Appendix A

The algorithm of four-neighborhood mask for the edge-detection can be explained using the following C++ codes.
int source-image[M][N];
/* a binary image before the edge-detection with a size of M$\times$N. In this image, if the gray level of a point in the binary image is 0, it is meant that the point locates in the background. On the contrary, if the gray level of a point is 1, the point locates in the foreground. */
int object-image[M-1][N-1];
/* the binary image after source-image[M][N] is processed by the edge-detection.*/
int p; //any detected point
int n,s,w,e;
//four neighborhood points of the detected point p
int i,j;//loop variables
for(i=1;i<M-1;i++)
    for(j=1;j<N-1;j++)
         {
         p=source-image[i][j];
         if(p==0)
         object-image[i][j]=0;
         else{
                  n=source-image[i-1][j];
                  s=source-image[i+1][j];
                  w=source-image[i][j-1];
                  e=source-image[i][j+1];
                  int temp=n+s+w+e;
                  if(temp==4)
                           object-image[i][j]=0;
                  else
                           object-image[i][j]=1;
/*if temp equals 4, the point p and its four neighborhood points are all in the foreground (i.e., the interior of the detected-edge). Therefore, only the exact edge points will be detected. */
                  }
          }
// end of the algorithm

Acknowledgements

We would like to thank the referee-Dr Dourneau G. for his valuable comments to improve the scientific quality of the paper. We are grateful to Prof Shen K.X. for giving us helpful suggests and doing some modifications on the original manuscript. We are also grateful to Dr Jacobson J.B. for his kind help for us to obtain correctly the newest ephemeride JUP204. It is a pleasure to thank Dr Vienne A., Dr Emelianov N.V. and Prof Zhang C.Z. for giving us helpful suggestions. This work was carried out with financial support partly from the National Natural Science Foundation of China (No 10273015), and partly from the College of Information Science and Technology, Jinan University.