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ryoppippi · Oct 22, 2019 · dc33ddf · dc33ddf
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diff --git a/Question_01_10/README.md b/Question_01_10/README.md
@@ -234,8 +234,12 @@ v = 1/|R| * Sum_{i in R} v_i
 ただし、画像の端はこのままではフィルタリングできないため、画素が足りない部分は0で埋める。これを**0パディング**と呼ぶ。
 かつ、重みは正規化する。(sum g = 1)
 
+重みはガウス分布から次式になる。
+
+<img src='assets/gaussian_filter.png' width=200>
+
 ```bash
-重み g(x,y,s) = 1/ (s*sqrt(2 * pi)) * exp( - (x^2 + y^2) / (2*s^2))
+重み g(x,y,s) = 1/ (2 * pi * sigma * sigma) * exp( - (x^2 + y^2) / (2*s^2))
 標準偏差s = 1.3による8近傍ガウシアンフィルタは
             1 2 1
 K =  1/16 [ 2 4 2 ]

diff --git a/Question_01_10/answers_image/answer_9.jpg b/Question_01_10/answers_image/answer_9.jpg
diff --git a/Question_01_10/answers_py/answer_9.py b/Question_01_10/answers_py/answer_9.py
@@ -21,7 +21,7 @@ def gaussian_filter(img, K_size=3, sigma=1.3):
 	for x in range(-pad, -pad + K_size):
 		for y in range(-pad, -pad + K_size):
 			K[y + pad, x + pad] = np.exp( -(x ** 2 + y ** 2) / (2 * (sigma ** 2)))
-	K /= (sigma * np.sqrt(2 * np.pi))
+	K /= (2 * np.pi * sigma * sigma)
 	K /= K.sum()
 
 	tmp = out.copy()
@@ -30,8 +30,9 @@ def gaussian_filter(img, K_size=3, sigma=1.3):
 	for y in range(H):
 		for x in range(W):
 			for c in range(C):
-				out[pad + y, pad + x] = np.sum(K * tmp[y: y + K_size, x: x + K_size])
+				out[pad + y, pad + x, c] = np.sum(K * tmp[y: y + K_size, x: x + K_size, c])
 
+	out = np.clip(out, 0, 255)
 	out = out[pad: pad + H, pad: pad + W].astype(np.uint8)
 
 	return out

diff --git a/Question_01_10/assets/gaussian_filter.png b/Question_01_10/assets/gaussian_filter.png
diff --git a/Question_41_50/README.md b/Question_41_50/README.md
@@ -87,7 +87,7 @@ if angle(x,y)  = 135
 2. LT以下のedge(x,y)=0
 3.  LT < edge(x,y) < HTの時、周り８ピクセルの勾配強度でHTより大きい値が存在すれば、edge(x,y)=255
 
-ここでは、HT=160, LT=80とする。ちなみに閾値の値は結果を見ながら判断するしかない。
+ここでは、HT=50, LT=20とする。ちなみに閾値の値は結果を見ながら判断するしかない。
 
 以上のアルゴリズムによって、Canny法が行われる。
 

diff --git a/Question_41_50/answers_image/.DS_Store b/Question_41_50/answers_image/.DS_Store
diff --git a/Question_41_50/answers_image/answer_41_1.jpg b/Question_41_50/answers_image/answer_41_1.jpg
diff --git a/Question_41_50/answers_image/answer_41_2.jpg b/Question_41_50/answers_image/answer_41_2.jpg
diff --git a/Question_41_50/answers_image/answer_42_1.jpg b/Question_41_50/answers_image/answer_42_1.jpg
diff --git a/Question_41_50/answers_image/answer_42_2.jpg b/Question_41_50/answers_image/answer_42_2.jpg
diff --git a/Question_41_50/answers_image/answer_43.jpg b/Question_41_50/answers_image/answer_43.jpg
diff --git a/Question_41_50/answers_py/answer_41.py b/Question_41_50/answers_py/answer_41.py
@@ -22,9 +22,11 @@ def gaussian_filter(img, K_size=3, sigma=1.3):
 
 		if len(img.shape) == 3:
 			H, W, C = img.shape
+			gray = False
 		else:
 			img = np.expand_dims(img, axis=-1)
 			H, W, C = img.shape
+			gray = True
 
 		## Zero padding
 		pad = K_size // 2
@@ -35,8 +37,8 @@ def gaussian_filter(img, K_size=3, sigma=1.3):
 		K = np.zeros((K_size, K_size), dtype=np.float)
 		for x in range(-pad, -pad + K_size):
 			for y in range(-pad, -pad + K_size):
-				K[y+pad, x+pad] = np.exp( -(x ** 2 + y ** 2) / (2 * (sigma ** 2)))
-		K /= (sigma * np.sqrt(2 * np.pi))
+				K[y + pad, x + pad] = np.exp( - (x ** 2 + y ** 2) / (2 * (sigma ** 2)))
+		K /= (2 * np.pi * sigma * sigma)
 		K /= K.sum()
 
 		tmp = out.copy()
@@ -45,9 +47,14 @@ def gaussian_filter(img, K_size=3, sigma=1.3):
 		for y in range(H):
 			for x in range(W):
 				for c in range(C):
-					out[pad + y, pad + x, c] = np.sum(K * tmp[y: y + K_size, x: x + K_size, c])
+					out[pad + y, pad + x, c] = np.sum(K * tmp[y : y + K_size, x : x + K_size, c]) 
+
+		out = np.clip(out, 0, 255)
+		out = out[pad : pad + H, pad : pad + W]
+		#out = out.astype(np.uint8)
 
-		out = out[pad: pad + H, pad: pad + W].astype(np.uint8)
+		if gray:
+			out = out[..., 0]
 
 		return out
 
@@ -57,13 +64,13 @@ def sobel_filter(img, K_size=3):
 		if len(img.shape) == 3:
 			H, W, C = img.shape
 		else:
-			img = np.expand_dims(img, axis=-1)
-			H, W, C = img.shape
+			#img = np.expand_dims(img, axis=-1)
+			H, W = img.shape
 
 		# Zero padding
 		pad = K_size // 2
 		out = np.zeros((H + pad * 2, W + pad * 2), dtype=np.float)
-		out[pad: pad + H, pad: pad + W] = gray.copy().astype(np.float)
+		out[pad : pad + H, pad : pad + W] = img.copy().astype(np.float)
 		tmp = out.copy()
 
 		out_v = out.copy()
@@ -77,14 +84,14 @@ def sobel_filter(img, K_size=3):
 		# filtering
 		for y in range(H):
 			for x in range(W):
-				out_v[pad + y, pad + x] = np.sum(Kv * (tmp[y: y + K_size, x: x + K_size]))
-				out_h[pad + y, pad + x] = np.sum(Kh * (tmp[y: y + K_size, x: x + K_size]))
+				out_v[pad + y, pad + x] = np.sum(Kv * (tmp[y : y + K_size, x : x + K_size]))
+				out_h[pad + y, pad + x] = np.sum(Kh * (tmp[y : y + K_size, x : x + K_size]))
 
 		out_v = np.clip(out_v, 0, 255)
 		out_h = np.clip(out_h, 0, 255)
 
-		out_v = out_v[pad: pad + H, pad: pad + W].astype(np.uint8)
-		out_h = out_h[pad: pad + H, pad: pad + W].astype(np.uint8)
+		out_v = out_v[pad : pad + H, pad : pad + W].astype(np.uint8)
+		out_h = out_h[pad : pad + H, pad : pad + W].astype(np.uint8)
 
 		return out_v, out_h
 
@@ -126,19 +133,22 @@ def angle_quantization(angle):
 	# angle quantization
 	angle = angle_quantization(angle)
 
-	return angle
+	return edge, angle
 
 
 # Read image
 img = cv2.imread("imori.jpg").astype(np.float32)
 
 # Canny (step1)
-angle = Canny_step1(img)
+edge, angle = Canny_step1(img)
 
-out = angle.astype(np.uint8)
+edge = edge.astype(np.uint8)
+angle = angle.astype(np.uint8)
 
 # Save result
-cv2.imwrite("out.jpg", out)
-cv2.imshow("result", out)
+cv2.imwrite("out.jpg", edge)
+cv2.imshow("result", edge)
+cv2.imwrite("out2.jpg", angle)
+cv2.imshow("result2", angle)
 cv2.waitKey(0)
 cv2.destroyAllWindows()
diff --git a/Question_41_50/answers_py/answer_42.py b/Question_41_50/answers_py/answer_42.py
@@ -35,8 +35,9 @@ def gaussian_filter(img, K_size=3, sigma=1.3):
 		K = np.zeros((K_size, K_size), dtype=np.float)
 		for x in range(-pad, -pad + K_size):
 			for y in range(-pad, -pad + K_size):
-				K[y+pad, x+pad] = np.exp( -(x ** 2 + y ** 2) / (2 * (sigma ** 2)))
-		K /= (sigma * np.sqrt(2 * np.pi))
+				K[y + pad, x + pad] = np.exp( - (x ** 2 + y ** 2) / (2 * (sigma ** 2)))
+		#K /= (sigma * np.sqrt(2 * np.pi))
+		K /= (2 * np.pi * sigma * sigma)
 		K /= K.sum()
 
 		tmp = out.copy()
@@ -45,22 +46,27 @@ def gaussian_filter(img, K_size=3, sigma=1.3):
 		for y in range(H):
 			for x in range(W):
 				for c in range(C):
-					out[pad + y, pad + x, c] = np.sum(K * tmp[y: y + K_size, x: x + K_size, c])
+					out[pad + y, pad + x, c] = np.sum(K * tmp[y : y + K_size, x : x + K_size, c])
 
-		out = out[pad: pad + H, pad: pad + W].astype(np.uint8)
+		out = np.clip(out, 0, 255)
+		out = out[pad : pad + H, pad : pad + W]
+		out = out.astype(np.uint8)
 		out = out[..., 0]
 
 		return out
 
 
 	# sobel filter
 	def sobel_filter(img, K_size=3):
-		H, W = img.shape
+		if len(img.shape) == 3:
+			H, W, C = img.shape
+		else:
+			H, W = img.shape
 
 		# Zero padding
 		pad = K_size // 2
 		out = np.zeros((H + pad * 2, W + pad * 2), dtype=np.float)
-		out[pad: pad + H, pad: pad + W] = gray.copy().astype(np.float)
+		out[pad: pad + H, pad: pad + W] = img.copy().astype(np.float)
 		tmp = out.copy()
 
 		out_v = out.copy()
@@ -109,12 +115,13 @@ def angle_quantization(angle):
 		_angle[np.where((angle > 67.5) & (angle <= 112.5))] = 90
 		_angle[np.where((angle > 112.5) & (angle <= 157.5))] = 135
 
-		return angle
+		return _angle
 
 
 	def non_maximum_suppression(angle, edge):
 		H, W = angle.shape
-
+		_edge = edge.copy()
+
 		for y in range(H):
 			for x in range(W):
 					if angle[y, x] == 0:
@@ -137,10 +144,10 @@ def non_maximum_suppression(angle, edge):
 					if y == H-1:
 							dy1 = min(dy1, 0)
 							dy2 = min(dy2, 0)
-					if max(max(edge[y, x], edge[y+dy1, x+dx1]), edge[y+dy2, x+dx2]) != edge[y, x]:
-							edge[y, x] = 0
+					if max(max(edge[y, x], edge[y + dy1, x + dx1]), edge[y + dy2, x + dx2]) != edge[y, x]:
+							_edge[y, x] = 0
 
-		return edge
+		return _edge
 
 	# grayscale
 	gray = BGR2GRAY(img)
@@ -160,19 +167,22 @@ def non_maximum_suppression(angle, edge):
 	# non maximum suppression
 	edge = non_maximum_suppression(angle, edge)
 
-	return edge
+	return edge, angle
 
 
 # Read image
 img = cv2.imread("imori.jpg").astype(np.float32)
 
 # Canny (step2)
-edge = Canny_step2(img)
+edge, angle = Canny_step2(img)
 
-out = edge.astype(np.uint8)
+edge = edge.astype(np.uint8)
+angle = angle.astype(np.uint8)
 
 # Save result
-cv2.imwrite("out.jpg", out)
-cv2.imshow("result", out)
+cv2.imwrite("out.jpg", edge)
+cv2.imshow("result", edge)
+cv2.imwrite("out2.jpg", angle)
+cv2.imshow("result2", angle)
 cv2.waitKey(0)
 cv2.destroyAllWindows()
diff --git a/Question_41_50/answers_py/answer_43.py b/Question_41_50/answers_py/answer_43.py
@@ -22,21 +22,24 @@ def gaussian_filter(img, K_size=3, sigma=1.3):
 
 		if len(img.shape) == 3:
 			H, W, C = img.shape
+			gray = False
 		else:
 			img = np.expand_dims(img, axis=-1)
 			H, W, C = img.shape
+			gray = True
 
 		## Zero padding
 		pad = K_size // 2
 		out = np.zeros([H + pad * 2, W + pad * 2, C], dtype=np.float)
-		out[pad: pad + H, pad: pad + W] = img.copy().astype(np.float)
+		out[pad : pad + H, pad : pad + W] = img.copy().astype(np.float)
 
 		## prepare Kernel
 		K = np.zeros((K_size, K_size), dtype=np.float)
 		for x in range(-pad, -pad + K_size):
 			for y in range(-pad, -pad + K_size):
-				K[y+pad, x+pad] = np.exp( -(x ** 2 + y ** 2) / (2 * (sigma ** 2)))
-		K /= (sigma * np.sqrt(2 * np.pi))
+				K[y + pad, x + pad] = np.exp( - (x ** 2 + y ** 2) / (2 * sigma * sigma))
+		#K /= (sigma * np.sqrt(2 * np.pi))
+		K /= (2 * np.pi * sigma * sigma)
 		K /= K.sum()
 
 		tmp = out.copy()
@@ -45,22 +48,29 @@ def gaussian_filter(img, K_size=3, sigma=1.3):
 		for y in range(H):
 			for x in range(W):
 				for c in range(C):
-					out[pad + y, pad + x, c] = np.sum(K * tmp[y: y + K_size, x: x + K_size, c])
+					out[pad + y, pad + x, c] = np.sum(K * tmp[y : y + K_size, x : x + K_size, c])
 
-		out = out[pad: pad + H, pad: pad + W].astype(np.uint8)
-		out = out[..., 0]
+		out = np.clip(out, 0, 255)
+		out = out[pad : pad + H, pad : pad + W]
+		out = out.astype(np.uint8)
+
+		if gray:
+			out = out[..., 0]
 
 		return out
 
 
 	# sobel filter
 	def sobel_filter(img, K_size=3):
-		H, W = img.shape
+		if len(img.shape) == 3:
+			H, W, C = img.shape
+		else:
+			H, W = img.shape
 
 		# Zero padding
 		pad = K_size // 2
 		out = np.zeros((H + pad * 2, W + pad * 2), dtype=np.float)
-		out[pad: pad + H, pad: pad + W] = gray.copy().astype(np.float)
+		out[pad : pad + H, pad : pad + W] = img.copy().astype(np.float)
 		tmp = out.copy()
 
 		out_v = out.copy()
@@ -74,14 +84,16 @@ def sobel_filter(img, K_size=3):
 		# filtering
 		for y in range(H):
 			for x in range(W):
-				out_v[pad + y, pad + x] = np.sum(Kv * (tmp[y: y + K_size, x: x + K_size]))
-				out_h[pad + y, pad + x] = np.sum(Kh * (tmp[y: y + K_size, x: x + K_size]))
+				out_v[pad + y, pad + x] = np.sum(Kv * (tmp[y : y + K_size, x : x + K_size]))
+				out_h[pad + y, pad + x] = np.sum(Kh * (tmp[y : y + K_size, x : x + K_size]))
 
 		out_v = np.clip(out_v, 0, 255)
 		out_h = np.clip(out_h, 0, 255)
 
-		out_v = out_v[pad: pad + H, pad: pad + W].astype(np.uint8)
-		out_h = out_h[pad: pad + H, pad: pad + W].astype(np.uint8)
+		out_v = out_v[pad : pad + H, pad : pad + W]
+		out_v = out_v.astype(np.uint8)
+		out_h = out_h[pad : pad + H, pad : pad + W]
+		out_h = out_h.astype(np.uint8)
 
 		return out_v, out_h
 
@@ -114,6 +126,7 @@ def angle_quantization(angle):
 
 	def non_maximum_suppression(angle, edge):
 		H, W = angle.shape
+		_edge = edge.copy()
 
 		for y in range(H):
 			for x in range(W):
@@ -137,10 +150,10 @@ def non_maximum_suppression(angle, edge):
 					if y == H-1:
 							dy1 = min(dy1, 0)
 							dy2 = min(dy2, 0)
-					if max(max(edge[y, x], edge[y+dy1, x+dx1]), edge[y+dy2, x+dx2]) != edge[y, x]:
-							edge[y, x] = 0
+					if max(max(edge[y, x], edge[y + dy1, x + dx1]), edge[y + dy2, x + dx2]) != edge[y, x]:
+							_edge[y, x] = 0
 
-		return edge
+		return _edge
 
 	def hysterisis(edge, HT=100, LT=30):
 		H, W = edge.shape
@@ -149,8 +162,8 @@ def hysterisis(edge, HT=100, LT=30):
 		edge[edge >= HT] = 255
 		edge[edge <= LT] = 0
 
-		_edge = np.zeros((H+2, W+2), dtype=np.float32)
-		_edge[1:H+1, 1:W+1] = edge
+		_edge = np.zeros((H + 2, W + 2), dtype=np.float32)
+		_edge[1 : H + 1, 1 : W + 1] = edge
 
 		## 8 - Nearest neighbor
 		nn = np.array(((1., 1., 1.), (1., 0., 1.), (1., 1., 1.)), dtype=np.float32)
@@ -187,7 +200,7 @@ def hysterisis(edge, HT=100, LT=30):
 	edge = non_maximum_suppression(angle, edge)
 
 	# hysterisis threshold
-	out = hysterisis(edge, 160, 80)
+	out = hysterisis(edge, 50, 20)
 
 	return out