Lexicographic Ordering

This topic was covered in Section 7.4 of the first edition of the Dudgeon & Mersereau but it is not available in the Chapter 2 handout. See Fig. 3.

Figure 3: Lexiographic ordering

• Consider an $N \times N$ image, $x(n_1, n_2)$
• Now create an $N^2$-point 1-D sequence by concatenating the columns of $x$. See Fig. 4

  Figure 4: 1-D Sequence

  

  
  

  $$g(Nn_1 + n_2) = x(n_1, n_2)$$
  
  
  
  
  $$n_1 = \mbox{Column Index} \;\;\; n_2 = \mbox{Row Index}$$