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图像处理之高斯金字塔

2024-06-07 15
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简介： 图像处理之高斯金字塔

一：图像金字塔基本操作

对一张图像不断的模糊之后向下采样，得到不同分辨率的图像，同时每次得到的

新的图像宽与高是原来图像的1/2, 最常见就是基于高斯的模糊之后采样，得到的

一系列图像称为高斯金字塔。


高斯金字塔不同(DoG)又称为拉普拉斯金字塔，其计算公式如下：

L(i) = G(i) – expand(G(i+1))

第i层拉普拉斯金字塔是由第i层高斯金字塔减去第i+1层高斯金字塔expand之后得到。

本文得到的DoG(Difference of Gaussian)结果如下：

二：关键代码解析

金字塔reduce操作实现代码如下：

  private BufferedImage pyramidReduce(BufferedImage src) {
    int width = src.getWidth();
        int height = src.getHeight();
        BufferedImage dest = createSubCompatibleDestImage(src, null);
        int[] inPixels = new int[width*height];
        int ow = width/2;
        int oh = height/2;
        int[] outPixels = new int[ow*oh];
        getRGB(src, 0, 0, width, height, inPixels );
        int inRow=0, inCol = 0, index = 0, oudex =0, ta = 0;
        float[][] keneralData = this.getHVGaussianKeneral();
        for(int row=0; row<oh; row++) {
          for(int col=0; col<ow; col++) {
            inRow = 2* row;
            inCol = 2* col;
            if(inRow >= height) {
              inRow = 0;
            }
            if(inCol >= width) {
              inCol = 0;
            }
            float sumRed = 0, sumGreen = 0, sumBlue = 0;
            for(int subRow = -2; subRow <= 2; subRow++) {
              int inRowOff = inRow + subRow;
              if(inRowOff >= height || inRowOff < 0) {
                inRowOff = 0;
              }
              for(int subCol = -2; subCol <= 2; subCol++) {
                int inColOff = inCol + subCol;
                if(inColOff >= width || inColOff < 0) {
                  inColOff = 0;
                }
                index = inRowOff * width + inColOff;
                ta = (inPixels[index] >> 24) & 0xff;
                int red = (inPixels[index] >> 16) & 0xff;
                int green = (inPixels[index] >> 8) & 0xff;
                int blue = inPixels[index] & 0xff;
                sumRed += keneralData[subRow + 2][subCol + 2] * red;
                sumGreen += keneralData[subRow + 2][subCol + 2] * green;
                sumBlue += keneralData[subRow + 2][subCol + 2] * blue;
              }
            }
            
            oudex = row * ow + col;
            outPixels[oudex] = (ta << 24) | (clamp(sumRed) << 16) | (clamp(sumGreen) << 8) | clamp(sumBlue);
          }
        }
        setRGB( dest, 0, 0, ow, oh, outPixels );
        return dest;
  }

金字塔expand实现代码如下：

public BufferedImage pyramidExpand(BufferedImage src) {
  int width = src.getWidth();
  int height = src.getHeight();
  int[] inPixels = new int[width*height];
  getRGB(src, 0, 0, width, height, inPixels );
  int ow = 2*width;
  int oh =2*height;
  int[] outPixels = new int[ow * oh];
  int index = 0, outdex = 0, ta = 0;
  float[][] keneralData = this.getHVGaussianKeneral();
  BufferedImage dest = createTwiceCompatibleDestImage(src, null);
  for(int row=0; row<oh; row++) {
    for(int col=0; col<ow; col++) {
        float sumRed = 0, sumGreen = 0, sumBlue = 0;
        for(int subRow = -2; subRow <= 2; subRow++) {
          double srcRow = (row + subRow)/2.0;
          double j = Math.floor(srcRow);
          double t = srcRow - j; 
          if(t > 0) {
            continue;
          }
          if(srcRow >= height || srcRow < 0) {
            srcRow = 0;
          }
          for(int subCol = -2; subCol <= 2; subCol++) {
            double srcColOff = (col + subCol)/2.0;
            j = Math.floor(srcColOff);
            t = srcColOff - j;
            if(t > 0) {
              continue;
            }
            if(srcColOff >= width || srcColOff < 0) {
              srcColOff = 0;
            }
            index = (int)(srcRow * width + srcColOff);
            ta = (inPixels[index] >> 24) & 0xff;
            int red = (inPixels[index] >> 16) & 0xff;
            int green = (inPixels[index] >> 8) & 0xff;
            int blue = inPixels[index] & 0xff;
            sumRed += keneralData[subRow + 2][subCol + 2] * red;
            sumGreen += keneralData[subRow + 2][subCol + 2] * green;
            sumBlue += keneralData[subRow + 2][subCol + 2] * blue;
          }
        }
      outdex = row * ow + col;
        outPixels[outdex] = (ta << 24) | (clamp(4.0f * sumRed) << 16) | (clamp(4.0f * sumGreen) << 8) | clamp(4.0f * sumBlue);
        // outPixels[outdex] = (ta << 24) | (clamp(sumRed) << 16) | (clamp(sumGreen) << 8) | clamp(sumBlue);
    }
  }
  setRGB( dest, 0, 0, ow, oh, outPixels );
  return dest;
}


图像金字塔的reduce与expand过程都是卷积采样实现。特别注意的是 expand

操作不是reduce的可逆操作。

关于什么是卷积，高斯滤波请参见博客上的其它相关文章。

高斯金字塔全部算法源代码如下：

package com.gloomyfish.image.pyramid;
 
import java.awt.image.BufferedImage;
import java.awt.image.ColorModel;
 
public class PyramidAlgorithm extends GaussianFilter {
  private float a;
 
  public PyramidAlgorithm() {
    a = 0.4f;
  }
  
  public void setParameter(float p) {
    this.a = p;
  }
 
  public BufferedImage[] pyramidDown(BufferedImage src, int level) {
    BufferedImage[] imagePyramids = new BufferedImage[level + 1];
    imagePyramids[0] = src;
    for(int i=1; i<imagePyramids.length; i++) {
      imagePyramids[i] = pyramidReduce(imagePyramids[i-1]);
    }
    return imagePyramids;
  }
  
  public BufferedImage[] pyramidUp(BufferedImage[] srcImage) {
    BufferedImage[] imagePyramids = new BufferedImage[srcImage.length];
    for(int i=0; i<srcImage.length; i++) {
      imagePyramids[i] = pyramidExpand(srcImage[i]);
    }
    return imagePyramids;
  }
  
  /***
   * l1 = g1 - expand(g2)
   * l2 = g2 - expand(g3)
   * l0 = g0 - expand(g1)
   * @param reduceImages
   * @param expandImages
   * @return
   */
  public BufferedImage[] getLaplacianPyramid(BufferedImage[] reduceImages) {
    BufferedImage[] laplaciImages = new BufferedImage[reduceImages.length -1];
    for(int i=1; i<reduceImages.length; i++) {
      BufferedImage expandImage = pyramidExpand(reduceImages[i]);
      laplaciImages[i-1] = createCompatibleDestImage(expandImage, null);
      int width = reduceImages[i-1].getWidth();
          int height = reduceImages[i-1].getHeight();
          
          int ewidth = expandImage.getWidth();
          width = (width > ewidth) ? ewidth : width;
          height = (height > expandImage.getHeight()) ? expandImage.getHeight():height;
          System.out.println(" width = " + width + " expand width = " + ewidth);
          
          int[] reducePixels = new int[width*height];
          int[] expandPixels = new int[width*height];
          int[] laPixels = new int[width*height];
          getRGB( reduceImages[i-1], 0, 0, width, height, reducePixels);
          getRGB( expandImage, 0, 0, width, height, expandPixels );
          int index = 0;
          int er = 0, eg = 0, eb = 0;
          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;
              ta = (reducePixels[index] >> 24) & 0xff;
                  tr = (reducePixels[index] >> 16) & 0xff;
                  tg = (reducePixels[index] >> 8) & 0xff;
                  tb = reducePixels[index] & 0xff;
                  
              ta = (expandPixels[index] >> 24) & 0xff;
                  er = (expandPixels[index] >> 16) & 0xff;
                  eg = (expandPixels[index] >> 8) & 0xff;
                  eb = expandPixels[index] & 0xff;
                  
                  tr = tr - er;
                  tg = tg - eg;
                  tb = tb - eb;
                  
                  laPixels[index] = (ta << 24) | (clamp(tr) << 16) | (clamp(tg) << 8) | clamp(tb);
            }
          }
          setRGB( laplaciImages[i-1], 0, 0, width, height, laPixels );
    }
 
        return laplaciImages;
  }
  
  private BufferedImage pyramidReduce(BufferedImage src) {
    int width = src.getWidth();
        int height = src.getHeight();
        BufferedImage dest = createSubCompatibleDestImage(src, null);
        int[] inPixels = new int[width*height];
        int ow = width/2;
        int oh = height/2;
        int[] outPixels = new int[ow*oh];
        getRGB(src, 0, 0, width, height, inPixels );
        int inRow=0, inCol = 0, index = 0, oudex =0, ta = 0;
        float[][] keneralData = this.getHVGaussianKeneral();
        for(int row=0; row<oh; row++) {
          for(int col=0; col<ow; col++) {
            inRow = 2* row;
            inCol = 2* col;
            if(inRow >= height) {
              inRow = 0;
            }
            if(inCol >= width) {
              inCol = 0;
            }
            float sumRed = 0, sumGreen = 0, sumBlue = 0;
            for(int subRow = -2; subRow <= 2; subRow++) {
              int inRowOff = inRow + subRow;
              if(inRowOff >= height || inRowOff < 0) {
                inRowOff = 0;
              }
              for(int subCol = -2; subCol <= 2; subCol++) {
                int inColOff = inCol + subCol;
                if(inColOff >= width || inColOff < 0) {
                  inColOff = 0;
                }
                index = inRowOff * width + inColOff;
                ta = (inPixels[index] >> 24) & 0xff;
                int red = (inPixels[index] >> 16) & 0xff;
                int green = (inPixels[index] >> 8) & 0xff;
                int blue = inPixels[index] & 0xff;
                sumRed += keneralData[subRow + 2][subCol + 2] * red;
                sumGreen += keneralData[subRow + 2][subCol + 2] * green;
                sumBlue += keneralData[subRow + 2][subCol + 2] * blue;
              }
            }
            
            oudex = row * ow + col;
            outPixels[oudex] = (ta << 24) | (clamp(sumRed) << 16) | (clamp(sumGreen) << 8) | clamp(sumBlue);
          }
        }
        setRGB( dest, 0, 0, ow, oh, outPixels );
        return dest;
  }
  
    public BufferedImage createSubCompatibleDestImage(BufferedImage src, ColorModel dstCM) {
        if ( dstCM == null )
            dstCM = src.getColorModel();
        return new BufferedImage(dstCM, dstCM.createCompatibleWritableRaster(src.getWidth()/2, src.getHeight()/2), dstCM.isAlphaPremultiplied(), null);
    }
    
    public BufferedImage createTwiceCompatibleDestImage(BufferedImage src, ColorModel dstCM) {
        if ( dstCM == null )
            dstCM = src.getColorModel();
        return new BufferedImage(dstCM, dstCM.createCompatibleWritableRaster(src.getWidth()*2, src.getHeight()*2), dstCM.isAlphaPremultiplied(), null);
    }
  
  public BufferedImage pyramidExpand(BufferedImage src) {
    int width = src.getWidth();
    int height = src.getHeight();
    int[] inPixels = new int[width*height];
    getRGB(src, 0, 0, width, height, inPixels );
    int ow = 2*width;
    int oh =2*height;
    int[] outPixels = new int[ow * oh];
    int index = 0, outdex = 0, ta = 0;
    float[][] keneralData = this.getHVGaussianKeneral();
    BufferedImage dest = createTwiceCompatibleDestImage(src, null);
    for(int row=0; row<oh; row++) {
      for(int col=0; col<ow; col++) {
          float sumRed = 0, sumGreen = 0, sumBlue = 0;
          for(int subRow = -2; subRow <= 2; subRow++) {
            double srcRow = (row + subRow)/2.0;
            double j = Math.floor(srcRow);
            double t = srcRow - j; 
            if(t > 0) {
              continue;
            }
            if(srcRow >= height || srcRow < 0) {
              srcRow = 0;
            }
            for(int subCol = -2; subCol <= 2; subCol++) {
              double srcColOff = (col + subCol)/2.0;
              j = Math.floor(srcColOff);
              t = srcColOff - j;
              if(t > 0) {
                continue;
              }
              if(srcColOff >= width || srcColOff < 0) {
                srcColOff = 0;
              }
              index = (int)(srcRow * width + srcColOff);
              ta = (inPixels[index] >> 24) & 0xff;
              int red = (inPixels[index] >> 16) & 0xff;
              int green = (inPixels[index] >> 8) & 0xff;
              int blue = inPixels[index] & 0xff;
              sumRed += keneralData[subRow + 2][subCol + 2] * red;
              sumGreen += keneralData[subRow + 2][subCol + 2] * green;
              sumBlue += keneralData[subRow + 2][subCol + 2] * blue;
            }
          }
        outdex = row * ow + col;
          outPixels[outdex] = (ta << 24) | (clamp(4.0f * sumRed) << 16) | (clamp(4.0f * sumGreen) << 8) | clamp(4.0f * sumBlue);
          // outPixels[outdex] = (ta << 24) | (clamp(sumRed) << 16) | (clamp(sumGreen) << 8) | clamp(sumBlue);
      }
    }
    setRGB( dest, 0, 0, ow, oh, outPixels );
    return dest;
  }
 
}

特别注意：我没有处理像素的宽与高，如果宽与高不是偶数可能

会有问题，使用时请自己处理吧。

UI实现源代码如下：

package com.gloomyfish.image.pyramid;
 
import java.awt.BorderLayout;
import java.awt.Dimension;
import java.awt.FlowLayout;
import java.awt.Graphics;
import java.awt.MediaTracker;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
 
import javax.imageio.ImageIO;
import javax.swing.JButton;
import javax.swing.JComponent;
import javax.swing.JFileChooser;
import javax.swing.JFrame;
import javax.swing.JPanel;
 
public class PyramidDemoUI extends JComponent implements ActionListener {
 
  /**
   * 
   */
  private static final long serialVersionUID = 1L;
  private JButton upButton;
  private JButton downButton;
  private BufferedImage[] reduceImages;
  private BufferedImage[] expandImages;
  private BufferedImage sourceImage;
  private Dimension mySize;
  private MediaTracker tracker;
  
  public PyramidDemoUI(File f)
  {
    initComponents(f);
  }
 
  private void initComponents(File f)
  {
    // TODO Auto-generated method stub
    try {  
      sourceImage = ImageIO.read(f);  
        } catch (IOException e1) {  
            e1.printStackTrace();  
        }  
          
        tracker = new MediaTracker(this);  
        tracker.addImage(sourceImage, 1);  
          
        // blocked 10 seconds to load the image data  
        try {  
            if (!tracker.waitForID(1, 10000)) {  
                System.out.println("Load error.");  
                System.exit(1);  
            }// end if  
        } catch (InterruptedException e) {  
            e.printStackTrace();  
            System.exit(1);  
        }// end catch  
        
        JPanel btnPanel = new JPanel();
        btnPanel.setLayout(new FlowLayout(FlowLayout.RIGHT));
        upButton = new JButton("Laplacian Pyramid");
        downButton = new JButton("Pyramid Down");
        upButton.addActionListener(this);
        downButton.addActionListener(this);
        btnPanel.add(upButton);
        btnPanel.add(downButton);
        mySize = new Dimension(800, 800);   
        JFrame mainFrame = new JFrame("Pyramid Demo - Gloomyfish");
        mainFrame.getContentPane().setLayout(new BorderLayout());
        mainFrame.getContentPane().add(this, BorderLayout.CENTER);
        mainFrame.getContentPane().add(btnPanel, BorderLayout.SOUTH);
        mainFrame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);  
        mainFrame.pack();  
        mainFrame.setVisible(true);  
  }
 
  @Override
  public Dimension getPreferredSize() {
    return mySize;
  }
 
  @Override
  protected void paintComponent(Graphics g) 
  {
//    g.drawImage(sourceImage, 10, 10, sourceImage.getWidth(), sourceImage.getHeight(), null);
    int width = 10;
//    if(reduceImages != null) {
//      for(int i=1; i<reduceImages.length; i++) {
//        width += (10 + reduceImages[i-1].getWidth());
//        g.drawImage(reduceImages[i], width, 10, reduceImages[i].getWidth(), reduceImages[i].getHeight(), null);
//      }
//    }
    
    width = 10;
    if(expandImages != null) {
      for(int i=0; i<expandImages.length; i++) {
        g.drawImage(expandImages[i], width, 15, expandImages[i].getWidth(), expandImages[i].getHeight(), null);
        // g.drawImage(expandImages[i], width, 15 + sourceImage.getHeight(), expandImages[i].getWidth(), expandImages[i].getHeight(), null);
        width += (10 + expandImages[i].getWidth());
      }
    }
    super.paintComponent(g);
  }
  
    public static void main(String[] args) {  
        JFileChooser chooser = new JFileChooser();  
        chooser.showOpenDialog(null);  
        File f = chooser.getSelectedFile();  
        new PyramidDemoUI(f);  
    }
 
  @Override
  public void actionPerformed(ActionEvent event) {
    if(event.getActionCommand().equals("Laplacian Pyramid")) {
      if(reduceImages != null) {
        // int size = reduceImages.length;
        PyramidAlgorithm pyramid = new PyramidAlgorithm();
        expandImages = pyramid.getLaplacianPyramid(reduceImages);
        // expandImages = pyramid.pyramidUp(reduceImages);
        repaint();
      } else {
        
      }
 
    } else if(event.getActionCommand().equals("Pyramid Down")) {
      // a.Smooth the image with Gaussian filter 5×5(1/4-a/2, 1/4, a, 1/4, 1/4-a/2) a = [0.3,0.6]
      // b.Sub sample the image by half - 选择偶数行与列
      // c.If reached desired size stop, else send the result to step 1
      PyramidAlgorithm pyramid = new PyramidAlgorithm();
      reduceImages = pyramid.pyramidDown(sourceImage, 3);
      repaint();
    } else {
      // do nothing
    }
    
  }  
 
}

转载请务必注明出处-GloomyFish

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