图像处理之距离变换
概述
距离变换是二值图像处理与操作中常用手段，在骨架提取，图像窄化中常有应用。距离
变换的结果是得到一张与输入图像类似的灰度图像，但是灰度值只出现在前景区域。并
且越远离背景边缘的像素灰度值越大。
基本思想
根据度量距离的方法不同，距离变换有几种不同的方法，假设像素点p1(x1, y1),
p2(x2, y2)计算距离的方法常见的有：
1. 欧几里德距离，Distance = 
2. 曼哈顿距离(City Block Distance)，公式如下：Distance = |x2-x1|+|y2-y1|
3. 象棋格距离(Chessboard Distance)，公式如下：Distance = max(|x2-x1|,|y2-y1|)
一旦距离度量公式选择，就可以在二值图像的距离变换中使用。一个最常见的距离变换
算法就是通过连续的腐蚀操作来实现，腐蚀操作的停止条件是所有前景像素都被完全
腐蚀。这样根据腐蚀的先后顺序，我们就得到各个前景像素点到前景中心骨架像素点的
距离。根据各个像素点的距离值，设置为不同的灰度值。这样就完成了二值图像的距离变换。
注意点：
腐蚀操作结构体的选取会影响距离变换的效果，例子使用3*3的矩阵完成。有很多快速
的距离变换算法，感兴趣的可以自己研究。
运行结果：
关键代码解析：
初始化二值图像，读取像素，获取前景边缘像素与背景边缘像素
public DistanceTransform(float scaleValue, float offsetValue, BufferedImage src) { this.scaleValue = scaleValue; this.offsetValue = offsetValue; this.inputImage = src; this.width = src.getWidth(); this.height = src.getHeight(); int[] inPixels = new int[width*height]; getRGB( src, 0, 0, width, height, inPixels ); int index = 0; pixels2D = new int[height][width]; // row, column greyLevel = new int[height][width]; for(int row=0; row < height; row++) { for(int col=0; col<width; col++) { index = row * width + col; int grayValue = (inPixels[index] >> 16) & 0xff; pixels2D[row][col] = grayValue; greyLevel[row][col] = 0; } } generateForegroundEdge(); generateBackgroundEdgeFromForegroundEdge(); }
现实距离变换的代码如下：
@Override public BufferedImage filter(BufferedImage src, BufferedImage dest) { // calculate the distance here!! int index = 1; while (foregroundEdgePixels.size() > 0) { distanceSingleIteration(index); ++index; } // loop the each pixel and assign the color value according to distance value for (int row = 0; row < inputImage.getHeight(); row++) { for (int col = 0; col < inputImage.getWidth(); col++) { if(greyLevel[row][col] > 0) { int colorValue = (int)Math.round(greyLevel[row][col] * scaleValue + offsetValue); colorValue = colorValue > 255 ? 255 : ((colorValue < 0) ? 0 : colorValue); this.pixels2D[row][col] = colorValue; } } } // build the result pixel data at here !!! if ( dest == null ) dest = createCompatibleDestImage(inputImage, null ); index = 0; int[] outPixels = new int[width*height]; for(int row=0; row<height; row++) { int ta = 0, tr = 0, tg = 0, tb = 0; for(int col=0; col<width; col++) { if(row == 75 && col > 60) { System.out.println("ddddd"); } index = row * width + col; tr = tg = tb = this.pixels2D[row][col]; ta = 255; outPixels[index] = (ta << 24) | (tr << 16) | (tg << 8) | tb; } } setRGB( dest, 0, 0, width, height, outPixels ); return dest; }
生成前景边缘像素与背景边缘像素的代码如下：
private void generateForegroundEdge() { foregroundEdgePixels.clear(); for (int row = 0; row < height; row++) for (int col = 0; col < width; col++) if (this.pixels2D[row][col] == foreground) { Point localPoint = new Point(col, row); for (int k = -1; k < 2; ++k) // 3*3 matrix for (int l = -1; l < 2; ++l) { if ((localPoint.x + l < 0) || (localPoint.x + l >= this.width) || (localPoint.y + k < 0) || (localPoint.y + k >= this.height) || (this.pixels2D[(localPoint.y + k)][(localPoint.x + l)] != background) || (this.foregroundEdgePixels.contains(localPoint))) continue; this.foregroundEdgePixels.add(localPoint); } } } private void generateBackgroundEdgeFromForegroundEdge() { this.backgroundEdgePixels.clear(); Iterator<Point> localIterator = this.foregroundEdgePixels.iterator(); while (localIterator.hasNext()) { Point localPoint1 = new Point((Point)localIterator.next()); for (int i = -1; i < 2; ++i) for (int j = -1; j < 2; ++j) if ((localPoint1.x + j >= 0) && (localPoint1.x + j < this.width) && (localPoint1.y + i >= 0) && (localPoint1.y + i < this.height)) { Point localPoint2 = new Point(localPoint1.x + j, localPoint1.y + i); if (this.pixels2D[localPoint2.y][localPoint2.x] == background) this.backgroundEdgePixels.add(localPoint2); } } }
