FeatureJ: Laplacian

General Description

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

Dialog Description

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 one to apply zero-crossing detection without having to compute the Laplacian first. If the size of the image is unity in the z-dimension (a single slice), the plugin computes the 2D Laplacian, otherwise it computes the 3D Laplacian (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 kernels used for computing the second-order derivatives of the Laplacian and must be larger than zero. See the algorithmic details in the description of the Derivatives dialog for boundary conditions in setting this parameter. If physically isotropic Gaussian image smoothing is to be applied (which can be specified in the Options dialog), then in each dimension the scale is divided by the sampling interval in that dimension (the pixel width/height/depth as specified in ImageJ > Image > Properties).

Detect zero-crossings. Selecting this option makes the plugin search the image for local sign changes and to set 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