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图像的放大与缩小(2)——双线性插值放大与均值缩小

2013年01月22日 ⁄ 综合 ⁄ 共 7081字 ⁄ 字号 评论关闭

概述

基于上一节“等距采样法”实现图片放大与缩小的缺点。要对其进行改进,对图像的缩小则可以用“局部均值法”,对于图像的放大则可以用“双线性插值法”。

效果如下:

      

                   2048*1536缩小为100*80时的效果
              100*80放大到600*400的效果

局部均值法缩小图像

(1)计算采样间隔

设原图的大小为W*H,将其放大(缩小)为(k1*W)*(K2*H),则采样区间为

ii=1/k1;       jj=1/k2;

当k1==k2时为等比例缩小;当k1!=k2时为不等比例放大(缩小);当k1<1&&k2<1时为图片放大,k1<1&&k2>1时时图片缩小

(2)求出局部子块

设原图为F(x,y)(i=1,2,……W; j=1,2,……H),缩小的图像为G(x,y)(i=1,2, ……M; j=1,2,……N,其中M=W*k1,N=H*k2),则有原图像局部子块为

f’(x,y) = f(ii*i, jj*j)        …… f(ii*i + ii-1, jj*j)

                ……                   ……

             f(ii*i, jj*j+jj-1) …… f(ii*i + ii-1, jj*j+jj-1)

(3)求出缩小的图像

G(x, y) = f’(x,y)的均值

例:

缩小后的图像

 

 

例如g11=(f11 +f12 + f21 + f22)/4

 

算法源代码(java)

/**
	 * 局部均值的图像缩小
	 * @param img 要缩小的图像对象
	 * @param m 缩小后图像的宽
	 * @param n 缩小后图像的高
	 * @return 返回处理后的图像对象
	 */
	public static BufferedImage shrink(BufferedImage img, int m, int n) {
		float k1 = (float)m/img.getWidth();
		float k2 = (float)n/img.getHeight();		
		return shrink(img, k1, k2);
	}
	
	/**
	  * 局部均值的图像缩小
	 * @param img 要缩小的图像对象
	 * @param k1 要缩小的列比列
	 * @param k2 要缩小的行比列
	 * @return 返回处理后的图像对象
	 */
	public static BufferedImage shrink(BufferedImage img, float k1, float k2) {
		if(k1 >1 || k2>1) {//如果k1 >1 || k2>1则是图片放大,不是缩小
			System.err.println("this is shrink image funcation, please set k1<=1 and k2<=1!");
			return null;
		} 
		float ii = 1/k1;	//采样的行间距
		float jj = 1/k2; //采样的列间距		
		int dd = (int)(ii*jj); 
		//int m=0 , n=0;				
		int imgType = img.getType();
		int w = img.getWidth();
		int h = img.getHeight();
		int m = (int) (k1*w);
		int n = (int) (k2*h);
		int[] pix = new int[w*h];
		pix = img.getRGB(0, 0, w, h, pix, 0, w);
		System.out.println(w + " * " + h);
		System.out.println(m + " * " + n);
		int[] newpix = new int[m*n];
		
		for(int j=0; j<n; j++) {
			for(int i=0; i<m; i++) {
				int r = 0, g=0, b=0;
				ColorModel cm = ColorModel.getRGBdefault();				
				for(int k=0; k<(int)jj; k++) {
					for(int l=0; l<(int)ii; l++) {
						r = r + cm.getRed(pix[(int)(jj*j+k)*w + (int)(ii*i+l)]);
						g = g + cm.getGreen(pix[(int)(jj*j+k)*w + (int)(ii*i+l)]);
						b = b + cm.getBlue(pix[(int)(jj*j+k)*w + (int)(ii*i+l)]);
					}
				}
				r = r/dd;
				g = g/dd;
				b = b/dd;
				newpix[j*m + i] = 255<<24 | r<<16 | g<<8 | b;
				//255<<24 | r<<16 | g<<8 | b  这个公式解释一下,颜色的RGB在内存中是
				//以二进制的形式保存的,从右到左1-8位表示blue,9-16表示green,17-24表示red
				//所以"<<24" "<<16" "<<8"分别表示左移24,16,8位
				
				//newpix[j*m + i] = new Color(r,g,b).getRGB();
			}
		}
		
		BufferedImage imgOut = new BufferedImage( m, n, imgType);
		
		imgOut.setRGB(0, 0, m, n, newpix, 0, m);			
		return imgOut;
	}

 

/**
	 * 局部均值的图像缩小
	 * @param img 要缩小的图像对象
	 * @param m 缩小后图像的宽
	 * @param n 缩小后图像的高
	 * @return 返回处理后的图像对象
	 */
	public static BufferedImage shrink(BufferedImage img, int m, int n) {
		float k1 = (float)m/img.getWidth();
		float k2 = (float)n/img.getHeight();		
		return shrink(img, k1, k2);
	}
	
	/**
	  * 局部均值的图像缩小
	 * @param img 要缩小的图像对象
	 * @param k1 要缩小的列比列
	 * @param k2 要缩小的行比列
	 * @return 返回处理后的图像对象
	 */
	public static BufferedImage shrink(BufferedImage img, float k1, float k2) {
		if(k1 >1 || k2>1) {//如果k1 >1 || k2>1则是图片放大,不是缩小
			System.err.println("this is shrink image funcation, please set k1<=1 and k2<=1!");
			return null;
		} 
		float ii = 1/k1;	//采样的行间距
		float jj = 1/k2; //采样的列间距		
		int dd = (int)(ii*jj); 
		//int m=0 , n=0;				
		int imgType = img.getType();
		int w = img.getWidth();
		int h = img.getHeight();
		int m = (int) (k1*w);
		int n = (int) (k2*h);
		int[] pix = new int[w*h];
		pix = img.getRGB(0, 0, w, h, pix, 0, w);
		System.out.println(w + " * " + h);
		System.out.println(m + " * " + n);
		int[] newpix = new int[m*n];
		
		for(int j=0; j<n; j++) {
			for(int i=0; i<m; i++) {
				int r = 0, g=0, b=0;
				ColorModel cm = ColorModel.getRGBdefault();				
				for(int k=0; k<(int)jj; k++) {
					for(int l=0; l<(int)ii; l++) {
						r = r + cm.getRed(pix[(int)(jj*j+k)*w + (int)(ii*i+l)]);
						g = g + cm.getGreen(pix[(int)(jj*j+k)*w + (int)(ii*i+l)]);
						b = b + cm.getBlue(pix[(int)(jj*j+k)*w + (int)(ii*i+l)]);
					}
				}
				r = r/dd;
				g = g/dd;
				b = b/dd;
				newpix[j*m + i] = 255<<24 | r<<16 | g<<8 | b;
				//255<<24 | r<<16 | g<<8 | b  这个公式解释一下,颜色的RGB在内存中是
				//以二进制的形式保存的,从右到左1-8位表示blue,9-16表示green,17-24表示red
				//所以"<<24" "<<16" "<<8"分别表示左移24,16,8位
				
				//newpix[j*m + i] = new Color(r,g,b).getRGB();
			}
		}
		
		BufferedImage imgOut = new BufferedImage( m, n, imgType);
		
		imgOut.setRGB(0, 0, m, n, newpix, 0, m);			
		return imgOut;
	}

双线性差值法放图像

子块四个顶点的坐标分别设为(0,0)、(1,0)、(0,1)、(1,1),对应的带处理的像素的坐标(c1,c2),0<c1<1, 0<y<1.则f(x,y)由上到下得到


f(x,0) = f(0,0) + c1*(f(1,0)-f(0,0))

f(x,1) = f(0,1) + c1*(f(1,1)-f(0,1))
f(x,y) = f(x,0) + c2*f(f(x,1)-f(x,0))

例,原图的像素矩阵如下。

将其放大成2.5*1.2倍,双线性插值发,填充顶点如下:

(1)

 

(2)

1  2  3  4  5  6  7  7

2  3  4  5  7  8  8  8

3  4  5  6  7  8  9  9

3  4  5  6  7  8  9  9

(3)

算法源代码(java)

/**
	 * 双线性插值法图像的放大
	 * @param img 要缩小的图像对象
	 * @param k1 要缩小的列比列
	 * @param k2 要缩小的行比列
	 * @return 返回处理后的图像对象
	 */
	public static BufferedImage amplify(BufferedImage img, float k1, float k2) {
		if(k1 <1 || k2<1) {//如果k1 <1 || k2<1则是图片缩小,不是放大
			System.err.println("this is shrink image funcation, please set k1<=1 and k2<=1!");
			return null;
		} 
		float ii = 1/k1;	//采样的行间距
		float jj = (1/k2); //采样的列间距		
		int dd = (int)(ii*jj); 
		//int m=0 , n=0;
		int imgType = img.getType();
		int w = img.getWidth();		//原图片的宽
		int h = img.getHeight();	//原图片的宽
		int m = Math.round(k1*w);	//放大后图片的宽
		int n = Math.round(k2*h);	//放大后图片的宽
		int[] pix = new int[w*h];
		pix = img.getRGB(0, 0, w, h, pix, 0, w);
		/*System.out.println(w + " * " + h);
		System.out.println(m + " * " + n);*/
		int[] newpix = new int[m*n];
		
		for(int j=0; j<h-1; j++){
			for(int i=0; i<w-1; i++) {
				int x0 = Math.round(i*k1);
				int y0 = Math.round(j*k2);
				int x1, y1;
				if(i == w-2) {
					x1 = m-1;
				} else {
					x1 = Math.round((i+1)*k1);
				}				
				if(j == h-2) {
					y1 = n-1;
				} else {
					y1 = Math.round((j+1)*k2);
				}				
				int d1 = x1 - x0;
				int d2 = y1 - y0;
				if(0 == newpix[y0*m + x0]) {
					newpix[y0*m + x0] =  pix[j*w+i];
				}
				if(0 == newpix[y0*m + x1]) {
					if(i == w-2) {
						newpix[y0*m + x1] = pix[j*w+w-1];
					} else {
						newpix[y0*m + x1] =  pix[j*w+i+1];
					}					
				}
				if(0 == newpix[y1*m + x0]){
					if(j == h-2) {
						newpix[y1*m + x0] = pix[(h-1)*w+i];
					} else {
						newpix[y1*m + x0] =  pix[(j+1)*w+i];
					}					
				}
				if(0 == newpix[y1*m + x1]) {
					if(i==w-2 && j==h-2) {
						newpix[y1*m + x1] = pix[(h-1)*w+w-1];
					} else {
						newpix[y1*m + x1] = pix[(j+1)*w+i+1];
					}					
				}
				int r, g, b;
				float c;
				ColorModel cm = ColorModel.getRGBdefault();				
				for(int l=0; l<d2; l++) {
					for(int k=0; k<d1; k++) {
						if(0 == l) {
							//f(x,0) = f(0,0) + c1*(f(1,0)-f(0,0))
							if(j<h-1 && newpix[y0*m + x0 + k] == 0) {
								c = (float)k/d1;
								 r = cm.getRed(newpix[y0*m + x0]) + (int)(c*(cm.getRed(newpix[y0*m + x1]) - cm.getRed(newpix[y0*m + x0])));//newpix[(y0+l)*m + k]
								 g = cm.getGreen(newpix[y0*m + x0]) + (int)(c*(cm.getGreen(newpix[y0*m + x1]) - cm.getGreen(newpix[y0*m + x0])));
								 b = cm.getBlue(newpix[y0*m + x0]) + (int)(c*(cm.getBlue(newpix[y0*m + x1]) - cm.getBlue(newpix[y0*m + x0])));
								 newpix[y0*m + x0 + k] = new Color(r,g,b).getRGB();
							}
							if(j+1<h && newpix[y1*m + x0 + k] == 0) {
								 c = (float)k/d1;
									r = cm.getRed(newpix[y1*m + x0]) + (int)(c*(cm.getRed(newpix[y1*m + x1]) - cm.getRed(newpix[y1*m + x0])));
									g = cm.getGreen(newpix[y1*m + x0]) + (int)(c*(cm.getGreen(newpix[y1*m + x1]) - cm.getGreen(newpix[y1*m + x0])));
									b = cm.getBlue(newpix[y1*m + x0]) + (int)(c*(cm.getBlue(newpix[y1*m + x1]) - cm.getBlue(newpix[y1*m + x0])));
									newpix[y1*m + x0 + k] = new Color(r,g,b).getRGB();
							 }
							//System.out.println(c);
						} else {
							//f(x,y) = f(x,0) + c2*f(f(x,1)-f(x,0))
							c = (float)l/d2;
							r = cm.getRed(newpix[y0*m + x0+k]) + (int)(c*(cm.getRed(newpix[y1*m + x0+k]) - cm.getRed(newpix[y0*m + x0+k])));
							g = cm.getGreen(newpix[y0*m + x0+k]) + (int)(c*(cm.getGreen(newpix[y1*m + x0+k]) - cm.getGreen(newpix[y0*m + x0+k])));
							b = cm.getBlue(newpix[y0*m + x0+k]) + (int)(c*(cm.getBlue(newpix[y1*m + x0+k]) - cm.getBlue(newpix[y0*m + x0+k])));
							newpix[(y0+l)*m + x0 + k] = new Color(r,g,b).getRGB(); 
							//System.out.println((int)(c*(cm.getRed(newpix[y1*m + x0+k]) - cm.getRed(newpix[y0*m + x0+k]))));
						}				
					}					
					if(i==w-2 || l==d2-1) {	//最后一列的计算
						//f(1,y) = f(1,0) + c2*f(f(1,1)-f(1,0))
						c = (float)l/d2;
						r = cm.getRed(newpix[y0*m + x1]) + (int)(c*(cm.getRed(newpix[y1*m + x1]) - cm.getRed(newpix[y0*m + x1])));
						g = cm.getGreen(newpix[y0*m + x1]) + (int)(c*(cm.getGreen(newpix[y1*m + x1]) - cm.getGreen(newpix[y0*m + x1])));
						b = cm.getBlue(newpix[y0*m + x1]) + (int)(c*(cm.getBlue(newpix[y1*m + x1]) - cm.getBlue(newpix[y0*m + x1])));
						newpix[(y0+l)*m + x1] = new Color(r,g,b).getRGB(); 
					}
				}
			}
		}
		/*
		for(int j=0; j<50; j++){
			for(int i=0; i<50; i++) {
				System.out.print(new Color(newpix[j*m + i]).getRed() + "\t");				
			}
			System.out.println();
		}
		*/
		BufferedImage imgOut = new BufferedImage( m, n, imgType);
		
		imgOut.setRGB(0, 0, m, n, newpix, 0, m);		
		return imgOut;
	}

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