图像增强-分数阶微分(vc++)

忘是亡心i 2022-09-28 14:25 156阅读 0赞

分数阶微分，Grumwald-Letnikov定义在图像的数值实现中更为准确：

![20170312211538705][]

Gamma函数：![20170312211613937][]

若s（t）的持续期t \[a,t\],将函数持续期间\[a,t\]按单位间隔h=1进行等分，得到：

![20170312211905142][]

推到一元函数是s（t）的 v 阶分数阶微分差分表达式为：

![20170312212224497][]

这n个非零系数只有常数“1”，其他都是n-1个都是分数阶微分阶次的函数。n个系数分别为：

![20170312212539583][]

![20170312210726818][]

**微分近似掩模算子**

**分数阶微分( ****0.1阶 ～ 0.9****阶)， 则可以检测到或部分检测到那些模糊边界和细微的弱边界， 而且还可以减少图像噪声的增加。**

**下左图：原图，下右图：0.5阶分数阶微分处理结果（v=0.5）**

![20170312205630226][]

void CShowPicView::OnFractionalCalculus( ) // 分数阶微积分 灰度图  单通道
    {
    	CShowPicDoc* pDoc = GetDocument();
    	CDC* pDC=GetDC();
    	CString str;
    	int  i,j;
    	double temp ;
    
    	int **g;
    	g = new int *[intHeight];
    	for(i=0; i<intHeight ;i++)
    		g[i]=new int [intWidth];
    
    
    	for(j = 0; j < intWidth; j++)
    		for(i = 0; i <intHeight ; i++)
    			g[i][j]=0;
    
    	double a0 , a1 , a2 ,v= 0.8 ;
    	a0=1;  a1=-v; a2=(-v)*(-v+1)/2;
    	double temp_1=(8+4*v*v-12*v);
    
    	for(j = 2; j < intWidth-2; j++)
    		for(i = 2; i <intHeight-2 ; i++)
    		{
    			temp = a2*(Data[i-2][j-2]+Data[i-2][j]+Data[i-2][j+2]
    					  +Data[i][j-2]                 +Data[i][j+2]
    					  +Data[i+2][j-2]+Data[i+2][j]+Data[i+2][j+2]);
    
    			temp+= a1*(Data[i-1][j-1]+Data[i-1][j]+Data[i-1][j+1]
    					  +Data[i][j-1]                 +Data[i][j+1]
    					  +Data[i+1][j-1]+Data[i+1][j]+Data[i+1][j+1]);
    		
    			temp+= 8*a0*Data[i][j];
    			temp = temp/ temp_1;
    	
    			if(temp<0)
    				temp=0;
                g[i][j] = (int)temp;
    
    		   pDC->SetPixel(j+intWidth,i,RGB(g[i][j],g[i][j],g[i][j]));
    		 
    		}
    	for(j = 0; j < intWidth; j++)
    		for(i = 0; i <intHeight ; i++)
    			Data[i][j]=g[i][j];
    
    
    	for(i=0; i<intHeight ;i++)
    		delete [] g[i];
    
    	delete []g;
    	
    	ReleaseDC(pDC);
    	
    }
    
    
    void CShowPicView::OnFractionalCalculusRGB()  // 分数阶微积分RGB
    {
    	CShowPicDoc* pDoc = GetDocument();
    	CDC* pDC=GetDC();
    	CString str;
    	int  i,j;
    	double temp_R , temp_G , temp_B  ;
    
    	int **g;
    	g = new int *[intHeight];
    	for(i=0; i<intHeight ;i++)
    		g[i]=new int [intWidth];
    
    	double  **m_imgData_R, **m_imgData_G, **m_imgData_B ;
    	double **I_enhanced_R ,  **I_enhanced_G ,  **I_enhanced_B ;
    
    	m_imgData_R=new double *[intHeight];
    	m_imgData_G=new double *[intHeight];
    	m_imgData_B=new double *[intHeight];
    
    	I_enhanced_R=new double *[intHeight];
    	I_enhanced_G=new double *[intHeight];
    	I_enhanced_B=new double *[intHeight];
    
    
    	for(i=0; i<intHeight; i++)
    	{
    		m_imgData_R[i] = new double [intWidth];
    		m_imgData_G[i] = new double [intWidth];
    		m_imgData_B[i] = new double [intWidth];
    
    		I_enhanced_R[i] = new double [intWidth];
    		I_enhanced_G[i] = new double [intWidth];
    		I_enhanced_B[i] = new double [intWidth];
    	}
    
    	for(j = 0; j < intWidth; j++)
    		for(i = 0; i < intHeight ; i++)
    		{
    			m_imgData_R[i][j]=pDoc->pic[i][j][0];
    			m_imgData_G[i][j]=pDoc->pic[i][j][1];
    			m_imgData_B[i][j]=pDoc->pic[i][j][2];
    
    			I_enhanced_R[i][j]=pDoc->pic[i][j][0];
    			I_enhanced_G[i][j]=pDoc->pic[i][j][1];
    			I_enhanced_B[i][j]=pDoc->pic[i][j][2];
    
    			g[i][j]=0;
    		}
    			
    
    	double a0 , a1 , a2 , v= 0.3;
    	a0=1;  a1=-v; a2=(-v)*(-v+1)/2;
    	double temp_1=(8+4*v*v-12*v);
    
    	for(j = 2; j < intWidth-2; j++)
    		for(i = 2; i <intHeight-2 ; i++)
    		{
    			temp_R = a2*(pDoc->pic[i-2][j-2][0]+pDoc->pic[i-2][j][0]+pDoc->pic[i-2][j+2][0]
    					    +pDoc->pic[i][j-2][0]                       +pDoc->pic[i][j+2][0]
    					    +pDoc->pic[i+2][j-2][0]+pDoc->pic[i+2][j][0]+pDoc->pic[i+2][j+2][0]);
    
    			temp_G = a2*(pDoc->pic[i-2][j-2][1]+pDoc->pic[i-2][j][1]+pDoc->pic[i-2][j+2][1]
    					    +pDoc->pic[i][j-2][1]                       +pDoc->pic[i][j+2][1]
    					    +pDoc->pic[i+2][j-2][1]+pDoc->pic[i+2][j][1]+pDoc->pic[i+2][j+2][1]);
    
    			temp_B = a2*(pDoc->pic[i-2][j-2][2]+pDoc->pic[i-2][j][2]+pDoc->pic[i-2][j+2][2]
    					    +pDoc->pic[i][j-2][2]                       +pDoc->pic[i][j+2][2]
    					    +pDoc->pic[i+2][j-2][2]+pDoc->pic[i+2][j][2]+pDoc->pic[i+2][j+2][2]);
    
    			temp_R += a1*(pDoc->pic[i-1][j-1][0]+pDoc->pic[i-1][j][0]+pDoc->pic[i-1][j+1][0]
    						 +pDoc->pic[i][j-1][0]                       +pDoc->pic[i][j+1][0]
    					     +pDoc->pic[i+1][j-1][0]+pDoc->pic[i+1][j][0]+pDoc->pic[i+1][j+1][0]);
    
    			temp_G += a1*(pDoc->pic[i-1][j-1][1]+pDoc->pic[i-1][j][1]+pDoc->pic[i-1][j+1][1]
    						 +pDoc->pic[i][j-1][1]                       +pDoc->pic[i][j+1][1]
    						 +pDoc->pic[i+1][j-1][1]+pDoc->pic[i+1][j][1]+pDoc->pic[i+1][j+1][1]);
    
    			temp_B += a1*(pDoc->pic[i-1][j-1][2]+pDoc->pic[i-1][j][2]+pDoc->pic[i-1][j+1][2]
    						 +pDoc->pic[i][j-1][2]                       +pDoc->pic[i][j+1][2]
    						 +pDoc->pic[i+1][j-1][2]+pDoc->pic[i+1][j][2]+pDoc->pic[i+1][j+1][2]);
    
    			temp_R += 8*a0*pDoc->pic[i][j][0];
    			temp_R = temp_R/ temp_1;
    			if(temp_R<0)
    				temp_R=0;
    			else if(temp_R>255)
    				temp_R=255;
    
    			temp_G += 8*a0*pDoc->pic[i][j][1];
    			temp_G = temp_G/ temp_1;
    			if(temp_G<0)
    				temp_G=0;
    			else if(temp_G>255)
    				temp_G=255;
    
    			temp_B += 8*a0*pDoc->pic[i][j][2];
    			temp_B = temp_B/ temp_1;
    			if(temp_B<0)
    				temp_B=0;
    			else if(temp_B>255)
    				temp_B=255;
    
    			I_enhanced_R[i][j]=(int)temp_R;
    			I_enhanced_G[i][j]=(int)temp_G;
    			I_enhanced_B[i][j]=(int)temp_B;
    
    			pDC->SetPixel(j+intWidth,i,RGB(I_enhanced_R[i][j],I_enhanced_G[i][j],I_enhanced_B[i][j]));
    		}
    
    	for(j = 0; j < intWidth; j++)
    		for(i = 0; i <intHeight ; i++)
    		{
    			pDoc->pic[i][j][0]=I_enhanced_R[i][j];
    			pDoc->pic[i][j][1]=I_enhanced_G[i][j];
    			pDoc->pic[i][j][2]=I_enhanced_B[i][j];
    		}
    
    
    	for(i=0; i<intHeight ;i++)
    		delete [] g[i];
    
    	for(i=0; i<intHeight; i++)
    	{
    		delete [] m_imgData_R[i];
    		delete [] m_imgData_G[i];
    		delete [] m_imgData_B[i];
    
    
    		delete [] I_enhanced_R[i];
    		delete [] I_enhanced_G[i];
    		delete [] I_enhanced_B[i];
    	}
    
    
    	delete m_imgData_R;
    	delete m_imgData_G;
    	delete m_imgData_B;
    
    
    	delete   I_enhanced_R ;
    	delete   I_enhanced_G ;
    	delete   I_enhanced_B ;
    
    	ReleaseDC(pDC);	
    
    	delete []g;
    	
    	ReleaseDC(pDC);
    	
    }

![20170312213453525][]

**原图，0.5阶增强效果**

最近有网友问我：直接把程序copy到vc里面，为什么运行不了？

答：那是当然运行不了，只是提供了分数阶微分的部分代码，并没有上传全部代码，需要把代码相应的接口修改并放到自己的代码里面才能运行。所以索性把所有的代码都打包上传，想要的自己下载吧。

**链接: https://pan.baidu.com/s/16y6g\_HWQk6oin3k8MLilzg 提取码: a2ah**

[20170312211538705]: /images/20220708/ba4074023b8a4bbeab0b04cbee593431.png
[20170312211613937]: /images/20220708/7ee5f178ce02433aa13d8a8b623fdc3c.png
[20170312211905142]: /images/20220708/83969a2f6528408ab4e12f7c5decc414.png
[20170312212224497]: /images/20220708/9b63b3edc8094231a79e437acc478419.png
[20170312212539583]: /images/20220708/d0636655a92d4c27bd7102643abe4a0c.png
[20170312210726818]: /images/20220708/d1871475812d40a1921b51debd33bb3f.png
[20170312205630226]: /images/20220708/1697a03eef25440ebd96f0e8ba2054ed.png
[20170312213453525]: /images/20220708/9f61700985464b6998ebee4617e9abda.png