Figure 11-12 illustrates unsharp masking using the 1/4 [+1,+2,+1] filter kernel as the first step’s smoothing mask.

  14 |------------------------------------------------------------ | 14
  13 |------------------------------------------------------------ | 13
  12 |------------------------------------------------------------ | 12
  11 | ----------------------------------------------------------- | 11
  10 |----------*---------------*-*---*----------------*---------- | 10
   9 |--------*-*------*--*-----*-*---*-*---*-*---*----*-*-------- | 9
   8 |--------***------****-----***---***---***---*----***-------- | 8
   7 |-------****----*-****-----***---***---***---*----****------- | 7
   6 |------*****----*******----***---***---********---*****------ | 6
   5 |-----******--*-*******----***---***---********---******----- | 5
   4 |----*******--**********---***---***-*-*********--*******---- | 4
   3 |---********--**********---***---***************--********--- | 3
   2 |--*********-*************-***-*-****************-*********-- | 2
   1 |-***********************************************-**********- | 1
   0
+-------------------------------------------------------------------------+
0
Input:012345678882244668888642228882228884448886668642088876543210

========+=+-=+=+=+==+====-+=+-=-+=+-=-+=+===+===-+=+========

Figure 11-12: Unsharp masking 1/4 [+1,+2,+1] output array

Finally, since each unsharp masking step references the input sequence, it is possible to perform the complete process as a single step. The logic follows:

Figure 11-13 illustrates the single step process’s identical result using the 1/4 [+1,+2,+1] filter kernel as the first step’s smoothing mask.

  14 |------------------------------------------------------------ | 14
  13 |------------------------------------------------------------ | 13
  12 |------------------------------------------------------------ | 12
  11 |------------------------------------------------------------ | 11
  10 |----------*---------------*-*---*----------------*---------- | 10
   9 |--------*-*------*--*-----*-*---*-*---*-*---*----*-*-------- | 9
   8 |--------***------****-----***---***---***---*----***-------- | 8
   7 |-------****----*-****-----***---***---***---*----****------- | 7
   6 |------*****----*******----***---***---********---*****------ | 6
   5 |-----******--*-*******----***---***---********---******----- | 5
   4 |----*******--**********---***---***-*-*********--*******---- | 4
   3 |---********--**********---***---***************--********--- | 3
   2 |--*********-*************-***-*-****************-*********-- | 2
   1 |-***********************************************-**********- | 1
   0
+-------------------------------------------------------------------------+
0
Input:012345678882244668888642228882228884448886668642088876543210

========+=+-=+=+=+==+====-+=+-=-+=+-=-+=+===+===-+=+========

Figure 11-13: Direct unsharp masking 1/4 [+1,+2,+1] output array

Summary

This chapter covered smoothing, sharpening, and unsharp masking. These three processes are fundamental digital image processing techniques that de-emphasize or accentuate numeric differences. As the next chapter shows, digital images are simply two-dimensional number collections. Digital image processing applies smoothing, sharpening, and unsharp masking techniques to these number collections using two-dimensional masks which, in degenerate cases, are one-dimensional masks similar to the ones this chapter uses.

With two-dimensional images:

• Smoothing blurs visual detail
• Sharpening accentuates visual detail selectively in one direction
• Unsharp masking accentuates visual detail by indulging the human visual system’s natural retinal sharpening process by providing transition exaggerations in all directions.

The MATH.C program in Appendix C provides a means to further study these operations on values that range from zero to 14.