This is an algorithm used to thin a black and white i.e. one bit per pixel images.

For example, with an input image of:
<pre>
 #################                   #############
 ##################               ################
 ###################            ##################
 ########     #######          ###################
   ######     #######         #######       ######
   ######     #######        #######
   #################         #######
   ################          #######
   #################         #######
   ######     #######        #######
   ######     #######        #######
   ######     #######         #######       ######
 ########     #######          ###################
 ########     ####### ######    ################## ######
 ########     ####### ######      ################ ######
 ########     ####### ######         ############# ######
                                                           </pre>
It produces the thinned output:
<pre>

    # ##########                       #######
     ##        #                   ####       #
     #          #                 ##
     #          #                #
     #          #                #
     #          #                #
     ############               #
     #          #               #
     #          #                #
     #          #                #
     #          #                #
     #                            ##
     #                             ############
                       ###                          ###

                                                           </pre>

;Algorithm:
Assume black pixels are one and white pixels zero, and that the input image is a rectangular N by M array of ones and zeroes.

The algorithm operates on all black pixels P1 that can have eight neighbours.

The neighbours are, in order, arranged as:

<table border="4">
     <tr><td> &nbsp; P9 &nbsp; </td><td>     &nbsp; P2 &nbsp; </td><td>      &nbsp; P3 &nbsp; </td></tr>
     <tr><td> &nbsp; P8 &nbsp; </td><td><b>  &nbsp; P1 &nbsp; </b></td><td>  &nbsp; P4 &nbsp; </td></tr>
     <tr><td> &nbsp; P7 &nbsp; </td><td>     &nbsp; P6 &nbsp; </td><td>      &nbsp; P5 &nbsp; </td></tr>
</table>


Obviously the boundary pixels of the image cannot have the full eight neighbours.

* Define <math>A(P1)</math> = the number of transitions from white to black, (0 -> 1) in the sequence P2,P3,P4,P5,P6,P7,P8,P9,P2. (Note the extra P2 at the end - it is circular).
* Define <math>B(P1)</math> = The number of black pixel neighbours of P1. ( = sum(P2 .. P9) )


;Step 1:
All pixels are tested and pixels satisfying all the following conditions (simultaneously) are just noted at this stage.
* (0) The pixel is black and has eight neighbours
* (1) <math>2 <= B(P1) <= 6</math>
* (2) A(P1) = 1
* (3) At least one of P2 and P4 and P6 is white
* (4) At least one of P4 and P6 and P8 is white

After iterating over the image and collecting all the pixels satisfying all step 1 conditions, all these condition satisfying pixels are set to white.


;Step 2:
All pixels are again tested and pixels satisfying all the following conditions are just noted at this stage.
* (0) The pixel is black and has eight neighbours
* (1) <math>2 <= B(P1) <= 6</math>
* (2) A(P1) = 1
* (3) At least one of P2 and P4 and '''P8''' is white
* (4) At least one of '''P2''' and P6 and P8 is white

After iterating over the image and collecting all the pixels satisfying all step 2 conditions, all these condition satisfying pixels are again set to white.


;Iteration:
If any pixels were set in this round of either step 1 or step 2 then all steps are repeated until no image pixels are so changed.


;Task:
# Write a routine to perform Zhang-Suen thinning on an image matrix of ones and zeroes.
# Use the routine to thin the following image and show the output here on this page as either a matrix of ones and zeroes, an image, or an ASCII-art image of space/non-space characters.

           00000000000000000000000000000000
           01111111110000000111111110000000
           01110001111000001111001111000000
           01110000111000001110000111000000
           01110001111000001110000000000000
           01111111110000001110000000000000
           01110111100000001110000111000000
           01110011110011101111001111011100
           01110001111011100111111110011100
           00000000000000000000000000000000


;Reference:
* [http://nayefreza.wordpress.com/2013/05/11/zhang-suen-thinning-algorithm-java-implementation/ Zhang-Suen Thinning Algorithm, Java Implementation] by Nayef Reza.
* "Character Recognition Systems: A Guide for Students and Practitioners" By Mohamed Cheriet, Nawwaf Kharma, Cheng-Lin Liu, Ching Suen
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