Non-maximum suppression

Our implementation of non-maximum suppression is based on morphological gray-scale dilation [1] defined by the formula

\left(F\oplus S\right)\left(x,y\right)=\max_{\left(x^{\prime},y^{\prime}\right% )\in D_{S}}\left[F\left(x-x^{\prime},y-y^{\prime}\right)+S\left(x^{\prime},y^{% \prime}\right)\right]\,,

where F is the filtered image, S is a structuring element, and D_{S} is the domain of S. Gray-scale dilation is a more general approach than the method of detection of local intensity maxima, because the structuring element can have an arbitrary form.

We first perform a gray-scale dilation of the filtered image F using a structuring element S of size l\times l with all entries set to zero, where l=2r+1, and r is a dilation radius given by the user. The approximate molecular positions are extracted by finding pixels in the image F that have intensities equal to corresponding pixels in the dilated image and also have an intensity greater than a user-specified threshold. Essentially, a binary image is built with all non-maximum pixels set to zero and with all local maxima set to one.

References

  • [1] M. Šonka, V. Hlaváč and R. Boyle(2007) Image Processing, Analysis, and Machine Vision, 3rd edition edition, Cengage Learning. Cited by: Non-maximum suppression.