import cv2
import numpy as np
import matplotlib.pyplot as plt


# hilditch thining
def hilditch(img):
    # get shape
    H, W, C = img.shape

    # prepare out image
    out = np.zeros((H, W), dtype=np.int)
    out[img[..., 0] > 0] = 1

    # inverse pixel value
    tmp = out.copy()
    _tmp = 1 - tmp

    count = 1
    while count > 0:
        count = 0
        tmp = out.copy()
        _tmp = 1 - tmp

        tmp2 = out.copy()
        _tmp2 = 1 - tmp2
        
        # each pixel
        for y in range(H):
            for x in range(W):
                # skip black pixel
                if out[y, x] < 1:
                    continue
                
                judge = 0
                
                ## condition 1
                if (tmp[y, min(x+1, W-1)] * tmp[max(y-1,0 ), x] * tmp[y, max(x-1, 0)] * tmp[min(y+1, H-1), x]) == 0:
                    judge += 1
                    
                ## condition 2
                c = 0
                c += (_tmp[y, min(x+1, W-1)] - _tmp[y, min(x+1, W-1)] * _tmp[max(y-1, 0), min(x+1, W-1)] * _tmp[max(y-1, 0), x])
                c += (_tmp[max(y-1, 0), x] - _tmp[max(y-1, 0), x] * _tmp[max(y-1, 0), max(x-1, 0)] * _tmp[y, max(x-1, 0)])
                c += (_tmp[y, max(x-1, 0)] - _tmp[y, max(x-1, 0)] * _tmp[min(y+1, H-1), max(x-1, 0)] * _tmp[min(y+1, H-1), x])
                c += (_tmp[min(y+1, H-1), x] - _tmp[min(y+1, H-1), x] * _tmp[min(y+1, H-1), min(x+1, W-1)] * _tmp[y, min(x+1, W-1)])
                if c == 1:
                    judge += 1
                    
                ## condition 3
                if np.sum(tmp[max(y-1, 0) : min(y+2, H), max(x-1, 0) : min(x+2, W)]) >= 3:
                    judge += 1

                ## condition 4
                if np.sum(out[max(y-1, 0) : min(y+2, H), max(x-1, 0) : min(x+2, W)]) >= 2:
                    judge += 1

                ## condition 5
                _tmp2 = 1 - out

                c = 0
                c += (_tmp2[y, min(x+1, W-1)] - _tmp2[y, min(x+1, W-1)] * _tmp2[max(y-1, 0), min(x+1, W-1)] * _tmp2[max(y-1, 0), x])
                c += (_tmp2[max(y-1, 0), x] - _tmp2[max(y-1, 0), x] * (1 - tmp[max(y-1, 0), max(x-1, 0)]) * _tmp2[y, max(x-1, 0)])
                c += (_tmp2[y, max(x-1, 0)] - _tmp2[y, max(x-1, 0)] * _tmp2[min(y+1, H-1), max(x-1, 0)] * _tmp2[min(y+1, H-1), x])
                c += (_tmp2[min(y+1, H-1), x] - _tmp2[min(y+1, H-1), x] * _tmp2[min(y+1, H-1), min(x+1, W-1)] * _tmp2[y, min(x+1, W-1)])
                if c == 1 or (out[max(y-1, 0), max(x-1,0 )] != tmp[max(y-1, 0), max(x-1, 0)]):
                    judge += 1

                c = 0
                c += (_tmp2[y, min(x+1, W-1)] - _tmp2[y, min(x+1, W-1)] * _tmp2[max(y-1, 0), min(x+1, W-1)] * (1 - tmp[max(y-1, 0), x]))
                c += ((1-tmp[max(y-1, 0), x]) - (1 - tmp[max(y-1, 0), x]) * _tmp2[max(y-1, 0), max(x-1, 0)] * _tmp2[y, max(x-1, 0)])
                c += (_tmp2[y, max(x-1,0 )] - _tmp2[y, max(x-1,0 )] * _tmp2[min(y+1, H-1), max(x-1, 0)] * _tmp2[min(y+1, H-1), x])
                c += (_tmp2[min(y+1, H-1), x] - _tmp2[min(y+1, H-1), x] * _tmp2[min(y+1, H-1), min(x+1, W-1)] * _tmp2[y, min(x+1, W-1)])
                if c == 1 or (out[max(y-1, 0), x] != tmp[max(y-1, 0), x]):
                    judge += 1

                c = 0
                c += (_tmp2[y, min(x+1, W-1)] - _tmp2[y, min(x+1, W-1)] * (1 - tmp[max(y-1, 0), min(x+1, W-1)]) * _tmp2[max(y-1, 0), x])
                c += (_tmp2[max(y-1, 0), x] - _tmp2[max(y-1, 0), x] * _tmp2[max(y-1, 0), max(x-1, 0)] * _tmp2[y, max(x-1, 0)])
                c += (_tmp2[y, max(x-1, 0)] - _tmp2[y, max(x-1, 0)] * _tmp2[min(y+1, H-1), max(x-1, 0)] * _tmp2[min(y+1, H-1), x])
                c += (_tmp2[min(y+1, H-1), x] - _tmp2[min(y+1, H-1), x] * _tmp2[min(y+1, H-1), min(x+1, W-1)] * _tmp2[y, min(x+1, W-1)])
                if c == 1 or (out[max(y-1, 0), min(x+1, W-1)] != tmp[max(y-1, 0), min(x+1, W-1)]):
                    judge += 1

                c = 0
                c += (_tmp2[y, min(x+1, W-1)] - _tmp2[y, min(x+1, W-1)] * _tmp2[max(y-1, 0), min(x+1, W-1)] * _tmp2[max(y-1, 0), x])
                c += (_tmp2[max(y-1, 0), x] - _tmp2[max(y-1, 0), x] * _tmp2[max(y-1, 0), max(x-1, 0)] * (1 - tmp[y, max(x-1, 0)]))
                c += ((1 - tmp[y, max(x-1, 0)]) - (1 - tmp[y, max(x-1, 0)]) * _tmp2[min(y+1, H-1), max(x-1, 0)] * _tmp2[min(y+1, H-1), x])
                c += (_tmp2[min(y+1, H-1), x] - _tmp2[min(y+1, H-1), x] * _tmp2[min(y+1, H-1), min(x+1, W-1)] * _tmp2[y, min(x+1, W-1)])
                if c == 1 or (out[y, max(x-1, 0)] != tmp[y, max(x-1, 0)]):
                    judge += 1
                
                if judge >= 8:
                    out[y, x] = 0
                    count += 1
                    
    out = out.astype(np.uint8) * 255

    return out


# Read image
img = cv2.imread("gazo.png").astype(np.float32)

# hilditch thining
out = hilditch(img)

# Save result
cv2.imwrite("out.png", out)
cv2.imshow("result", out)
cv2.waitKey(0)
cv2.destroyAllWindows()
pythonを用いて、gazo.pngにヒルディッチの細線化を行え。

アルゴリズムは、次の通り。

1. 左上からラスタスキャンする。
2. x0(x,y)=0ならば、処理なし。x0(x,y)=1ならば次の5条件を満たす時にx0=-1に変える。
    1. 注目画素の4近傍に0が一つ以上存在する
    2. x0の8-連結数が1である
    3. x1〜x8の絶対値の合計が2以上
    4. x0の8近傍に1が1つ以上存在する
    5. xn(n=1〜8)全てに対して以下のどちらかが成り立つ
        - xnが-1以外
        - xnを0とした時、x0の8-連結数が1である
3. 各画素の-1を0に変える
4. 一回のラスタスキャンで3の変更数が0になるまで、ラスタスキャンを繰り返す。