Transform - Laplace

The Laplace filters in the Transform toolbar for images detect rapid changes in pixels using two different analytic matrices. The Laplace filters often result in "negative" images with brighter tones at detected features and dark or black tones elsewhere. These filters will emphasize linear features such as edges.

 

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The examples below are based on an example image that is a screen shot of a drawing, converted to a raster image and shown above. The image therefore provides a nice mix of strong horizontal and vertical linear features made up of evenly aligned single pixels as well as pixels arranged in uneven linear patterns.

 

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Laplace 1 - Good edge detection with emphasis on horizontal and vertical changes.

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Laplace 2 - Strongest changes at point of intersection of horizontal and vertical lines, resulting at a small X pixel pattern at the point of intersection; fuzzy detection of linear features at other angles.

 

Historical Note

 

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Pierre Simon Laplace

 

These filters are named for Pierre Simon Laplace (1749 - 1827), the famous French astronomer and mathematician. Laplace is best known for his mathematical analysis of Newton's theory of gravity as applied to planetary motion, just one of many works of astonishing power and originality. Perhaps it is best that Laplace is remembered for his immortal contributions to science since his contemporary life was colored by his servile political social climbing and occasional misrepresentation of the findings of others (including such later luminaries as Legendre and Fourier) as his own.

 

See the Image - Filter topic for a detailed discussion of how matrices are used in filter effects.