The Laplacian-of-Gaussian (LoG) is a spatial filter used for edge enhancement and is closely related to the difference-of-Gaussians filter (`DiffOfGaussianFilter`). The formulation of the LoG filter algorithm is based on the equation provided in the Hypermedia Image Processing Reference (HIPR) 2. The LoG operator calculates the second spatial derivative of an image. In areas where image intensity is constant, the LoG response will be zero. Near areas of change in intensity the LoG will be positive on the darker side, and negative on the lighter side. This means that at a sharp edge, or boundary, between two regions of uniform but different intensities, the LoG response will be:

- zero at a long distance from the edge,
- positive just to one side of the edge,
- negative just to the other side of the edge,
- zero at some point in between, on the edge itself.

The user may optionally choose to reflecting the data along image edges. NoData values in the input image are similarly valued in the output. The output raster is of the float data type and continuous data scale.

## Reference

Fisher, R. 2004. Hypertext Image Processing Resources 2 (HIPR2). Available online: http://homepages.inf.ed.ac.uk/rbf/HIPR2/roberts.htm

## See Also

`DiffOfGaussianFilter`

## Function Signature

`def laplacian_of_gaussians_filter(self, raster: Raster, sigma: float = 0.75) -> Raster: ...`

## Project Links

WbW Homepage User Manual Support WbW