sorting points to form a continuous line

Question

I have a list of (x,y)-coordinates that represent a line skeleton. The list is obtained directly from a binary image:

import numpy as np    
list=np.where(im         


        

Answer 1

I am working on a similar problem, but it has an important constraint (much like the example given by the OP) which is that each pixel has either one or two neighboring pixel, in the 8-connected sense. With this constraint, there is a very simple solution.

def sort_to_form_line(unsorted_list):
    """
    Given a list of neighboring points which forms a line, but in random order, 
    sort them to the correct order.
    IMPORTANT: Each point must be a neighbor (8-point sense) 
    to a least one other point!
    """
    sorted_list = [unsorted_list.pop(0)]

    while len(unsorted_list) > 0:
        i = 0
        while i < len(unsorted_list):
            if are_neighbours(sorted_list[0], unsorted_list[i]):
                #neighbours at front of list
                sorted_list.insert(0, unsorted_list.pop(i))
            elif are_neighbours(sorted_list[-1], unsorted_list[i]):
                #neighbours at rear of list
                sorted_list.append(unsorted_list.pop(i))
            else:
                i = i+1

    return sorted_list

def are_neighbours(pt1, pt2):
    """
    Check if pt1 and pt2 are neighbours, in the 8-point sense
    pt1 and pt2 has integer coordinates
    """
    return (np.abs(pt1[0]-pt2[0]) < 2) and (np.abs(pt1[1]-pt2[1]) < 2)