FeatureJ: Hessian

General Description

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

Dialog Description

Largest/Middle/Smallest eigenvalue of Hessian tensor. After computation 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). These options determine which of these so-called eigenimages will be displayed by the plugin. If the size of the image is one in the z-dimension (a single slice), the plugin computes 2D-Hessian eigenvalues, otherwise it computes 3D-Hessian eigenvalues (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 kernels used for computing the second-order derivatives in the Hessian tensor 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).

References