algorithm - 双边过滤器

Question

给定高斯滤波器，如何实现双边滤波器？

Answer 1

一个简单的双边滤波器可以定义为

Inew (x,y) = 求和(j=yn/2; j<=y+n/2)求和(i=xm/2; j<=x+m/2)w(i,j,x,y )I(i,j)

其中常见的低通滤波器，例如高斯滤波器，具有基于内核中心 (x,y) 到每个像素 (i,j) 的距离的权重 w(i,j,x,y)。对于双边滤波器，权重基于两个距离确定：图像空间距离和颜色空间距离。

下面是一个简单的 C 实现

void convolution(uchar4 *_in, uchar4 *_out, int width, int height, int ~ halfkernelsize, float id, float cd)
{ 
  int kernelDim = 2*halfkernelsize+1;

  for(int y=0; y

  float sumWeight = 0;

  unsigned int ctrIdx = y*width + x;

  float ctrPix[3];
  ctrPix[0] = _in[ctrIdx].x;
  ctrPix[1] = _in[ctrIdx].y;
  ctrPix[2] = _in[ctrIdx].z;

  // neighborhood of current pixel
  int kernelStartX, kernelEndX, kernelStartY, kernelEndY;
  kernelStartX = x-halfkernelsize;
  kernelEndX   = x+halfkernelsize;
  kernelStartY = y-halfkernelsize;
  kernelEndY   = y+halfkernelsize; 

  for(int j= kernelStartY; j<= kernelEndY; j++)
    {       
      for(int i= kernelStartX; i<= kernelEndX; i++)
    {                       
      unsigned int idx = max(0, min(j, height-1))*width + max(0, min(i,width-1));

      float curPix[3];
      curPix[0] = _in[idx].x;
      curPix[1] = _in[idx].y;
      curPix[2] = _in[idx].z;


      float currWeight;

      // define bilateral filter kernel weights
      float imageDist = sqrt( (float)((i-x)*(i-x) + (j-y)*(j-y)) );

      float colorDist = sqrt( (float)( (curPix[0] - ctrPix[0])*(curPix[0] - ctrPix[0]) +
                       (curPix[1] - ctrPix[1])*(curPix[1] - ctrPix[1]) +
                       (curPix[2] - ctrPix[2])*(curPix[2] - ctrPix[2]) ) );

      currWeight = 1.0f/(exp((imageDist/id)*(imageDist/id)*0.5)*exp((colorDist/cd)*(colorDist/cd)*0.5));
      sumWeight += currWeight;

      _sum[0] += currWeight*curPix[0]; 
      _sum[1] += currWeight*curPix[1];
      _sum[2] += currWeight*curPix[2];
    }  
    }

  _sum[0] /= sumWeight;
  _sum[1] /= sumWeight;
  _sum[2] /= sumWeight;

  _out[ctrIdx].x = (int)(floor(_sum[0]));
  _out[ctrIdx].y = (int)(floor(_sum[1]));
  _out[ctrIdx].z = (int)(floor(_sum[2]));
  _out[ctrIdx].w = _in[ctrIdx].w;
}
}

}