java - vector 卷积 - 计算相邻元素的索引

Question

我正在尝试实现一种采用两个 vector 的卷积方法:图像；和一个内核。我的问题是，当我将内核“滑动”到图像 vector 上时，我不知道如何计算图像相邻元素的索引。例如，对于两个相同的 vector {0, 1, 2, 3, 4, 5, 6, 7, 8} 我希望获得以下结果:

到目前为止我的代码如下:

public int[] convolve(int[] image, int[] kernel)
{       
  int imageValue; 
  int kernelValue;
  int outputValue;
  int[] outputImage = new int[image.length()];

  // loop through image
  for(int i = 0; i < image.length(); i++)
  {      
    outputValue = 0;

    // loop through kernel
    for(int j = 0; j < kernel.length(); j++)
    {
      neighbour = ?;

      // discard out of bound neighbours 
      if (neighbour >= 0 && neighbour < imageSize)
      {
        imageValue = image[neighbour];
        kernelValue = kernel[j];          
        outputValue += imageValue * kernelValue;
      }
    }

    output[i] = outputValue;
  }        

  return output;
}

Answer 1

由于 i + j - (kernel.length/2) 对于答案来说可能太短:

public class Convolution
{
    public static void main(String[] args)
    {
        int image[] = { 0,1,2,3,4,5,6,7,8 };
        int kernel[] = { 0,1,2,3,4,5,6,7,8 };

        int output[] = convolve(image, kernel);

        for (int i=0; i<image.length; i++)
        {
            System.out.printf(output[i]+" ");
        }
    }

    public static int[] convolve(int[] image, int[] kernel)
    {       
        int[] output = new int[image.length];

        // loop through image
        for(int i = 0; i < image.length; i++)
        {      
            System.out.println("Compute output["+i+"]");
            int outputValue = 0;

            // loop through kernel
            for(int j = 0; j < kernel.length; j++)
            {
                int neighbour = i + j - (kernel.length / 2);

                // discard out of bound neighbours 
                if (neighbour >= 0 && neighbour < image.length)
                {
                    int imageValue = image[neighbour];
                    int kernelValue = kernel[j];          
                    outputValue += imageValue * kernelValue;

                    System.out.println("image["+neighbour+"] and kernel["+j+"]");
                }
            }

            output[i] = outputValue;
        }        

        return output;
    }
}

请注意，只有当内核长度为奇数时，此方法才能正常工作。事实上，您所做的是将内核的中心移动到图像空间(这是kernel.length/2的来源)。对于偶数长度的内核，例如0 1 2 3，您必须决定是否要包含...

0 1 2 3 4 (image)
3                   <- This line and/or ...
2 3
1 2 3
0 1 2 3
  0 1 2 3
    0 1 2
      0 1 
        0           <- ... this line