图像处理之一阶微分应用
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; } }
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