Second Derivative Filters

Finite Difference Formulas

result in the following masks:

Second derivative by repeated convolution

Example

original image	dx^2	dy^2

Laplacian (lap1)

filter text: lap1.con

Second Derivative with Smoothing (I)

original image	dx^2	dy^2

Laplacian (lap2)

filter text: lap2.con

Second Derivative with Smoothing (II)

original image	dx^2	dy^2

Laplacian (lap3)

filter text: lap3.con

Linear Combinations of Laplacian Filters

Take linear combinations of lap1 and lap2. The formula below produces a very symmetric sequence of filters.

	mask		mask

Maintained by John Loomis, last updated June 18, 1997