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前言

  腐蚀是指周围的介质作用下产生损耗与破坏的过程，如生锈、腐烂等。而腐蚀算法也类似一种能够产生损坏，抹去部分像素的算法。

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一、膨胀腐蚀

  膨胀腐蚀之前需要对图像进行二值化处理，然后进行以下处理。

  腐蚀：$$P=P1\&P2\&P3\&P4\&P5\&P6\&P7\&P8\&P9$$
  膨胀：$$P=P1|P2|P3|P4|P5|P6|P7|P8|P9$$
  图像二值化如下。

import numpy as np
import matplotlib.pyplot as plt
img = plt.imread("lenna.png")
gray = 0.299 * img[:, :, 0] + 0.587 * img[:, :, 1] + 0.114 * img[:, :, 2] 
gray = gray * 255#图像是[0-1]--->[0-255]
bin_image = np.where(gray >= 128, 1, 0)#处理成[0,1]像素

二、Python实现腐蚀算法

def bin_erosion(binary, n):h, w = gray.shapem = int((n - 1) / 2)erosion_image = np.zeros((h, w))for i in range(m, h - m):for j in range(m, w - m):erosion_image[i, j] = binary[i - 1, j - 1] & binary[i - 1, j] & binary[i - 1, j + 1] &\binary[i, j - 1] & binary[i, j] & binary[i, j + 1] & binary[i + 1, j - 1] &\binary[i + 1, j] & binary[i + 1, j + 1]return erosion_image

三、Python实现膨胀算法

def bin_dialtion(binary, n):h, w = gray.shapem = int((n - 1) / 2)dialtion_image = np.zeros((h, w))for i in range(m, h - m):for j in range(m, w - m):dialtion_image[i, j] = binary[i - 1, j - 1] | binary[i - 1, j] | binary[i - 1, j + 1] |\binary[i, j - 1] | binary[i, j] | binary[i, j + 1] | binary[i + 1, j - 1] |\binary[i + 1, j] | binary[i + 1, j + 1]return dialtion_image

四、Python实现阈值算法

  阈值算法介于膨胀腐蚀之间，可以调整膨胀腐蚀的程度。

def threshold_method(binary, n, value):h, w = gray.shapem = int((n - 1) / 2)th_image = np.zeros((h, w))for i in range(m, h - m):for j in range(m, w - m):temp = binary[i - 1, j - 1] + binary[i - 1, j] + binary[i - 1, j + 1] +\binary[i, j - 1] + binary[i, j] + binary[i, j + 1] + binary[i + 1, j - 1] +\binary[i + 1, j] + binary[i + 1, j + 1]if temp >= value:th_image[i, j] = 1else:th_image[i, j] = 0return th_image

erosion_image = bin_erosion(bin_image, 3)
dialtion_image = bin_dialtion(bin_image, 3)
th_image = threshold_method(bin_image, 3, 8)
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(2, 2, 1)
ax.set_title("bin image")
ax.set_xlabel("width")
ax.set_ylabel("height")
plt.imshow(bin_image, cmap="gray")
ax = fig.add_subplot(2, 2, 2)
ax.set_title("erosion image")
ax.set_xlabel("width")
ax.set_ylabel("height")
plt.imshow(erosion_image, cmap="gray")
ax = fig.add_subplot(2, 2, 3)
ax.set_title("dialtion image")
ax.set_xlabel("width")
ax.set_ylabel("height")
plt.imshow(dialtion_image, cmap="gray")
ax = fig.add_subplot(2, 2, 4)
ax.set_title("threshold image")
ax.set_xlabel("width")
ax.set_ylabel("height")
plt.imshow(th_image, cmap="gray")

  画图结果如下。

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五、FPGA实现腐蚀算法

module  ycbcr_to_erosion
(input	wire			vga_clk		,//vga时钟input	wire			sys_rst_n	,//复位信号input	wire	[7:0]	y_data	,//灰度处理的图像像素input	wire			rgb_valid	,//vga显示有效区域output	wire	[15:0]	erosion_data	//二值化像素
);
//binary data
wire [7: 0] 	bin_data;//shift ram
wire	[7:0]	data_row1	;
wire	[7:0]	data_row2	;
wire	[7:0]	data_row3	;
//3*3像素数据
reg		[7:0]	p11			;
reg		[7:0]	p12			;
reg		[7:0]	p13			;
reg		[7:0]	p21			;
reg		[7:0]	p22			;
reg		[7:0]	p23			;
reg		[7:0]	p31			;
reg		[7:0]	p32			;
reg		[7:0]	p33			;wire	[7:0]	temp	    ;
//Y值有效信号
reg				y_valid		;
//二值化
assign  bin_data  = (y_data >= 8'd128) ? 8'd255: 8'd0;
assign  data_row3 = bin_data  ;
//腐蚀
assign  temp = (p11 & p12 & p13 & p21 & p22 & p23 & p31 & p32 & p33);
//像素拼接565
assign  erosion_data = {temp[7:3], temp[7:2], temp[7:3]};
always@(posedge vga_clk or negedge sys_rst_n)	if(sys_rst_n == 1'b0)y_valid  <=  1'b0  ;elsey_valid  <=  rgb_valid  ;always@(posedge vga_clk or negedge sys_rst_n)if(sys_rst_n == 1'b0)begin{p11,p12,p13}  <=  24'd0  ;{p21,p22,p23}  <=  24'd0  ;{p31,p32,p33}  <=  24'd0  ;endelse  if(y_valid == 1'b1)begin{p11,p12,p13}  <= {p12,p13,data_row1}  ;{p21,p22,p23}  <= {p22,p23,data_row2}  ;{p31,p32,p33}  <= {p32,p33,data_row3}  ;end	elsebegin{p11,p12,p13}  <=  24'd0  ;{p21,p22,p23}  <=  24'd0  ;{p31,p32,p33}  <=  24'd0  ;end	
//移位寄存器
shift_ram_gen  shift_ram_gen_inst
(.clock 		(vga_clk	),.shiftin	(data_row3	),.shiftout 	(			),.taps0x 	(data_row2	),.taps1x 	(data_row1	)
);endmodule

  FPGA实现中，只讲解腐蚀算法，膨胀算法及阈值算法，感兴趣的小伙伴可以自行实现，非常easy。

总结

  膨胀腐蚀算法图像处理中常用的算法，有必要掌握。虽然简单，还是需要自己去实现，写多了，也就顺了。下期帧差法。帧差法只做Python，不做FPGA，为什么？下期揭晓答案。