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


# Gray scale
def BGR2GRAY(img):
	b = img[:, :, 0].copy()
	g = img[:, :, 1].copy()
	r = img[:, :, 2].copy()

	# Gray scale
	out = 0.2126 * r + 0.7152 * g + 0.0722 * b
	out = out.astype(np.uint8)

	return out

# Otsu Binalization
def otsu_binarization(img, th=128):
	H, W = img.shape
	out = img.copy()

	max_sigma = 0
	max_t = 0

	# determine threshold
	for _t in range(1, 255):
		v0 = out[np.where(out < _t)]
		m0 = np.mean(v0) if len(v0) > 0 else 0.
		w0 = len(v0) / (H * W)
		v1 = out[np.where(out >= _t)]
		m1 = np.mean(v1) if len(v1) > 0 else 0.
		w1 = len(v1) / (H * W)
		sigma = w0 * w1 * ((m0 - m1) ** 2)
		if sigma > max_sigma:
			max_sigma = sigma
			max_t = _t

	# Binarization
	print("threshold >>", max_t)
	th = max_t
	out[out < th] = 0
	out[out >= th] = 255

	return out


# Erosion
def Erode(img, Erode_time=1):
	H, W = img.shape
	out = img.copy()

	# kernel
	MF = np.array(((0, 1, 0),
				(1, 0, 1),
				(0, 1, 0)), dtype=np.int)

	# each erode
	for i in range(Erode_time):
		tmp = np.pad(out, (1, 1), 'edge')
		# erode
		for y in range(1, H+1):
			for x in range(1, W+1):
				if np.sum(MF * tmp[y-1:y+2, x-1:x+2]) < 255*4:
					out[y-1, x-1] = 0

	return out


# Dilation
def Dilate(img, Dil_time=1):
	H, W = img.shape

	# kernel
	MF = np.array(((0, 1, 0),
				(1, 0, 1),
				(0, 1, 0)), dtype=np.int)

	# each dilate time
	out = img.copy()
	for i in range(Dil_time):
		tmp = np.pad(out, (1, 1), 'edge')
		for y in range(1, H+1):
			for x in range(1, W+1):
				if np.sum(MF * tmp[y-1:y+2, x-1:x+2]) >= 255:
					out[y-1, x-1] = 255

	return out


# Read image
img = cv2.imread("imori.jpg").astype(np.float32)

# Grayscale
gray = BGR2GRAY(img)

# Otsu's binarization
otsu = otsu_binarization(gray)

# Erode image
eroded = Erode(otsu)

# Delate image
dilated = Dilate(otsu)

# Morphology
out = np.abs(eroded - dilated) * 255
                
# Save result
cv2.imwrite("out.jpg", out)
cv2.imshow("result", out)
cv2.waitKey(0)
cv2.destroyAllWindows()
pythonを用いて、大津の二値化を行った後、モルフォロジー勾配を求めよ。

モルフォロジー勾配とはモルフォロジー膨張の画像と収縮の画像の差分をとることで、物体の境界線を抽出する手法である。

ここではモルフォロジー処理のN=1とする。