FeatureJ: Hessian

General Description

This plugin enables you to compute, for all image elements (pixels/voxels), the eigenvalues of the Hessian, which can be used e.g. to discriminate locally between plate-like, line-like, and blob-like image structures [1,2,3].

Description of Dialog Components

Largest/Middle/Smallest eigenvalue of Hessian tensor. After computation of the elements of the Hessian tensor, the resulting eigenvalues are ordered for each image element (pixel/voxel). All largest eigenvalues are put in a separate image, as are all smallest (and all middle, in 3D). With these options you can choose which of these so-called eigenimages should be displayed by the plugin. If the size of the image is unity in the z-dimension (single slice), the plugin computes 2D-Hessian eigenvalues. Otherwise it computes 3D-Hessian eigenvalues. The computations are repeated for every time frame and channel in a 5D image.

Absolute eigenvalue comparison. Eigenvalues of the Hessian can be positive or negative. By default the plugin orders and displays the actual eigenvalues. Switching on this option causes the plugin to order and display only their magnitudes.

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 Hessian tensor 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).

References