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:

                                                           
 #################                   #############         
 ##################               ################         
 ###################            ##################         
 ########     #######          ###################         
   ######     #######         #######       ######         
   ######     #######        #######                       
   #################         #######                       
   ################          #######                       
   #################         #######                       
   ######     #######        #######                       
   ######     #######        #######                       
   ######     #######         #######       ######         
 ########     #######          ###################         
 ########     ####### ######    ################## ######  
 ########     ####### ######      ################ ######  
 ########     ####### ######         ############# ######  
                                                           
It produces the thinned output:

                                                           
                                                           
    # ##########                       #######             
     ##        #                   ####       #            
     #          #                 ##                       
     #          #                #                         
     #          #                #                         
     #          #                #                         
     ############               #                          
     #          #               #                          
     #          #                #                         
     #          #                #                         
     #          #                #                         
     #                            ##                       
     #                             ############            
                       ###                          ###    
                                                           
                                                           
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:


   P9      P2      P3   
   P8      P1      P4   
   P7      P6      P5   



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

 Define 



A
(
P
1
)


{\displaystyle A(P1)}

 = 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 



B
(
P
1
)


{\displaystyle B(P1)}

 = 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) 



2
<=
B
(
P
1
)
<=
6


{\displaystyle 2<=B(P1)<=6}


 (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) 



2
<=
B
(
P
1
)
<=
6


{\displaystyle 2<=B(P1)<=6}


 (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

 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


Public n As Variant
Private Sub init()
    n = [{-1,0;-1,1;0,1;1,1;1,0;1,-1;0,-1;-1,-1;-1,0}]
End Sub
 
Private Function AB(text As Variant, y As Integer, x As Integer, step As Integer) As Variant
    Dim wtb As Integer
    Dim bn As Integer
    Dim prev As String: prev = "#"
    Dim next_ As String
    Dim p2468 As String
    For i = 1 To UBound(n)
        next_ = Mid(text(y + n(i, 1)), x + n(i, 2), 1)
        wtb = wtb - (prev = "." And next_ <= "#")
        bn = bn - (i > 1 And next_ <= "#")
        If (i And 1) = 0 Then p2468 = p2468 & prev
        prev = next_
    Next i
    If step = 2 Then '-- make it p6842
        p2468 = Mid(p2468, 3, 2) & Mid(p2468, 1, 2)
        'p2468 = p2468(3..4)&p2468(1..2)
    End If
    Dim ret(2) As Variant
    ret(0) = wtb
    ret(1) = bn
    ret(2) = p2468
    AB = ret
End Function
 
Private Sub Zhang_Suen(text As Variant)
    Dim wtb As Integer
    Dim bn As Integer
    Dim changed As Boolean, changes As Boolean
    Dim p2468 As String     '-- (p6842 for step 2)
    Dim x As Integer, y As Integer, step As Integer
    Do While True
        changed = False
        For step = 1 To 2
            changes = False
            For y = 1 To UBound(text) - 1
                For x = 2 To Len(text(y)) - 1
                    If Mid(text(y), x, 1) = "#" Then
                        ret = AB(text, y, x, step)
                        wtb = ret(0)
                        bn = ret(1)
                        p2468 = ret(2)
                        If wtb = 1 _
                            And bn >= 2 And bn <= 6 _
                            And InStr(1, Mid(p2468, 1, 3), ".") _
                            And InStr(1, Mid(p2468, 2, 3), ".") Then
                            changes = True
                            text(y) = Left(text(y), x - 1) & "!" & Right(text(y), Len(text(y)) - x)
                        End If
                    End If
                Next x
            Next y
            If changes Then
                For y = 1 To UBound(text) - 1
                    text(y) = Replace(text(y), "!", ".")
                Next y
                changed = True
            End If
        Next step
        If Not changed Then Exit Do
    Loop
    Debug.Print Join(text, vbCrLf)
End Sub
 
Public Sub main()
    init
    Dim Small_rc(9) As String
    Small_rc(0) = "................................"
    Small_rc(1) = ".#########.......########......."
    Small_rc(2) = ".###...####.....####..####......"
    Small_rc(3) = ".###....###.....###....###......"
    Small_rc(4) = ".###...####.....###............."
    Small_rc(5) = ".#########......###............."
    Small_rc(6) = ".###.####.......###....###......"
    Small_rc(7) = ".###..####..###.####..####.###.."
    Small_rc(8) = ".###...####.###..########..###.."
    Small_rc(9) = "................................"
    Zhang_Suen (Small_rc)
End Sub