2D

The fractional splines are an extension of the polynomial splines for all fractional degrees α > -1. Their basic constituents are piecewise power functions of degree α. One constructs the corresponding B-splines through a localization process similar to the classical one, replacing finite differences by fractional differences. The fractional B-splines share virtually all the properties of the classical B-splines, including the two-scale relation, and can therefore be used to define new wavelet bases with a continuously-varying order parameter

This version replaces the old Arrow_.class tool that was present in Fiji before. The main changes are the ability to draw the arrow as a floating selection, and to tune its shape.

Warning: Since ImageJ version 1.43n, a similar tool, made by Wayne Rasband, does a similar thing from the ImageJ core, see here.

The smoothing is applied by the way of a bi-exponential filter, itself realized by a pair of one-tap recursions. It is therefore very fast; moreover, its computational cost is truly independent of the amount of smoothing. Meanwhile, the preservation of edges is obtained by a range filter akin to the range filter found in a bilateral filter. More technical details are available here.

The plugin allows one to control the amount of smoothing, the type of range filter, its broadness, and to iterate the filter several times if desired. We illustrate in Figure 2 a possible outcome of this filter. Here, we iterated the BEEPS 10 times with a Gaussian range filter, σ = 10, and the spatial decay λ = 0.1.

Dithering is a type of half tone thresholding where greyscale (or RGB channel) intensity is converted into a local density of binary pixels. This is ideal for rendering images in devices with a binary output such as printers (greyscale) or with a small number of colours (colour dithering). The following methods have been implemented (there are several more):

• Floyd-Steinberg
• Atkinson
• Jarvis-Judice-Ninke
• Stucki
• Bayer_2x2
• Bayer_4x4
• Bayer_8x8
• Clustered_4x4
• Random

Here is a good text explaining various dithering algorithm.