Revisions to Replace interior of matrix with zeros

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If there are no zeros on the perimeter of the input matrix, you can do

x MorphologicalPerimeter[x]MorphologicalPerimeter[$MaxMachineNumber + x] // MatrixForm // TeXForm

$\left( \begin{array}{cccccccccc} 2 & 5 & 5 & 11 & 11 & 23 & 37 & 41 & 43 & 47 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 67 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 73 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 79 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 89 \\ 11 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 97 \\ 29 & 29 & 37 & 41 & 53 & 67 & 71 & 79 & 79 & 97 \\ \end{array} \right)$

In general, ifIf there may beare no zeros on the perimeter of the input matrix, you can use, for example MorphologicalPerimeter[$MaxMachineNumber + #]MorphologicalPerimeter[x] instead of MorphologicalPerimeter[#]MorphologicalPerimeter[$MaxMachineNumber + x] to get the desired result:.

# MorphologicalPerimeter[$MaxMachineNumber + #] &@RandomInteger[5, {5, 15}] // 
  MatrixForm // TeXForm

$\left(\begin{array}{ccccccccccccccc} 4 & 0 & 2 & 1 & 5 & 0 & 1 & 5 & 0 & 2 & 2 & 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 \\ 0 & 1 & 2 & 5 & 3 & 4 & 4 & 3 & 4 & 0 & 2 & 4 & 5 & 3 & 4 \\ \end{array}\right)$

##MorphologicalPerimeter

If there are no zeros on the perimeter of the input matrix, you can do

x MorphologicalPerimeter[x] // MatrixForm // TeXForm

$\left( \begin{array}{cccccccccc} 2 & 5 & 5 & 11 & 11 & 23 & 37 & 41 & 43 & 47 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 67 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 73 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 79 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 89 \\ 11 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 97 \\ 29 & 29 & 37 & 41 & 53 & 67 & 71 & 79 & 79 & 97 \\ \end{array} \right)$

In general, if there may be zeros on the perimeter, you can use, for example MorphologicalPerimeter[$MaxMachineNumber + #] instead of MorphologicalPerimeter[#] to get the desired result:

# MorphologicalPerimeter[$MaxMachineNumber + #] &@RandomInteger[5, {5, 15}] // 
  MatrixForm // TeXForm

$\left(\begin{array}{ccccccccccccccc} 4 & 0 & 2 & 1 & 5 & 0 & 1 & 5 & 0 & 2 & 2 & 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 \\ 0 & 1 & 2 & 5 & 3 & 4 & 4 & 3 & 4 & 0 & 2 & 4 & 5 & 3 & 4 \\ \end{array}\right)$

##MorphologicalPerimeter

x MorphologicalPerimeter[$MaxMachineNumber + x] // MatrixForm // TeXForm

$\left( \begin{array}{cccccccccc} 2 & 5 & 5 & 11 & 11 & 23 & 37 & 41 & 43 & 47 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 67 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 73 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 79 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 89 \\ 11 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 97 \\ 29 & 29 & 37 & 41 & 53 & 67 & 71 & 79 & 79 & 97 \\ \end{array} \right)$

If there are no zeros on the perimeter of the input matrix, you can use MorphologicalPerimeter[x] instead of MorphologicalPerimeter[$MaxMachineNumber + x].

# MorphologicalPerimeter[$MaxMachineNumber + #] &@RandomInteger[5, {5, 15}] // 
  MatrixForm // TeXForm

$\left(\begin{array}{ccccccccccccccc} 4 & 0 & 2 & 1 & 5 & 0 & 1 & 5 & 0 & 2 & 2 & 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 \\ 0 & 1 & 2 & 5 & 3 & 4 & 4 & 3 & 4 & 0 & 2 & 4 & 5 & 3 & 4 \\ \end{array}\right)$

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kglr

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##MorphologicalPerimeter

This works as is ifIf there are no zeros on the perimeter of the input matrix., you can do

x MorphologicalPerimeter[x] // MatrixForm // TeXForm

$\left( \begin{array}{cccccccccc} 2 & 5 & 5 & 11 & 11 & 23 & 37 & 41 & 43 & 47 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 67 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 73 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 79 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 89 \\ 11 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 97 \\ 29 & 29 & 37 & 41 & 53 & 67 & 71 & 79 & 79 & 97 \\ \end{array} \right)$

# MorphologicalPerimeter[#] & @ RandomInteger[{1, 9}, {5, 15}] // MatrixForm // TeXForm

$\left( \begin{array}{ccccccccccccccc} 7 & 7 & 3 & 8 & 7 & 6 & 2 & 8 & 4 & 1 & 2 & 1 & 2 & 6 & 5 \\ 4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 4 \\ 8 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 9 & 4 & 1 & 6 & 6 & 8 & 4 & 2 & 2 & 3 & 4 & 7 & 5 & 1 & 8 \\ \end{array} \right)$

In general, if there may be zeros on the perimeter, you can use, for example MorphologicalPerimeter[$MaxMachineNumber + #] instead of MorphologicalPerimeter[#] to get the desired result:

# MorphologicalPerimeter[$MaxMachineNumber + #] &@RandomInteger[5, {5, 15}] // 
  MatrixForm // TeXForm
> $\left(MorphologicalPerimeter[$MaxMachineNumber + #] &@RandomInteger[5, {5, 15}] // 
  MatrixForm // TeXForm

\begin{array}{ccccccccccccccc} 4 & 0 & 2 & 1 & 5 & 0 & 1 & 5 & 0 & 2 & 2 & 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 \\ 0 & 1 & 2 & 5 & 3 & 4 & 4 & 3 & 4 & 0 & 2 & 4 & 5 & 3 & 4 \\ \end{array} \right)$

$\left(\begin{array}{ccccccccccccccc} 4 & 0 & 2 & 1 & 5 & 0 & 1 & 5 & 0 & 2 & 2 & 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 \\ 0 & 1 & 2 & 5 & 3 & 4 & 4 & 3 & 4 & 0 & 2 & 4 & 5 & 3 & 4 \\ \end{array}\right)$

##MorphologicalPerimeter

This works as is if there are no zeros on the perimeter of the matrix.

x MorphologicalPerimeter[x] // MatrixForm // TeXForm

$\left( \begin{array}{cccccccccc} 2 & 5 & 5 & 11 & 11 & 23 & 37 & 41 & 43 & 47 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 67 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 73 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 79 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 89 \\ 11 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 97 \\ 29 & 29 & 37 & 41 & 53 & 67 & 71 & 79 & 79 & 97 \\ \end{array} \right)$

# MorphologicalPerimeter[#] & @ RandomInteger[{1, 9}, {5, 15}] // MatrixForm // TeXForm

$\left( \begin{array}{ccccccccccccccc} 7 & 7 & 3 & 8 & 7 & 6 & 2 & 8 & 4 & 1 & 2 & 1 & 2 & 6 & 5 \\ 4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 4 \\ 8 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 9 & 4 & 1 & 6 & 6 & 8 & 4 & 2 & 2 & 3 & 4 & 7 & 5 & 1 & 8 \\ \end{array} \right)$

In general, if there may be zeros on the perimeter, you can use, for example MorphologicalPerimeter[$MaxMachineNumber + #] instead of MorphologicalPerimeter[#] to get the desired result:

# MorphologicalPerimeter[$MaxMachineNumber + #] &@RandomInteger[5, {5, 15}] // 
  MatrixForm // TeXForm
> $\left(

\begin{array}{ccccccccccccccc} 4 & 0 & 2 & 1 & 5 & 0 & 1 & 5 & 0 & 2 & 2 & 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 \\ 0 & 1 & 2 & 5 & 3 & 4 & 4 & 3 & 4 & 0 & 2 & 4 & 5 & 3 & 4 \\ \end{array} \right)$

##MorphologicalPerimeter

If there are no zeros on the perimeter of the input matrix, you can do

x MorphologicalPerimeter[x] // MatrixForm // TeXForm

$\left( \begin{array}{cccccccccc} 2 & 5 & 5 & 11 & 11 & 23 & 37 & 41 & 43 & 47 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 67 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 73 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 79 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 89 \\ 11 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 97 \\ 29 & 29 & 37 & 41 & 53 & 67 & 71 & 79 & 79 & 97 \\ \end{array} \right)$

In general, if there may be zeros on the perimeter, you can use, for example MorphologicalPerimeter[$MaxMachineNumber + #] instead of MorphologicalPerimeter[#] to get the desired result:

# MorphologicalPerimeter[$MaxMachineNumber + #] &@RandomInteger[5, {5, 15}] // 
  MatrixForm // TeXForm

$\left(\begin{array}{ccccccccccccccc} 4 & 0 & 2 & 1 & 5 & 0 & 1 & 5 & 0 & 2 & 2 & 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 \\ 0 & 1 & 2 & 5 & 3 & 4 & 4 & 3 & 4 & 0 & 2 & 4 & 5 & 3 & 4 \\ \end{array}\right)$

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edited Jan 16, 2018 at 0:38

kglr

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##MorphologicalPerimeter

This works as is if there are no zeros on the perimeter of the matrix.

x MorphologicalPerimeter[x] // MatrixForm // TeXForm

$\left( \begin{array}{cccccccccc} 2 & 5 & 5 & 11 & 11 & 23 & 37 & 41 & 43 & 47 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 67 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 73 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 79 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 89 \\ 11 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 97 \\ 29 & 29 & 37 & 41 & 53 & 67 & 71 & 79 & 79 & 97 \\ \end{array} \right)$

# MorphologicalPerimeter[#] & @ RandomInteger[{1, 9}, {5, 15}] // MatrixForm // TeXForm

$\left( \begin{array}{ccccccccccccccc} 7 & 7 & 3 & 8 & 7 & 6 & 2 & 8 & 4 & 1 & 2 & 1 & 2 & 6 & 5 \\ 4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 4 \\ 8 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 9 & 4 & 1 & 6 & 6 & 8 & 4 & 2 & 2 & 3 & 4 & 7 & 5 & 1 & 8 \\ \end{array} \right)$

In general, if there may be zeros on the perimeter, you can use, for example MorphologicalPerimeter[$MaxMachineNumber + #] instead of MorphologicalPerimeter[#] to get the desired result:

# MorphologicalPerimeter[$MaxMachineNumber + #] &@RandomInteger[5, {5, 15}] // 
  MatrixForm // TeXForm
> $\left(

\begin{array}{ccccccccccccccc} 4 & 0 & 2 & 1 & 5 & 0 & 1 & 5 & 0 & 2 & 2 & 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 \\ 0 & 1 & 2 & 5 & 3 & 4 & 4 & 3 & 4 & 0 & 2 & 4 & 5 & 3 & 4 \\ \end{array} \right)$

##MorphologicalPerimeter

This works if there are no zeros on the perimeter of the matrix.

x MorphologicalPerimeter[x] // MatrixForm // TeXForm

$\left( \begin{array}{cccccccccc} 2 & 5 & 5 & 11 & 11 & 23 & 37 & 41 & 43 & 47 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 67 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 73 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 79 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 89 \\ 11 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 97 \\ 29 & 29 & 37 & 41 & 53 & 67 & 71 & 79 & 79 & 97 \\ \end{array} \right)$

# MorphologicalPerimeter[#] & @ RandomInteger[{1, 9}, {5, 15}] // MatrixForm // TeXForm

$\left( \begin{array}{ccccccccccccccc} 7 & 7 & 3 & 8 & 7 & 6 & 2 & 8 & 4 & 1 & 2 & 1 & 2 & 6 & 5 \\ 4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 4 \\ 8 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 9 & 4 & 1 & 6 & 6 & 8 & 4 & 2 & 2 & 3 & 4 & 7 & 5 & 1 & 8 \\ \end{array} \right)$

##MorphologicalPerimeter

This works as is if there are no zeros on the perimeter of the matrix.

x MorphologicalPerimeter[x] // MatrixForm // TeXForm

$\left( \begin{array}{cccccccccc} 2 & 5 & 5 & 11 & 11 & 23 & 37 & 41 & 43 & 47 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 67 \\ 2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 73 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 79 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 83 \\ 7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 89 \\ 11 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 97 \\ 29 & 29 & 37 & 41 & 53 & 67 & 71 & 79 & 79 & 97 \\ \end{array} \right)$

# MorphologicalPerimeter[#] & @ RandomInteger[{1, 9}, {5, 15}] // MatrixForm // TeXForm

$\left( \begin{array}{ccccccccccccccc} 7 & 7 & 3 & 8 & 7 & 6 & 2 & 8 & 4 & 1 & 2 & 1 & 2 & 6 & 5 \\ 4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 4 \\ 8 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 9 & 4 & 1 & 6 & 6 & 8 & 4 & 2 & 2 & 3 & 4 & 7 & 5 & 1 & 8 \\ \end{array} \right)$

In general, if there may be zeros on the perimeter, you can use, for example MorphologicalPerimeter[$MaxMachineNumber + #] instead of MorphologicalPerimeter[#] to get the desired result:

# MorphologicalPerimeter[$MaxMachineNumber + #] &@RandomInteger[5, {5, 15}] // 
  MatrixForm // TeXForm
> $\left(

\begin{array}{ccccccccccccccc} 4 & 0 & 2 & 1 & 5 & 0 & 1 & 5 & 0 & 2 & 2 & 0 & 0 & 0 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 5 \\ 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 \\ 0 & 1 & 2 & 5 & 3 & 4 & 4 & 3 & 4 & 0 & 2 & 4 & 5 & 3 & 4 \\ \end{array} \right)$

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