FeatureJ: Laplacian

General Description

This plugin enables you to compute the Laplacian of an image and detect its zero-crossings - features that have been shown by psychophysical and neurophysiological research to play a key role in human vision as well [1,2].

Description of Dialog Components

Compute Laplacian image. Laplacian computation and zero-crossing detection are completely separated in this plugin. Being able to switch them on or off independently enables you to apply zero-crossing detection without having to compute the Laplacian first. If the size of the image is unity in the z-dimension (single slice), the plugin computes the 2D Laplacian. Otherwise it computes the 3D Laplacian. The computations are repeated for every time frame and channel in a 5D image.

Smoothing scale. The smoothing scale is equal to the standard deviation of the Gaussian derivative kernel used in computing the second-order derivatives constituting the Laplacian and must be larger than or equal to zero. If you have indicated in the Options dialog that you would like to apply (physically) isotropic Gaussian image smoothing, then in each dimension the scale is divided by the sampling interval in that dimension (that is, the pixel width/height/depth as specified in ImageJ > Image > Properties).

Detect zero-crossings. When selecting this operation, the plugin searches the image for local sign changes and sets the gray-value of elements (pixels/voxels) closest to estimated sign-change locations to 255 and all others to zero.

Algorithmic Details

In order to determine whether or not there is a zero-crossing, the algorithm compares the signs of neighboring image elements, and if they are opposite, it uses a linear interpolation scheme to make a more accurate estimate of the precise sign-change location.

References