圖像處理之一階微分應用

一：數學背景

首先看一下一維的微分公式Δf = f(x+1) – f(x), 對于一幅二維的數字圖像f(x,y)而言，需要完

成XY兩個方向上的微分，所以有如下的公式：

分別對X,Y兩個方向上求出它們的偏微分，最終得到梯度Delta F.

對于離散的圖像來說,一階微分的數學表達相當于兩個相鄰像素的差值，根據選擇的梯度算

子不同，效果可能有所不同，但是基本原理不會變化。最常見的算子為Roberts算子，其它

常見還有Sobel，Prewitt等算子。以Roberts算子為例的X,Y的梯度計算演示如下圖：

二：圖像微分應用

圖像微分(梯度計算)是圖像邊緣提取的重要的中間步驟，根據X,Y方向的梯度向量值，可以

得到如下兩個重要參數振幅magnitude, 角度theta，計算公式如下：

Theta = tan^-1(yGradient/xGradient)

magnitude表示邊緣強度信息

theta預言邊緣的方向走勢。

假如對一幅數字圖像，求出magnitude之后與原來每個像素點對應值相加，則圖像邊緣將被

大大加強，輪廓更加明顯，是一個很典型的sharp filter的效果。

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三：程序效果

X, Y梯度效果，及magnitude效果

圖像微分的Sharp效果：

四：程序源代碼

package com.process.blur.study; import java.awt.image.BufferedImage; // roberts operator // X direction 1, 0 // 0,-1 // Y direction 0, 1 // -1, 0 public class ImageGradientFilter extends AbstractBufferedImageOp { public final static int X_DIRECTION = 0; public final static int Y_DIRECTION = 2; public final static int XY_DIRECTION = 4; private boolean sharp; private int direction; public ImageGradientFilter() { direction = XY_DIRECTION; // default; sharp = false; } public boolean isSharp() { return sharp; } public void setSharp(boolean sharp) { this.sharp = sharp; } public int getDirection() { return direction; } public void setDirection(int direction) { this.direction = direction; } @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; double mred, mgreen, mblue; int newX, newY; int index1, index2, index3; 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; // base on roberts operator newX = col + 1; newY = row + 1; if(newX > 0 && newX < width) { newX = col + 1; } else { newX = 0; } if(newY > 0 && newY < height) { newY = row + 1; } else { newY = 0; } index1 = newY * width + newX; index2 = row * width + newX; index3 = newY * width + col; ta = (inPixels[index] >> 24) & 0xff; tr = (inPixels[index] >> 16) & 0xff; tg = (inPixels[index] >> 8) & 0xff; tb = inPixels[index] & 0xff; int ta1 = (inPixels[index1] >> 24) & 0xff; int tr1 = (inPixels[index1] >> 16) & 0xff; int tg1 = (inPixels[index1] >> 8) & 0xff; int tb1 = inPixels[index1] & 0xff; int xgred = tr -tr1; int xggreen = tg - tg1; int xgblue = tb - tb1; int ta2 = (inPixels[index2] >> 24) & 0xff; int tr2 = (inPixels[index2] >> 16) & 0xff; int tg2 = (inPixels[index2] >> 8) & 0xff; int tb2 = inPixels[index2] & 0xff; int ta3 = (inPixels[index3] >> 24) & 0xff; int tr3 = (inPixels[index3] >> 16) & 0xff; int tg3 = (inPixels[index3] >> 8) & 0xff; int tb3 = inPixels[index3] & 0xff; int ygred = tr2 - tr3; int yggreen = tg2 - tg3; int ygblue = tb2 - tb3; mred = Math.sqrt(xgred * xgred + ygred * ygred); mgreen = Math.sqrt(xggreen * xggreen + yggreen * yggreen); mblue = Math.sqrt(xgblue * xgblue + ygblue * ygblue); if(sharp) { tr = (int)(tr + mred); tg = (int)(tg + mgreen); tb = (int)(tb + mblue); outPixels[index] = (ta << 24) | (clamp(tr) << 16) | (clamp(tg) << 8) | clamp(tb); } else { outPixels[index] = (ta << 24) | (clamp((int)mred) << 16) | (clamp((int)mgreen) << 8) | clamp((int)mblue); // outPixels[index] = (ta << 24) | (clamp((int)ygred) << 16) | (clamp((int)yggreen) << 8) | clamp((int)ygblue); // outPixels[index] = (ta << 24) | (clamp((int)xgred) << 16) | (clamp((int)xggreen) << 8) | clamp((int)xgblue); } } } setRGB(dest, 0, 0, width, height, outPixels ); return dest; } public static int clamp(int c) { if (c < 0) return 0; if (c > 255) return 255; return c; } } 轉載時請務必注明

轉載于:https://blog.51cto.com/gloomyfish/1400361

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