图像处理之三种常见双立方插值算法

图像处理之三种常见双立方插值算法图像处理之三种常见双立方插值算法双立方插值计算涉及到16个像素点，其中(i’, j’)表示待计算像素点在源图像中的包含小数部分的像素坐标，dx表示X方向的小数坐标，dy表示Y方向的小数坐标。

具体可以看下图：根据上述图示与双立方插值的数学表达式可以看出，双立方插值本质上图像16个像素点权重卷积之和作为新的像素值。

其中R(x)表示插值表达式，可以根据需要选择的表达式不同。

常见有基于三角取值、Bell分布表达、B样条曲线表达式。

1. 基于三角形采样数学公式为最简单的线性分布，代码实现如下：[java] view plain copy private double triangleInterpolation( double f ) { f =f / 2.0; if( f < 0.0 ) { return ( f +1.0 ); } else { return ( 1.0 -f ); } } 2.基于Bell分布采样的数学公式如下：Bell分布采样数学公式基于三次卷积计算实现。

代码实现如下：[java] view plain copy private doublebellInterpolation( double x ) { double f = ( x / 2.0 ) * 1.5; if( f > -1.5 && f < -0.5 ){ return( 0.5 * Math.pow(f + 1.5, 2.0)); } else if( f > -0.5 && f < 0.5 ){ return 3.0 / 4.0 - ( f * f ); } else if( ( f > 0.5 && f < 1.5 ) ){ return( 0.5 * Math.pow(f - 1.5, 2.0)); } return 0.0; } 3.基于B样条曲线采样的数学公式如下：是一种基于多项式的四次卷积的采样计算，代码如下：[java] view plain copy private doublebspLineInterpolation( double f ) { if( f < 0.0 ){ f = -f; } if( f >= 0.0&& f <= 1.0 ) { return ( 2.0 / 3.0 ) + ( 0.5 ) * ( f* f * f ) - (f*f); } else if( f >1.0 && f <=2.0 ) { return 1.0 / 6.0 * Math.pow( ( 2.0 - f ),3.0 ); } return1.0; } 实现图像双立方插值的完整源代码如下：[java] view plain copy package com.gloomyfish.zoom.study; import java.awt.image.BufferedImage; importjava.awt.image.ColorModel; importcom.gloomyfish.filter.study.AbstractBufferedImageOp; public class BicubicInterpolationFilter extends AbstractBufferedImageOp { public final static int TRIANGLE__INTERPOLATION = 1; public final static int BELL__INTERPOLATION = 2; public final static int BSPLINE__INTERPOLATION = 4; publicfinal static int CATMULLROOM__INTERPOLATION = 8; public final static double B = 0.0; public final static double C = 0.5; // constant private int destH; // zoom height private int destW; // zoom width private int type; public BicubicInterpolationFilter(){ this.type =BSPLINE__INTERPOLATION; } public void setType(int type) { this.type = type; } public void setDestHeight(int destH) { this.destH = destH; } public void setDestWidth(int destW) { this.destW = destW; }private double bellInterpolation( double x ){ double f = ( x / 2.0 ) * 1.5; if( f >-1.5 && f < -0.5 ){ return( 0.5 * Math.pow(f + 1.5,2.0)); } else if( f > -0.5 &&f < 0.5 ) { return 3.0 / 4.0 - ( f * f ); } else if( ( f > 0.5 && f < 1.5 ) ) { return( 0.5 *Math.pow(f - 1.5, 2.0)); } return0.0; } private double bspLineInterpolation( double f ) { if( f <0.0 ) { f = -f; }if( f >= 0.0 && f <= 1.0 ){ return ( 2.0 / 3.0 ) + ( 0.5 ) * ( f* f * f ) -(f*f); } else if( f > 1.0 && f <= 2.0 ) { return 1.0 / 6.0 * Math.pow( ( 2.0 - f ), 3.0 ); } return 1.0; } private double triangleInterpolation( double f ) { f = f / 2.0; if( f < 0.0 ) { return ( f +1.0 ); } else{ return ( 1.0 - f ); } } private double CatMullRomInterpolation( double f ){ if( f < 0.0 ) { f = Math.abs(f); } if( f < 1.0 ){ return ( ( 12 - 9 * B - 6 * C ) * ( f * f * f ) + ( -18 + 12 * B + 6 *C ) * ( f * f ) + ( 6 - 2 * B ) ) / 6.0; } else if( f >= 1.0&& f < 2.0 ) { return ( ( -B - 6 * C ) * ( f * f * f ) + ( 6 * B + 30 * C ) * ( f *f ) + ( - ( 12 * B ) - 48 * C ) * f + 8 * B + 24 * C)/ 6.0; }else { return0.0; } } @Override public BufferedImage filter(BufferedImage src, BufferedImage dest) { int width = src.getWidth(); int height = src.getHeight(); if (dest == null)dest = createCompatibleDestImage(src, null);int[] inPixels = new int[width * height]; int[] outPixels = new int[destH * destW]; getRGB(src, 0, 0, width, height, inPixels); float rowRatio = ((float) height) / ((float) destH); float colRatio = ((float) width) / ((float) destW); int index = 0;for (int row = 0; row < destH; row++) { int ta = 0, tr = 0, tg = 0, tb = 0; double srcRow = ((float) row) * rowRatio; // 获取整数部分坐标row Index double j = Math.floor(srcRow); // 获取行的小数部分坐标double t = srcRow - j; for (int col = 0; col < destW; col++) { double srcCol = ((float) col) * colRatio; // 获取整数部分坐标column Index double k = Math.floor(srcCol);// 获取列的小数部分坐标double u = srcCol - k; double[] rgbData = new double[3]; double rgbCoffeData = 0.0;for(int m=-1; m<3; m++){ for(int n=-1; n<3; n++){ int[] rgb = getPixel(j+m, k+n, width, height, inPixels);double f1 = 0.0d; double f2 = 0.0d; if(type ==TRIANGLE__INTERPOLATION){ f1 = triangleInterpolation( ((double) m ) - t );f2 = triangleInterpolation ( -(( (double) n ) -u ) ); }else if(type == BELL__INTERPOLATION){ f1 = bellInterpolation( ((double) m ) - t );f2 = bellInterpolation ( -(( (double) n ) -u ) ); }else if(type == BSPLINE__INTERPOLATION){ f1 = bspLineInterpolation( ((double) m ) - t );f2 = bspLineInterpolation ( -(( (double) n ) -u ) ); }else{ f1 = CatMullRomInterpolation( ((double) m ) - t );f2 = CatMullRomInterpolation ( -(( (double) n ) -u ) );} // sum of weight rgbCoffeData += f2*f1; // sum of the RGB values rgbData[0] += rgb[0] * f2 * f1; rgbData[1] += rgb[1] * f2 * f1; rgbData[2] += rgb[2] * f2 *f1; } }ta = 255; // get Red/green/blue value for sample pixel tr = (int)(rgbData[0]/rgbCoffeData); tg = (int) (rgbData[1]/rgbCoffeData); tb = (int) (rgbData[2]/rgbCoffeData); index = row * destW + col; outPixels[index] = (ta<< 24) | (clamp(tr) << 16)| (clamp(tg) << 8) |clamp(tb); } }setRGB(dest, 0, 0, destW, destH, outPixels);return dest; } public int clamp(int value){ return value > 255 ? 255 :(value < 0 ? 0 : value); } private int[] getPixel(double j, double k, int width, int height,int[] inPixels) { int row = (int) j; int col = (int) k; if (row >= height){ row = height - 1; } if (row < 0) { row = 0; }if (col < 0) { col = 0; }if (col >= width) { col = width -1; } int index = row * width + col;int[] rgb = new int[3]; rgb[0] = (inPixels[index]>> 16) & 0xff; rgb[1] = (inPixels[index] >> 8) & 0xff; rgb[2] = inPixels[index] & 0xff; return rgb; } public BufferedImagecreateCompatibleDestImage( BufferedIma ge src, ColorModel dstCM) { if ( dstCM == null ) dstCM = src.getColorModel(); return new BufferedImage(dstCM,dstCM.createCompatibleWritableRaster(destW, destH), dstCM.isAlphaPremultiplied(), null); } } 运行效果：原图双立方插值放大以后：总结：基于这里三种方法实现的双立方插值以后图片跟原图像相比，都有一定模糊这里时候可以通过后续处理实现图像锐化与对比度提升即可得到Sharpen版本当然也可以通过寻找更加合适的R(x)函数来实现双立方卷积插值过程时保留图像边缘与对比度。