:

s1 I - s2 k * I = (s1 δ - s2 k) * I

with k a smoothing kernel, δ The identity kernel, I an image, * the convolution, and the other two variables appropriate scaling.

So a smoothing kernel could be

| 0 1 0 |
| 1 1 1 | / 5
| 0 1 0 |

The identity kernel is

| 0 0 0 |
| 0 1 0 |
| 0 0 0 |

And choosing s1=6 and s2=5 we get the following sharpening kernel:

|  0 -1  0 |
| -1  5 -1 |
|  0 -1  0 |

To build a 3D version we do exactly the same process, but with a 3D smoothing kernel. You could end up with two other -1 values, and the central pixel would get a value of 7.