Centroid of connected components

This algorithm is based on segmentation of molecules which is performed by applying a user-defined threshold on the filtered image F. Users also have the option to combine the thresholded image with the result of a watershed algorithm [3] applied to the image F. This procedure was proposed in [1]. The position of each molecule is determined by computing the centroid of the relevant segmented object using

\tilde{x}_{p}=\frac{1}{c_{p}}\sum_{i=1}^{c_{p}}{x_{i,p}}\,,\quad\tilde{y}_{p}=% \frac{1}{c_{p}}\sum_{i=1}^{c_{p}}{y_{i,p}}\,.

Here p indexes the objects, c_{p} is the number of elements in each object, and x_{i,p} and y_{i,p} are the integer pixel coordinates within each object. Segmented objects are determined as connected components by an algorithm based on a breadth-first search [2]. The watershed algorithm is based on the ImageJ ‘‘Find Maxima’’ function.

References

  • [1] I. Izeddin, J. Boulanger, V. Racine, C. G. Specht, A. Kechkar, D. Nair, A. Triller, D. Choquet, M. Dahan and J. B. Sibarita(2012) Wavelet analysis for single molecule localization microscopy, Optics Express 20 (3), pp. 2081–95. External Links: Document. Cited by: Centroid of connected components.
  • [2] D. E. Knuth(1997) The Art Of Computer Programming, 3rd edition, Vol. 1, Addison-Wesley, Boston. Cited by: Centroid of connected components.
  • [3] M. Šonka, V. Hlaváč and R. Boyle(2007) Image Processing, Analysis, and Machine Vision, 3rd edition edition, Cengage Learning. Cited by: Centroid of connected components.