圖像處理之高斯金字塔

一：圖像金字塔基本操做

對一張圖像不斷的模糊以後向下採樣，獲得不一樣分辨率的圖像，同時每次獲得的

新的圖像寬與高是原來圖像的1/2, 最多見就是基於高斯的模糊以後採樣，獲得的

一系列圖像稱爲高斯金字塔。

高斯金字塔不一樣(DoG)又稱爲拉普拉斯金字塔，其計算公式以下：

L(i) = G(i) – expand(G(i+1))

第i層拉普拉斯金字塔是由第i層高斯金字塔減去第i+1層高斯金字塔expand以後獲得。

本文獲得的DoG(Difference of Gaussian)結果以下：

二：關鍵代碼解析

金字塔reduce操做實現代碼以下：

	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實現代碼以下：

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; }

圖像金字塔的reduce與expand過程都是卷積採樣實現。特別注意的是 expand

操做不是reduce的可逆操做。

關於什麼是卷積，高斯濾波請參見博客上的其它相關文章。

高斯金字塔所有算法源代碼以下：

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; 	}  } 

特別注意：我沒有處理像素的寬與高，若是寬與高不是偶數可能

會有問題，使用時請本身處理吧。

UI實現源代碼以下：

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 - 選擇偶數行與列 			// 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 		} 		 	}    } 

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