Підрахунок кількості груп 1 в булевій карті numpy.array

Зараз я маю справу з деякою обробкою зображень на Python через PIL (Python Image Library). Моя основна мета - підрахунок кількості кольорових клітин на зображенні на імуногістохімії. Я знаю, що про це є відповідні програми, бібліотеки, функції та навчальні посібники, і я перевірив майже всі їх. Моя головна мета - написати код вручну з нуля, наскільки це можливо. Тому я намагаюся уникати використання безлічі зовнішніх бібліотек та функцій. Я написав більшу частину програми. Отже ось що відбувається покроково:

Програма приймає у файл зображення:

І обробляє його для червоних комірок (в основному він вимикає значення RGB нижче певного порогу для червоних):

І створює булеву карту його (збираю частину її, оскільки вона велика), яка в основному просто ставить 1, де б не стикався з червоним пікселем на обробленому другому зображенні вище.

22222222222222222222222222222222222222222
20000000111111110000000000000000000000002
20000000111111110000000000000000000000002
20000000111111110000000000000000000000002
20000000011111100000000000000000001100002
20000000001111100000000000000000011111002
20000000000110000000000000000000011111002
20000000000000000000000000000000111111002
20000000000000000000000000000000111111102
20000000000000000000000000000001111111102
20000000000000000000000000000001111111102
20000000000000000000000000000000111111002
20000000000000000000000000000000010000002
20000000000000000000000000000000000000002
22222222222222222222222222222222222222222

Я навмисно генерував цей кадр, як річ на кордонах з 2-х, щоб допомогти мені підрахувати кількість груп 1 в цій булевій карті.

Моє запитання до вас, хлопці, як я можу ефективно підрахувати кількість комірок (груп по 1s) у такій булевій карті? Я знайшов http://en.wikipedia.org/wiki/Connected-component_labeling, які виглядають надзвичайно пов'язаними та подібними, але, наскільки я бачу, це на рівні пікселів. Шахта знаходиться на булевому рівні. Всього 1 і 0.

Дуже дякую.

Щось підхід грубої сили, але зроблено шляхом інвертування проблеми індексувати колекції пікселів, щоб знайти регіони, а не раструювати масив.

data = """\
000000011111111000000000000000000000000
000000011111111000000000000000000000000
000000011111111000000000000000000000000
000000001111110000000001000000000110000
000000000111110000000011000000001111100
000000000011100000000000100000011111100
000000000000000000000000000000011111100
000000000000000000000000000000011111110
000000000000000000000000000000111111110
000000000000000000000000000000111111110
000000000000000000000000000000011111100
000000000000000000000000000000001000000
000000000000000000000000000000000000000"""

from collections import namedtuple
Point = namedtuple('Point', 'x y')

def points_adjoin(p1, p2):
    # to accept diagonal adjacency, use this form
    #return -1 <= p1.x-p2.x <= 1 and -1 <= p1.y-p2.y <= 1
    return (-1 <= p1.x-p2.x <= 1 and p1.y == p2.y or
             p1.x == p2.x and -1 <= p1.y-p2.y <= 1)

def adjoins(pts, pt):
    return any(points_adjoin(p,pt) for p in pts)

def locate_regions(datastring):
    data = map(list, datastring.splitlines())
    regions = []
    datapts = [Point(x,y) 
                for y,row in enumerate(data) 
                    for x,value in enumerate(row) if value=='1']
    for dp in datapts:
        # find all adjoining regions
        adjregs = [r for r in regions if adjoins(r,dp)]
        if adjregs:
            adjregs[0].add(dp)
            if len(adjregs) > 1:
                # joining more than one reg, merge
                regions[:] = [r for r in regions if r not in adjregs]
                regions.append(reduce(set.union, adjregs))
        else:
            # not adjoining any, start a new region
            regions.append(set([dp]))
    return regions

def region_index(regs, p):
    return next((i for i,reg in enumerate(regs) if p in reg), -1)

def print_regions(regs):
    maxx = max(p.x for r in regs for p in r)
    maxy = max(p.y for r in regs for p in r)
    allregionpts = reduce(set.union, regs)
    for y in range(-1,maxy+2):
        line = []
        for x in range(-1,maxx+2):
            p = Point(x, y)
            if p in allregionpts:
                line.append(str(region_index(regs, p)))
            else:
                line.append('.')
        print ''.join(line)
    print


# test against data set
regs = locate_regions(data)
print len(regs)
print_regions(regs)

Друкує:

4
........................................
........00000000........................
........00000000........................
........00000000........................
.........000000.........1.........33....
..........00000........11........33333..
...........000...........2......333333..
................................333333..
................................3333333.
...............................33333333.
...............................33333333.
................................333333..
.................................3......
........................................

Ви можете використовувати ndimage.label, що це приємний спосіб зробити це. Він повертає новий масив, причому кожна функція має унікальне значення та кількість функцій. Ви також можете вказати елемент з'єднання.

import scipy
from scipy import ndimage
import matplotlib.pyplot as plt

#flatten to make greyscale, using your second red-black image as input.
im = scipy.misc.imread('blobs.jpg',flatten=1)
#smooth and threshold as image has compression artifacts (jpg)
im = ndimage.gaussian_filter(im, 2)
im[im<10]=0
blobs, number_of_blobs = ndimage.label(im)
print 'Number of blobls:', number_of_blobs

plt.imshow(blobs)
plt.show()

#Output is:
Number of blobls: 30

Ось алгоритм, який є O (загальна кількість пікселів + кількість пікселів комірки). Ми просто скануємо зображення на пікселі комірок, і коли знайдемо його, ми заповнимо комірку, щоб стерти її.

Реалізація в Common Lisp, але ви зможете тривіально перекласти його на Python.

(defun flood-fill (picture i j target-color replacement-color)
  ;; http://en.wikipedia.org/wiki/Flood_fill
  (when (= (aref picture i j) target-color)
    (setf (aref picture i j) replacement-color)
    (when (plusp i)
      (flood-fill picture (1- i) j target-color replacement-color))
    (when (< (1+ i) (array-dimension picture 0))
      (flood-fill picture (1+ i) j target-color replacement-color))
    (when (plusp j)
      (flood-fill picture i (1- j) target-color replacement-color))
    (when (< (1+ j) (array-dimension picture 1))
      (flood-fill picture i (1+ j) target-color replacement-color)))
  picture)


(defun count-cells (picture)
  (loop
    :with cell-count = 0
    :for i :from 0 :below (array-dimension picture 0)
    :do (loop
          :for j :from 0 :below (array-dimension picture 1)
          :unless (zerop (aref picture i j))
          :do (progn (incf cell-count)
                     (flood-fill picture i j 1 0)))
    :finally (return cell-count)))




(count-cells
  (make-array '(128 171) :element-type 'bit
              :initial-contents
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--> 30

Більше розширеного коментаря, ніж відповіді:

Як натякнув @interjay, у бінарному зображенні, тобто такому, у якому є лише два кольори, пікселі приймають значення або 1, або 0. Це може бути, а може і не бути правдою у форматі подання зображення, який ви використовуєте, але це правда у «концептуальному» поданні вашого образу; не дозволяйте детальним відомостям про заплутаність вас у цьому питанні. Однією з таких деталей реалізації є використання 2-х кольорів навколо межі зображення - ідеально розумний спосіб ідентифікації мертвої зони навколо зображення, але якісно не впливає на бінарність зображення.

Щодо вивчення пікселів N, NE, NW та W: це пов'язано із сполучністю пікселів при формуванні компонента. Кожен піксель (смуга прикордонних спеціальних випадків) має 8 сусідів (N, S, E, W, NE, NW, SE, SW), але які з них є кандидатами для включення до одного компонента? Іноді компоненти, які зустрічаються лише в кутах (NE, NW, SE, SW), не розглядаються як з'єднані, іноді вони є.

Ви повинні вирішити, що підходить для вашої заявки. Я пропоную вам вручну розробити кілька операцій послідовного алгоритму, перевіряючи різних сусідів на кожен піксель, щоб відчути, що відбувається.