数学原理:
首先看两张图片,大小均为256 * 256个像素, 第一张是纯蓝色
图一:
第二张是加有随机噪声的蓝色
图二:
产生随机噪声的算法简单的不能再简单了
假设RGB的R与G颜色分量均为零, 则 Blue = 255 * Math.Random() 随机数的取值范围在
[0, 1]之间, 程序的核心代码如下:
for(int row=0; row<256; row++) {
for(int col=0; col<256; col++) {
b = (int)(255.0d * Math.random());
rgbData[index]= ((clamp(a) & 0xff) << 24) |
((clamp(r)& 0xff) << 16) |
((clamp(g)& 0xff) << 8) |
((clamp(b)& 0xff));
index++;
}
}
上面显然不是我想要的结果,我想要的是下面两种:
图三:
图四:
对的,只要我们对上面的算法稍加改进,就可以实现这样漂亮的噪声效果
实现第二张图效果的算法缺点在于,它每次都产生一个新的随机数,假设[0,1] = 255,接着第
二点随机可以能为[0, 2] = 0 第三个点可能随机值为[0, 3] = 125, 毫无规律可言,而我希望是
假设第一点随机[0, 1] = 255则间隔N个点以后再产生下个随机颜色值[0,N+1] =125, 在下一
个点则为[0, 2N +1] = 209…..于是问题产生了, 我们怎么计算[1, N]的之间的每个像素点的值
哇,这个问题不正是关于图像放缩的插值问题嘛,一个最简单的选择是双线性插值算法,
算法解释参考这里:http://blog.csdn.net/jia20003/article/details/6915185
有了算法选择,下面的问题就是我们怎么计算点值的问题,面临两个选择,一个值照搬双线
性插值中的计算方法,但是有点不自然,我们想要的是噪声,显然线性的计算结果不是最好
的最好的选择,cos(x)如何,在[0, PI]内是递减,在[PI,2PI]内是递增,而且值的范围在[-1, 1]
之间,而我们的随机数值要在[0, 1]之间于是综合上述考虑我们有cos(PI + (x-x0/x1-x0)* PI) + 1, 现
在计算出来的值是[0, 1]区间之内 根据插值公式最终有:
y= (y1-y0) * cos(PI + (x-x0/x1-x0) * PI) + 1 + y0
其中[x, y]代表要计算的点,周围四个采样点为:[x-N, y-N], [x+N,y-N], [x-N, y+N], [x+N, y+N ]
运用双线性插值原理即可计算出[1, N]个每个像素点的值。
关键代码实现及解释:
获取四个采样点,及其值,然后使用类似双线性算法计算出[x,y]的随机数值进而计算出像素值
的程序代码如下:
[java] view plaincopy
- // bi-line interpolation algorithm here!!!
- Double GetColor(int x, int y, int M, int colorType)
- {
- int x0 = x - (x % M);
- int x1 = x0 + M;
- int y0 = y - (y % M);
- int y1 = y0 + M;
- Double x0y0 = Noise(x0,y0, colorType);
- Double x1y0 = Noise(x1,y0, colorType);
- Double x0y1 = Noise(x0,y1, colorType);
- Double x1y1 = Noise(x1,y1, colorType);
- Double xx0 =Interpolate(x0, x0y0, x1, x1y0, x);
- Double xx1 = Interpolate(x0,x0y1, x1, x1y1, x);
- Double N =Interpolate(y0, xx0, y1, xx1, y);
- return N;
- }
根据两个点计算插入值的公式代码如下:
[java] view plaincopy
- return (1.0 + Math.cos(Math.PI + (Math.PI / (x1-x0)) * (x-x0))) / 2.0
- * (xx1-xx0) + xx0;
对一张图像实现随机噪声值得出像素值计算的代码如下:
[java] view plaincopy
- for(int row=0; row<256; row++) {
- for(int col=0; col<256; col++) {
- // set random color value for each pixel
- r = (int)(255.0d * GetColor(row, col, intervalPixels, 1));
- g = (int)(255.0d * GetColor(row, col, intervalPixels, 2));
- b = (int)(255.0d * GetColor(row, col, intervalPixels, 4));
- rgbData[index] = ((clamp(a) & 0xff) << 24) |
- ((clamp(r) & 0xff) << 16) |
- ((clamp(g) & 0xff) << 8) |
- ((clamp(b) & 0xff));
- index++;
- }
- }
完全源代码如下:
[java] view plaincopy
- import java.awt.BorderLayout;
- import java.awt.Dimension;
- import java.awt.Graphics;
- import java.awt.Graphics2D;
- import java.awt.RenderingHints;
- import java.awt.image.BufferedImage;
- import java.util.Random;
- import javax.swing.JComponent;
- import javax.swing.JFrame;
- public class RandomNoiseImage extends JComponent {
- /**
- *
- */
- private static final long serialVersionUID = -2236160343614397287L;
- private BufferedImage image = null;
- private double[] blue_random;
- private double[] red_random;
- private double[] green_random;
- private int intervalPixels = 40; // default
- public RandomNoiseImage() {
- super();
- this.setOpaque(false);
- }
- protected void paintComponent(Graphics g) {
- Graphics2D g2 = (Graphics2D)g;
- g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
- g2.drawImage(getImage(), 5, 5, image.getWidth(), image.getHeight(), null);
- }
- private BufferedImage getImage() {
- if(image == null) {
- image = new BufferedImage(256, 256, BufferedImage.TYPE_INT_ARGB);
- int[] rgbData = new int[256*256];
- generateNoiseImage(rgbData);
- setRGB(image, 0, 0, 256, 256, rgbData);
- }
- return image;
- }
- private void generateNoiseImage(int[] rgbData) {
- int index = 0;
- int a = 255;
- int r = 0;
- int g = 0;
- int b = 0;
- int sum = 256 * 256;
- blue_random = new double[sum];
- red_random = new double[sum];
- green_random = new double[sum];
- Random random = new Random();
- for(int i=0; i< sum; i++) {
- blue_random[i] = random.nextDouble();
- red_random[i] = random.nextDouble();
- green_random[i] = random.nextDouble();
- }
- for(int row=0; row<256; row++) {
- for(int col=0; col<256; col++) {
- // set random color value for each pixel
- r = (int)(255.0d * GetColor(row, col, intervalPixels, 1));
- g = (int)(255.0d * GetColor(row, col, intervalPixels, 2));
- b = (int)(255.0d * GetColor(row, col, intervalPixels, 4));
- rgbData[index] = ((clamp(a) & 0xff) << 24) |
- ((clamp(r) & 0xff) << 16) |
- ((clamp(g) & 0xff) << 8) |
- ((clamp(b) & 0xff));
- index++;
- }
- }
- }
- private int clamp(int rgb) {
- if(rgb > 255)
- return 255;
- if(rgb < 0)
- return 0;
- return rgb;
- }
- // bi-line interpolation algorithm here!!!
- Double GetColor(int x, int y, int M, int colorType)
- {
- int x0 = x - (x % M);
- int x1 = x0 + M;
- int y0 = y - (y % M);
- int y1 = y0 + M;
- Double x0y0 = Noise(x0, y0, colorType);
- Double x1y0 = Noise(x1, y0, colorType);
- Double x0y1 = Noise(x0, y1, colorType);
- Double x1y1 = Noise(x1, y1, colorType);
- Double xx0 = Interpolate(x0, x0y0, x1, x1y0, x);
- Double xx1 = Interpolate(x0, x0y1, x1, x1y1, x);
- Double N = Interpolate(y0, xx0, y1, xx1, y);
- return N;
- }
- // algorithm selection here !!!
- private Double Interpolate(double x0, double xx0, double x1, double xx1, double x) {
- return (1.0 + Math.cos(Math.PI +
- (Math.PI / (x1-x0)) * (x-x0))) / 2.0 * (xx1-xx0) + xx0;
- }
- Double Noise(int x, int y, int colorType)
- {
- if(colorType == 1) {
- if (x < 256 && y < 256)
- return red_random[y * 256 + x];
- else
- return 0.0;
- } else if(colorType == 2) {
- if (x < 256 && y < 256)
- return green_random[y * 256 + x];
- else
- return 0.0;
- } else {
- if (x < 256 && y < 256)
- return blue_random[y * 256 + x];
- else
- return 0.0;
- }
- }
- public void setRGB( BufferedImage image, int x, int y, int width, int height, int[] pixels ) {
- int type = image.getType();
- if ( type == BufferedImage.TYPE_INT_ARGB || type == BufferedImage.TYPE_INT_RGB )
- image.getRaster().setDataElements( x, y, width, height, pixels );
- else
- image.setRGB( x, y, width, height, pixels, 0, width );
- }
- public static void main(String[] args) {
- JFrame frame = new JFrame("Noise Art Panel");
- frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
- frame.getContentPane().setLayout(new BorderLayout());
- // Display the window.
- frame.getContentPane().add(new RandomNoiseImage(), BorderLayout.CENTER);
- frame.setPreferredSize(new Dimension(280,305));
- frame.pack();
- frame.setVisible(true);
- }
- }