## Center of Mass (CM)

In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the system's mass behaves as if it were concentrated. (Wikipedia)

In the Huygens Software's Object Analyzer, the center of mass of a segmented object is calculated considering the recorded light intensity in the image as local mass density. This makes some sense, because there is the implicit assumption that the recorded light is proportional to the concentration of dyed molecules. Still of course some "dark matter" could exist that is not fluorescent and therefore not accounted for the center of mass computation!!!

The CM of a collection of VoXels is defined as the average of their positions, weighted by their recorded light intensities I_i. This gives three figures in 3D, the three coordinates (x, y, z) of the center of mass:

$$\text{CM}_x = \sum_i{ \frac{x_i \ I_i}{I} }$$

$$\text{CM}_y = \sum_i{ \frac{y_i \ I_i}{I} }$$

$$\text{CM}_z = \sum_i{ \frac{z_i \ I_i}{I} }$$

$$I = \sum_i{\ I_i}$$