Algorithm 2. Pol-IER for PolSAR images.

given: the initial grid width $S$ , PolSAR image $I$

step 1. (Initialization)

Initialize the superpixels of image $I$ as regular grids with interval $S$ . Create the models (mean coherency matrices and geometric centers) for all the superpixels. Initialize the unstable pixels as all the pixels of the PolSAR image. Set the iteration index iter = 0.

step 2. (Local relabeling)

If iter ≥ itermax, the maximum iteration times reached, or the unstable point set is empty, then the algorithm ends and goes to Step 4. Or relabel all the unstable pixels by the combined distance defined in Equation (16). Assign each unstable pixel whose searching area is $2S\times 2S$ to the closest cluster whose location is covered by the searching area.

step 3. (Updating)

Update the superpixel models and the unstable pixel set by the definition (1). Set iter = iter + 1 and return to Step2.

step 4. (Postprocessing)

Search the superpixels with the size smaller than $N_{th}$ . If the smallest dissimilarity calculated by Equation (18) is smaller than $G_{th}$ , merge it into the closest adjacent superpixel. If not, move to the next superpixel until each superpixel is checked.

output: superpixels