Random Walker in a nutshell

Random Walker is an image segmentation algorithm based on the statistical algorithm random walk which finds all likelihoods of a certain point taking a next step. Random Walker then assigns the step with the highest probabibility to that particular steps' respective label. 

To understand this more easily, we can make the analogy of an electric circuit. Each pixel in the image would be represented as a node in the circuit. Each node is connected to every other node by a "resistor". These resistor values can differ depending on what the segmention-determinant is (intensity, colour, brightness, etc). Of course, an equation is derived for each of these determinants. 

Once the resistor values are in place, we need to take each seed (represented by a voltage source), one at a time, and figure out the potential between the voltage source and the node, going through all the resistors in between. Analogously, we would be finding which seed each pixel belongs to based on the numeric values between the pixel and each seed and assinging the pixel to the seed which produces the greatest value (potential).

To find these values, we use the Combinatorial Dirichlet problem (as far as I understand). The boundary limits to this problem would be the location of the pixel being examined and the location of the seed being examined.