Lowered Gaussian filter

This filter was reported to perform well in the DAOPHOT [2] and DAOSTORM [1] algorithms. The convolution kernel is based on the Gaussian kernel which has been lowered to have the sum of all its entries equal to zero,

K_{\mathrm{LG}}\left(x,y\mid\sigma\right)=K_{\mathrm{G}}\left(x,y\mid\sigma% \right)-b\,,

where b is the mean value of all of the elements in K_{\mathrm{G}}. The standard deviation \sigma is a user-specified parameter.

Although the kernel K_{\mathrm{LG}} is not separable, the filtered image can be obtained by subtracting two images filtered with two separable kernels (see convolution with separable kernels),

F=I*K_{\mathrm{LG}}=I*K_{\mathrm{G}}-I*K_{\mathrm{AV}}\,.

The lowered Gaussian is a band-pass filter. The sizes of both K_{\mathrm{G}} and K_{\mathrm{AV}} kernels are computed as l=1+2\left\lceil 3\sigma\right\rceil.

Threshold for approximate localization of molecules

The threshold value can be specified by users as an expression combining mathematical functions and operators with variables based on the current raw or filtered image. Variables provided by this filter are:

LowGauss.I current raw input image
LowGauss.F corresponding filtered image

References

  • [1] S. J. Holden, S. Uphoff and A. N. Kapanidis(2011) DAOSTORM: an algorithm for high- density super-resolution microscopy, Nature Methods 8 (4), pp. 279–80. External Links: Document. Cited by: Lowered Gaussian filter.
  • [2] P. B. Stetson(1987) DAOPHOT - A computer program for crowded-field stellar photometry, Publications of the Astronomical Society of the Pacific 99, pp. 191. External Links: Document. Cited by: Lowered Gaussian filter.