一：数学背景
首先看一下一维的微分公式Δf = f(x+1) – f(x), 对于一幅二维的数字图像f(x,y)而言，需要完
成XY两个方向上的微分，所以有如下的公式：
分别对X,Y两个方向上求出它们的偏微分，最终得到梯度Delta F.
对于离散的图像来说,一阶微分的数学表达相当于两个相邻像素的差值，根据选择的梯度算
子不同，效果可能有所不同，但是基本原理不会变化。最常见的算子为Roberts算子，其它
常见还有Sobel，Prewitt等算子。以Roberts算子为例的X,Y的梯度计算演示如下图：
二：图像微分应用
图像微分(梯度计算)是图像边缘提取的重要的中间步骤，根据X,Y方向的梯度向量值，可以
得到如下两个重要参数振幅magnitude, 角度theta，计算公式如下：
Theta = tan-1(yGradient/xGradient)
magnitude表示边缘强度信息
theta预言边缘的方向走势。
假如对一幅数字图像，求出magnitude之后与原来每个像素点对应值相加，则图像边缘将被
大大加强，轮廓更加明显，是一个很典型的sharp filter的效果。
三：程序效果
X, Y梯度效果，及magnitude效果
图像微分的Sharp效果：
四：程序源代码 package com.process.blur.study;
import java.awt.image.BufferedImage;
// roberts operator
// X direction 1, 0
// 0,-1
// Y direction 0, 1
// -1, 0
public class ImageGradientFilter extends AbstractBufferedImageOp {
public final static int X_DIRECTION = 0;
public final static int Y_DIRECTION = 2;
public final static int XY_DIRECTION = 4;
private boolean sharp;
private int direction;
public ImageGradientFilter() {
direction = XY_DIRECTION; // default;
sharp = false;
}
public boolean isSharp() {
return sharp;
}
public void setSharp(boolean sharp) {
this.sharp = sharp;
}
public int getDirection() {
return direction;
}
public void setDirection(int direction) {
this.direction = direction;
}
@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[width*height];
getRGB( src, 0, 0, width, height, inPixels );
int index = 0;
double mred, mgreen, mblue;
int newX, newY;
int index1, index2, index3;
for(int row=0; row<height; row++) {
int ta = 0, tr = 0, tg = 0, tb = 0;
for(int col=0; col<width; col++) {
index = row * width + col;
// base on roberts operator
newX = col + 1;
newY = row + 1;
if(newX > 0 && newX < width) {
newX = col + 1;
} else {
newX = 0;
}
if(newY > 0 && newY < height) {
newY = row + 1;
} else {
newY = 0;
}
index1 = newY * width + newX;
index2 = row * width + newX;
index3 = newY * width + col;
ta = (inPixels[index] >> 24) & 0xff;
tr = (inPixels[index] >> 16) & 0xff;
tg = (inPixels[index] >> 8) & 0xff;
tb = inPixels[index] & 0xff;
int ta1 = (inPixels[index1] >> 24) & 0xff;
int tr1 = (inPixels[index1] >> 16) & 0xff;
int tg1 = (inPixels[index1] >> 8) & 0xff;
int tb1 = inPixels[index1] & 0xff;
int xgred = tr -tr1;
int xggreen = tg - tg1;
int xgblue = tb - tb1;
int ta2 = (inPixels[index2] >> 24) & 0xff;
int tr2 = (inPixels[index2] >> 16) & 0xff;
int tg2 = (inPixels[index2] >> 8) & 0xff;
int tb2 = inPixels[index2] & 0xff;
int ta3 = (inPixels[index3] >> 24) & 0xff;
int tr3 = (inPixels[index3] >> 16) & 0xff;
int tg3 = (inPixels[index3] >> 8) & 0xff;
int tb3 = inPixels[index3] & 0xff;
int ygred = tr2 - tr3;
int yggreen = tg2 - tg3;
int ygblue = tb2 - tb3;
mred = Math.sqrt(xgred * xgred + ygred * ygred);
mgreen = Math.sqrt(xggreen * xggreen + yggreen * yggreen);
mblue = Math.sqrt(xgblue * xgblue + ygblue * ygblue);
if(sharp) {
tr = (int)(tr + mred);
tg = (int)(tg + mgreen);
tb = (int)(tb + mblue);
outPixels[index] = (ta << 24) | (clamp(tr) << 16) | (clamp(tg) << 8) | clamp(tb);
} else {
outPixels[index] = (ta << 24) | (clamp((int)mred) << 16) | (clamp((int)mgreen) << 8) | clamp((int)mblue);
// outPixels[index] = (ta << 24) | (clamp((int)ygred) << 16) | (clamp((int)yggreen) << 8) | clamp((int)ygblue);
// outPixels[index] = (ta << 24) | (clamp((int)xgred) << 16) | (clamp((int)xggreen) << 8) | clamp((int)xgblue);
}
}
}
setRGB(dest, 0, 0, width, height, outPixels );
return dest;
}
public static int clamp(int c) {
if (c < 0)
return 0;
if (c > 255)
return 255;
return c;
}
}
http://blog.csdn.net/jia20003/article/details/7562092 | 
