Module: Proximity Field

Description:

Generates a scalar field in a given phase, that represents how much of another phase is nearby. It's a bit like a gravity field, but with no directional component, i.e. two opposite gravity forces will not cancel out. Therefore, the value attributed to each pixel is the sum of the inverse of the squared distance to all the pixels in a given phase. Because this can take a reeeeaally long time to compute on images with millions of pixels in the phases, you can specify a cut-off value, for a distance above which we don't look at the interactions. This is reasonable since we're looking at 1/r�, which decreases quite rapidly.

Illustration of the process and what it can be used for. The left image shows an image generated with Create_Sphere_Pack_Image, having three phases: porosity (0), ball outer shell (1), and ball core (2). The ball cores have a radius of 20 pixels. A proximity field was generated in the porosity, shown in the center image, computing the proximity (as defined above) with the outer shell, and using a cut-off value of half the radius, 10 pixels. The right image shows an example of an application of this module, in which we use the proximity field as a priority function for adding pixels of the outer shell to the porosity, using the Invade module (for the latter, the proximity field had to be inverted). The result places pixels preferentially near the contact points between balls.