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图像增强之拉普拉斯锐化---高斯一阶导二阶导数

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图像处理之高斯一阶及二阶导数计算

 

图像的一阶与二阶导数计算在图像特征提取与边缘提取中十分重要。一阶与二阶导数的

作用,通常情况下:

一阶导数可以反应出图像灰度梯度的变化情况

二阶导数可以提取出图像的细节同时双响应图像梯度变化情况

常见的算子有Robot, Sobel算子,二阶常见多数为拉普拉斯算子,如图所示:

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对于一个1D的有限集合数据f(x) = {1…N}, 假设dx的间隔为1则一阶导数计算公式如下:

Df(x) = f(x+1) – f(x-1) 二阶导数的计算公式为:df(x)= f(x+1) + f(x-1) – 2f(x);

稍微难一点的则是基于高斯的一阶导数与二阶导数求取,首先看一下高斯的1D与2D的

公式。一维高斯对应的X阶导数公式:

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二维高斯对应的导数公式:

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二:算法实现

1.      高斯采样,基于间隔1计算,计算mask窗口计算,这样就跟普通的卷积计算差不多

2.      设置sigma的值,本例默认为10,首先计算高斯窗口函数,默认为3 * 3

3.      根据2的结果,计算高斯导数窗口值

4.      卷积计算像素中心点值。

注意点:计算高斯函数一定要以零为中心点, 如果窗口函数大小为3,则表达为-1, 0, 1

三:程序实现关键点

1.      归一化处理,由于高斯计算出来的窗口值非常的小,必须实现归一化处理。

2.      亮度提升,对X,Y的梯度计算结果进行了亮度提升,目的是让大家看得更清楚。

3.      支持一阶与二阶单一方向X,Y偏导数计算

四:运行效果:

高斯一阶导数X方向效果

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高斯一阶导数Y方向效果

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五:算法全部源代码:

[java] view plaincopy
 
    1. /*
      * @author: gloomyfish
      * @date: 2013-11-17
      *
      * Title - Gaussian fist order derivative and second derivative filter
      */
      package com.gloomyfish.image.harris.corner;
      import java.awt.image.BufferedImage;

      import com.gloomyfish.filter.study.AbstractBufferedImageOp;

      public class GaussianDerivativeFilter extends AbstractBufferedImageOp {

      public final static int X_DIRECTION = 0;
      public final static int Y_DIRECTION = 16;
      public final static int XY_DIRECTION = 2;
      public final static int XX_DIRECTION = 4;
      public final static int YY_DIRECTION = 8;

      // private attribute and settings
      private int DIRECTION_TYPE = 0;
      private int GAUSSIAN_WIN_SIZE = 1; // N*2 + 1
      private double sigma = 10; // default

      public GaussianDerivativeFilter()
      {
      System.out.println("高斯一阶及多阶导数滤镜");
      }

      public int getGaussianWinSize() {
      return GAUSSIAN_WIN_SIZE;
      }

      public void setGaussianWinSize(int gAUSSIAN_WIN_SIZE) {
      GAUSSIAN_WIN_SIZE = gAUSSIAN_WIN_SIZE;
      }
      public int getDirectionType() {
      return DIRECTION_TYPE;
      }

      public void setDirectionType(int dIRECTION_TYPE) {
      DIRECTION_TYPE = dIRECTION_TYPE;
      }

      @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, index2 = 0;
      double xred = 0, xgreen = 0, xblue = 0;
      // double yred = 0, ygreen = 0, yblue = 0;
      int newRow, newCol;
      double[][] winDeviationData = getDirectionData();

      for(int row=0; row<height; row++) {
      int ta = 255, tr = 0, tg = 0, tb = 0;
      for(int col=0; col<width; col++) {
      index = row * width + col;
      for(int subrow = -GAUSSIAN_WIN_SIZE; subrow <= GAUSSIAN_WIN_SIZE; subrow++) {
      for(int subcol = -GAUSSIAN_WIN_SIZE; subcol <= GAUSSIAN_WIN_SIZE; subcol++) {
      newRow = row + subrow;
      newCol = col + subcol;
      if(newRow < 0 || newRow >= height) {
      newRow = row;
      }
      if(newCol < 0 || newCol >= width) {
      newCol = col;
      }
      index2 = newRow * width + newCol;
      tr = (inPixels[index2] >> 16) & 0xff;
      tg = (inPixels[index2] >> 8) & 0xff;
      tb = inPixels[index2] & 0xff;
      xred += (winDeviationData[subrow + GAUSSIAN_WIN_SIZE][subcol + GAUSSIAN_WIN_SIZE] * tr);
      xgreen +=(winDeviationData[subrow + GAUSSIAN_WIN_SIZE][subcol + GAUSSIAN_WIN_SIZE] * tg);
      xblue +=(winDeviationData[subrow + GAUSSIAN_WIN_SIZE][subcol + GAUSSIAN_WIN_SIZE] * tb);
      }
      }

      outPixels[index] = (ta << 24) | (clamp((int)xred) << 16) | (clamp((int)xgreen) << 8) | clamp((int)xblue);

      // clean up values for next pixel
      newRow = newCol = 0;
      xred = xgreen = xblue = 0;
      // yred = ygreen = yblue = 0;
      }
      }

      setRGB( dest, 0, 0, width, height, outPixels );
      return dest;
      }

      private double[][] getDirectionData()
      {
      double[][] winDeviationData = null;
      if(DIRECTION_TYPE == X_DIRECTION)
      {
      winDeviationData = this.getXDirectionDeviation();
      }
      else if(DIRECTION_TYPE == Y_DIRECTION)
      {
      winDeviationData = this.getYDirectionDeviation();
      }
      else if(DIRECTION_TYPE == XY_DIRECTION)
      {
      winDeviationData = this.getXYDirectionDeviation();
      }
      else if(DIRECTION_TYPE == XX_DIRECTION)
      {
      winDeviationData = this.getXXDirectionDeviation();
      }
      else if(DIRECTION_TYPE == YY_DIRECTION)
      {
      winDeviationData = this.getYYDirectionDeviation();
      }
      return winDeviationData;
      }

      public int clamp(int value) {
      // trick, just improve the lightness otherwise image is too darker...
      if(DIRECTION_TYPE == X_DIRECTION || DIRECTION_TYPE == Y_DIRECTION)
      {
      value = value * 10 + 50;
      }
      return value < 0 ? 0 : (value > 255 ? 255 : value);
      }

      // centered on zero and with Gaussian standard deviation
      // parameter : sigma
      public double[][] get2DGaussianData()
      {
      int size = GAUSSIAN_WIN_SIZE * 2 + 1;
      double[][] winData = new double[size][size];
      double sigma2 = this.sigma * sigma;
      for(int i=-GAUSSIAN_WIN_SIZE; i<=GAUSSIAN_WIN_SIZE; i++)
      {
      for(int j=-GAUSSIAN_WIN_SIZE; j<=GAUSSIAN_WIN_SIZE; j++)
      {
      double r = i*1 + j*j;
      double sum = -(r/(2*sigma2));
      winData[i + GAUSSIAN_WIN_SIZE][j + GAUSSIAN_WIN_SIZE] = Math.exp(sum);
      }
      }
      return winData;
      }

      public double[][] getXDirectionDeviation()
      {
      int size = GAUSSIAN_WIN_SIZE * 2 + 1;
      double[][] data = get2DGaussianData();
      double[][] xDeviation = new double[size][size];
      double sigma2 = this.sigma * sigma;
      for(int x=-GAUSSIAN_WIN_SIZE; x<=GAUSSIAN_WIN_SIZE; x++)
      {
      double c = -(x/sigma2);
      for(int i=0; i<size; i++)
      {
      xDeviation[i][x + GAUSSIAN_WIN_SIZE] = c * data[i][x + GAUSSIAN_WIN_SIZE];
      }
      }
      return xDeviation;
      }

      public double[][] getYDirectionDeviation()
      {
      int size = GAUSSIAN_WIN_SIZE * 2 + 1;
      double[][] data = get2DGaussianData();
      double[][] yDeviation = new double[size][size];
      double sigma2 = this.sigma * sigma;
      for(int y=-GAUSSIAN_WIN_SIZE; y<=GAUSSIAN_WIN_SIZE; y++)
      {
      double c = -(y/sigma2);
      for(int i=0; i<size; i++)
      {
      yDeviation[y + GAUSSIAN_WIN_SIZE][i] = c * data[y + GAUSSIAN_WIN_SIZE][i];
      }
      }
      return yDeviation;
      }

      /***
      *
      * @return
      */
      public double[][] getXYDirectionDeviation()
      {
      int size = GAUSSIAN_WIN_SIZE * 2 + 1;
      double[][] data = get2DGaussianData();
      double[][] xyDeviation = new double[size][size];
      double sigma2 = sigma * sigma;
      double sigma4 = sigma2 * sigma2;
      // TODO:zhigang
      for(int x=-GAUSSIAN_WIN_SIZE; x<=GAUSSIAN_WIN_SIZE; x++)
      {
      for(int y=-GAUSSIAN_WIN_SIZE; y<=GAUSSIAN_WIN_SIZE; y++)
      {
      double c = -((x*y)/sigma4);
      xyDeviation[x + GAUSSIAN_WIN_SIZE][y + GAUSSIAN_WIN_SIZE] = c * data[x + GAUSSIAN_WIN_SIZE][y + GAUSSIAN_WIN_SIZE];
      }
      }
      return normalizeData(xyDeviation);
      }

      private double[][] normalizeData(double[][] data)
      {
      // normalization the data
      double min = data[0][0];
      for(int x=-GAUSSIAN_WIN_SIZE; x<=GAUSSIAN_WIN_SIZE; x++)
      {
      for(int y=-GAUSSIAN_WIN_SIZE; y<=GAUSSIAN_WIN_SIZE; y++)
      {
      if(min > data[x + GAUSSIAN_WIN_SIZE][y + GAUSSIAN_WIN_SIZE])
      {
      min = data[x + GAUSSIAN_WIN_SIZE][y + GAUSSIAN_WIN_SIZE];
      }
      }
      }

      for(int x=-GAUSSIAN_WIN_SIZE; x<=GAUSSIAN_WIN_SIZE; x++)
      {
      for(int y=-GAUSSIAN_WIN_SIZE; y<=GAUSSIAN_WIN_SIZE; y++)
      {
      data[x + GAUSSIAN_WIN_SIZE][y + GAUSSIAN_WIN_SIZE] = data[x + GAUSSIAN_WIN_SIZE][y + GAUSSIAN_WIN_SIZE] /min;
      }
      }

      return data;
      }

      public double[][] getXXDirectionDeviation()
      {
      int size = GAUSSIAN_WIN_SIZE * 2 + 1;
      double[][] data = get2DGaussianData();
      double[][] xxDeviation = new double[size][size];
      double sigma2 = this.sigma * sigma;
      double sigma4 = sigma2 * sigma2;
      for(int x=-GAUSSIAN_WIN_SIZE; x<=GAUSSIAN_WIN_SIZE; x++)
      {
      double c = -((x - sigma2)/sigma4);
      for(int i=0; i<size; i++)
      {
      xxDeviation[i][x + GAUSSIAN_WIN_SIZE] = c * data[i][x + GAUSSIAN_WIN_SIZE];
      }
      }
      return xxDeviation;
      }

      public double[][] getYYDirectionDeviation()
      {
      int size = GAUSSIAN_WIN_SIZE * 2 + 1;
      double[][] data = get2DGaussianData();
      double[][] yyDeviation = new double[size][size];
      double sigma2 = this.sigma * sigma;
      double sigma4 = sigma2 * sigma2;
      for(int y=-GAUSSIAN_WIN_SIZE; y<=GAUSSIAN_WIN_SIZE; y++)
      {
      double c = -((y - sigma2)/sigma4);
      for(int i=0; i<size; i++)
      {
      yyDeviation[y + GAUSSIAN_WIN_SIZE][i] = c * data[y + GAUSSIAN_WIN_SIZE][i];
      }
      }
      return yyDeviation;
      }

      }

    2. http://blog.csdn.net/jia20003/article/details/16369143

图像增强之拉普拉斯锐化---高斯一阶导二阶导数

标签:des   blog   http   io   ar   java   sp   for   strong   

原文地址:http://www.cnblogs.com/pengkunfan/p/4089113.html

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