Python与FPGA——图像锐化

文章目录

前言
一、图像锐化
二、Python robert锐化
三、Python sobel锐化
四、Python laplacian锐化
五、FPGA sobel锐化
总结

前言

在增强图像之前一般会先对图像进行平滑处理以减少或消除噪声，图像的能量主要集中在低频部分，而噪声和图像边缘信息的能量主要集中在高频部分。因此，平滑处理会使原始的图像边缘和轮廓变得模糊。为了减少不利效果的影响，需要利用图像锐化技术。

一、图像锐化

图像锐化其实就是使用robert，sobel，laplacian这些人发明的窗口，进行图像的处理。图像锐化过程和sobel边缘检测的过程类似，可以移步至《Python与FPGA——sobel边缘检测》课程，一探究竟。

一阶微分的边缘检测
图像f（x, y）在像素（x, y）梯度的定义为
$\frac{\partial f}{\partial x} + \frac{\partial f}{\partial y}$
也可以用差分来替代微分，即
$\frac{\partial f}{\partial x} = f(i + 1, j) - f(i, j)$
$\frac{\partial f}{\partial y} = f(i, j + 1) - f(i, j)$
梯度的幅值即模值，为
$\sqrt{(\frac{\partial f}{\partial x})^2 + (\frac{\partial f}{\partial y})^2} = \sqrt{[f(i + 1, j) - f(i, j)]^2 + [f(i, j ) - f(i, j)]^2}$
梯度方向为
$\theta = arctan(\frac{\partial f}{\partial y}/\frac{\partial f}{\partial x}) = arctan[\frac{f(i, j + 1) - f(i, j)}{f(i + 1, j) - f(i, j)}]$
图像f(i, j)处的梯度g为
$g (i, j) = G [f (i, j)]$
使用 $g (i, j)$ 去替代原来的像素。
一阶导算子有robert算子，perwitt算子，sobel算子。
1. Roberts算子
$G_x = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \quad\quad\quad G_y = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$
2. Prewitt算子
$G_x = \begin{bmatrix} -1 & 0 & 1\\ -1 & 0 & 1\\ -1 & 0 & 1 \end{bmatrix} \quad\quad\quad G_y = \begin{bmatrix} -1 & -1 & -1\\ 0 & 0 & 0\\ 1 & 1 & 1 \end{bmatrix}$
3. Sobel算子
$G_x = \begin{bmatrix} -1 & 0 & +1\\ -2 & 0 & +2\\ -1 & 0 & +1 \end{bmatrix} \quad\quad\quad G_y = \begin{bmatrix} +1 & +2 & +1\\ 0 & 0 & 0\\ -1 & -2 & 1 \end{bmatrix}$

二阶微分的边缘检测
二阶微分公式用差分法，推理如下
$\frac{\partial^2 f}{\partial x^2}=2f(x,y)-f(x-1,y)-f(x+1, y)$
$\frac{\partial^2 f}{\partial y^2}=2f(x,y)-f(x,y-1)-f(x, y+1)$
$\triangledown^2f=4f(x,y)-[f(x-1,y)+f(x,y-1)+f(x,y+1)+f(x+1,y)]$
符合二阶微分的算子是laplacian。

$G_x = \begin{bmatrix} 0 & -1 & 0\\ -1 & 4 & -1\\ 0 & -1 & 0 \end{bmatrix} \quad\quad\quad G_y = \begin{bmatrix} -1 & -1 & -1\\ -1 & 8 & -1\\ -1 & -1 & -1 \end{bmatrix}$

二、Python robert锐化

import numpy as np
import matplotlib.pyplot as plt
def image_gray(image):gray = np.dot(image[:, :, ...], [0.299, 0.587, 0.114])#等同0.299 * image[:, :, 0] + 0.587 * image[:, :, 1] + 0.114 * image[:, :, 2]return gray.astype(np.uint8)def robert_sharpen(image, gx, gy):h, w = image.shapen, n = gx.shapefiltered_image = np.zeros((h, w))m = int(n / 2)for i in range(m, h - m):for j in range(m, w - m):   gx_value = np.sum(np.multiply(gx, image[i - m: i + m, j - m: j + m]))gy_value = np.sum(np.multiply(gy, image[i - m: i + m, j - m: j + m]))gxy_value = np.sqrt(gx_value ** 2 + gy_value ** 2)filtered_image[i, j] = gxy_valuereturn filtered_image.astype(np.uint8)img = plt.imread("lenna.png")
img = img * 255#图像是[0-1]--->[0-255],确认一下自己的图像是[0-1]还是[0-255]
img = img.astype(np.uint8)
gx = np.array([[1, 0],[0, -1]])
gy = np.array([[0, 1],[-1, 0]])
gray = image_gray(img)
robert_image = robert_sharpen(gray, gx, gy)
fig = plt.figure(figsize=(10, 6))
ax = plt.subplot(1, 2, 1)
ax.set_title("raw image")
ax.set_xlabel("width")
ax.set_ylabel("height")
plt.imshow(gray, cmap="gray")
ax = plt.subplot(1, 2, 2)
ax.set_title("robert image")
ax.set_xlabel("width")
ax.set_ylabel("height")
plt.imshow(robert_image, cmap="gray")

在这里插入图片描述

三、Python sobel锐化

import numpy as np
import matplotlib.pyplot as plt
def image_gray(image):gray = np.dot(image[:, :, ...], [0.299, 0.587, 0.114])#等同0.299 * image[:, :, 0] + 0.587 * image[:, :, 1] + 0.114 * image[:, :, 2]return gray.astype(np.uint8)def sobel_sharpen(image, gx, gy):h, w = image.shapen, n = gx.shapefiltered_image = np.zeros((h, w))m = int((n-1) / 2)for i in range(m, h - m):for j in range(m, w - m):   gx_value = np.sum(np.multiply(gx, image[i - m: i + m + 1, j - m: j + m + 1]))gy_value = np.sum(np.multiply(gy, image[i - m: i + m + 1, j - m: j + m + 1]))gxy_value = np.sqrt(gx_value ** 2 + gy_value ** 2)filtered_image[i, j] = gxy_valuereturn filtered_image.astype(np.uint8)img = plt.imread("lenna.png")
img = img * 255#图像是[0-1]--->[0-255],确认一下自己的图像是[0-1]还是[0-255]
img = img.astype(np.uint8)
gx = np.array([[-1, 0, 1],[-2, 0, 2],[-1, 0, 1]])
gy = np.array([[-1, -2, -1],[0, 0, 0],[1, 2, 1]])
gray = image_gray(img)
sobel_image = sobel_sharpen(gray, gx, gy)
fig = plt.figure(figsize=(10, 6))
ax = plt.subplot(1, 2, 1)
ax.set_title("raw image")
ax.set_xlabel("width")
ax.set_ylabel("height")
plt.imshow(gray, cmap="gray")
ax = plt.subplot(1, 2, 2)
ax.set_title("sobel image")
ax.set_xlabel("width")
ax.set_ylabel("height")
plt.imshow(sobel_image, cmap="gray")

在这里插入图片描述

四、Python laplacian锐化

import numpy as np
import matplotlib.pyplot as plt
def image_gray(image):gray = np.dot(image[:, :, ...], [0.299, 0.587, 0.114])#等同0.299 * image[:, :, 0] + 0.587 * image[:, :, 1] + 0.114 * image[:, :, 2]return gray.astype(np.uint8)def laplacian_sharpen(image, gx, gy):h, w = image.shapen, n = gx.shapefiltered_image = np.zeros((h, w))m = int((n-1) / 2)for i in range(m, h - m):for j in range(m, w - m):   gx_value = np.sum(np.multiply(gx, image[i - m: i + m + 1, j - m: j + m + 1]))gy_value = np.sum(np.multiply(gy, image[i - m: i + m + 1, j - m: j + m + 1]))gxy_value = np.sqrt(gx_value ** 2 + gy_value ** 2)filtered_image[i, j] = gxy_valuereturn filtered_image.astype(np.uint8)img = plt.imread("lenna.png")
img = img * 255#图像是[0-1]--->[0-255],确认一下自己的图像是[0-1]还是[0-255]
img = img.astype(np.uint8)
gx = np.array([[0, -1, 0],[-1, 4, -1],[0, -1, 0]])
gy = np.array([[-1, -1, -1],[-1, 8, -1],[-1, -1, -1]])
gray = image_gray(img)
sobel_image = sobel_sharpen(gray, gx, gy)
fig = plt.figure(figsize=(10, 6))
ax = plt.subplot(1, 2, 1)
ax.set_title("raw image")
ax.set_xlabel("width")
ax.set_ylabel("height")
plt.imshow(gray, cmap="gray")
ax = plt.subplot(1, 2, 2)
ax.set_title("sobel image")
ax.set_xlabel("width")
ax.set_ylabel("height")
plt.imshow(sobel_image, cmap="gray")

在这里插入图片描述

五、FPGA sobel锐化

//3*3图像
//P11   P12   P13
//P21   P22   P23
//P31   P32   P33//Gx算子
//-1     0     1
//-2     0     2
//-1     0     1
//Gx = -P11 + P13 - 2*P21 + 2*P23 - P31 + P33
//Gx = (P13 - P11) + 2*(P23 - P21) + (P33 - P31)//Gy算子
//1      2     1
//0      0     0
//-1     -2    -1
//Gy = P11 + 2*P12 + P13 - P31 - 2*P32 - P33
//Gy = (P11 - P31) + 2*(P12 - P32) + (P13 - P33)
module  ycbcr_sobel_sharpen
(input	wire			sys_clk		,	//系统时钟，频率为50MHZinput	wire			sys_rst_n	,	//系统复位，低电平有效input	wire			rgb_valid	,	//RGB565图像显示有效信号input	wire	[7:0]	y_data		,	//Y分量input	wire	[11:0]	pixel_x		,	//有效显示区域横坐标input	wire	[11:0]	pixel_y		,	//有效显示区域纵坐标output	reg		[15:0]	sobel_data		//Sobel算法处理后的图像数据
);reg				y_valid		;	//Y分量有效信号
//shift ram
wire	[7:0]	data_row1	;	//移位寄存器第一行数据
wire	[7:0]	data_row2	;	//移位寄存器第二行数据
wire	[7:0]	data_row3	;	//移位寄存器第三行数据
//3*3像素数据，左上角至右下角共9个数据
reg		[7:0]	p11			;	//3*3第1个像素数据
reg		[7:0]	p12			;	//3*3第2个像素数据
reg		[7:0]	p13			;	//3*3第3个像素数据
reg		[7:0]	p21			;	//3*3第4个像素数据
reg		[7:0]	p22			;	//3*3第5个像素数据
reg		[7:0]	p23			;	//3*3第6个像素数据
reg		[7:0]	p31			;	//3*3第7个像素数据
reg		[7:0]	p32			;	//3*3第8个像素数据
reg		[7:0]	p33			;	//3*3第9个像素数据
//Sobel算子
wire	[15:0]	Gx			;	//水平梯度值
wire	[15:0]	Gy			;	//数值梯度值
wire	[7:0]	Gxy			;	//总体梯度值assign  data_row3 = y_data  ;
assign  Gx = (p13 - p11) + 2*(p23 - p21) + (p33 - p31)  ;
assign  Gy = (p11 - p31) + 2*(p12 - p32) + (p13 - p33)  ;//设定第一行、第二行，第一列、第二列显示全白色
always@(*)if((pixel_y == 12'd0)||(pixel_y == 12'd1)||(pixel_x == 12'd2)||(pixel_x == 12'd3))sobel_data = 16'hffff  ;elsesobel_data = {Gxy[7:3],Gxy[7:2],Gxy[7:3]}  ;//锐化核心代码always@(posedge sys_clk or negedge sys_rst_n)if(sys_rst_n == 1'b0)y_valid  <=  1'b0  ;elsey_valid  <=  rgb_valid  ;always@(posedge sys_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		shift_ram_gen  shift_ram_gen_inst
(.clock 		(sys_clk	),.shiftin	(data_row3	),.shiftout 	(			),.taps0x 	(data_row2	),.taps1x 	(data_row1	)
);sqrt_gen  sqrt_gen_inst 
(.radical	(Gx*Gx + Gy*Gy),.q 			(Gxy	),.remainder 	()
);endmodule