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ImageStat (alpha)

Image analysis

The image is first analyzed by a consecutive application of elliptical masks of increasing area. When the second moments' derivatives are minimized, the code will determine optimal mask sizes and perform a final calculation. The method proved to be effective even on noisy images (without background subtraction), however, the user will have to adjust the step and mask sizes. The main signal has to be close to uniform or Gaussian; when significant segmentation is present, one has to adjust the initial mask size. Default parameters fit mostly clean Gaussian images with minor noise and segmentation.

Usage

python image.py

If need, adjust the parameters in parameters.py

Method

Let our image be defined as (a contribution of a "clean" function plus a noise term):

$Im(x,y) = f(x,y) + \zeta(x,y)$ ,

where f(x,y) is a Gaussian function:

$f(x,y) = Ae^{-r^2/2\sigma^2}$

Then, the second order statistical moment in x is calculated as:

$\langle xx \rangle = \iint_{-a}^{a}x^2[f(x,y)+\zeta(x,y)]dxdy$ .

Now consider a derivative:

$\frac{d}{da}\langle xx \rangle = \frac{d}{da}\langle xx \rangle_0 + \frac{d}{da}\langle xx \rangle_\zeta$