matlabconvex-polygon

expand a polygon region in a matrix

I have the following matrix:

1 1 1 1 1 1 1 1 
1 1 1 1 1 1 1 1
1 1 2 2 2 1 1 3
1 1 2 2 2 2 1 3
1 1 1 1 2 1 1 3
1 1 1 1 1 1 1 1

I want to expand the region of value 2 by size 1, which means after expansion, the output is:

1 1 2 2 2 1 1 1 
1 2 2 2 2 2 1 1
2 2 2 2 2 2 2 3
2 2 2 2 2 2 2 2
1 2 2 2 2 2 2 3
1 1 2 2 2 1 1 1

I think imerode can expand and shrink for binary image, while is not applicable in this case. Is there any methods in matlab can solve this problem?

Solution

  • One-Liner Solution

    Use:

    mat(imdilate(mat==2,strel('disk',2)))=2;

    Result

    mat =

 1     1     2     2     2     1     1     1
 1     2     2     2     2     2     1     1
 2     2     2     2     2     2     2     3
 2     2     2     2     2     2     2     2
 1     2     2     2     2     2     2     3
 1     1     2     2     2     2     1     1

    Step By Step explanation

    The solution for this problem is based on dilation operation on the the areas in which the matrix is equal to 2. This can be done as follow:

    %initializes the input matrix
mat = [1,1,1,1,1,1,1,1 ; 1,1,1,1,1,1,1,1; 1,1,2,2,2,1,1,3 ; 1,1,2,2,2,2,1,3; 1,1,1,1,2,1,1,3 ; 1,1,1,1,1,1,1,1];

%initilizes a mask which represents the reion which we want to exapand
roiMask = mat==2;

%perform expansion to this mask by imdilate function
dilatedRoi = imdilate(mat==2,strel('disk',2));

%assigns the new value into the original matrix
mat(dilatedRoi) = 2;

    Notice that the dilation operation is characterized by a structuring element object, which is basically a binary matrix which defines the way to perform the expansion. In my example, I used MATLAB's strel function, which generates the following:

    strel('disk',2)

ans = 
 0     0     1     0     0
 0     1     1     1     0
 1     1     1     1     1
 0     1     1     1     0
 0     0     1     0     0

    You may want to change the strel in order to fully control the desired expansion behavior.