Image processing

This plugin calculates the Nyquist sampling, in the radial and axial direction for your Microscope.

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

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.

This plugin perform various 3D filters on 8-bits or 16-bits gray-levels stacks :

• 3D median

• 3D mean

• 3D minimum

• 3D maximum

• 3D maximum local

• 3D tophat (detect bright spots, TH=I-max(min(I)) )