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HomeHomeXTensionsXTensionsMatlabMatlabwhat's the padding option in gaussian filter of Imariswhat's the padding option in gaussian filter of Imaris
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what's the padding option in gaussian filter of Imaris
 

For matlab gaussian filter, there are four options for padding :

'Padding' — Type of padding to be used on image before filtering

'replicate' (default) | 'circular' | 'symmetric' | real, numeric, or logical scalar.

Which one was used in Imaris´╝č


 
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To test  which kind of padding was used for Imaris:

 

Firstly, generate as tif image with a middle line as 64455 and right most line as 64455, other pixels set zero.

    a = zeros(100,100);

    a(:,[30,100]) = 64455;

    imwrite(uint16(a),'D:\TestImarisPadding.tif');

   

Then open this tif with imaris, and do gaussian filter with default parameter.

 

We could see that the pixel intensity in the middle single line has been dispersed as [2,11,53,239,1018,4001,13379,27041,13379,4001,1018,239,53,11,2].

sum([2,11,53,239,1018,4001,13379,27041,13379,4001,1018,239,53,11,2]) =  64447,which is nicely close to the raw intensity 64455.

 

Then we turn to look at the right part, the pixel intensity is [3,14,68,307,1324,5327,18706,45748].

 

 

From this data I got the conclusion that Imaris use "Replicating the boundary intensity" as padding.

It assumes that outside the right boundary, there is an infinite space with intensity equal to right boundary 64455.

Considering the disperse of middle single line intensity after Gaussian filtering,

the intensity on the right part could be deduced by offset with one pixel length as below:

%disperse from raw right most line:

[2,11,53,239,1018,4001,13379,27041];

%disperse from the right outside first line:

[0,2,11,53,239,1018,4001,13379];

%disperse from the right outside second line:

[0, 0,2,11, 53, 239,1018,4001];

%disperse from the right outside third line:

[0, 0, 0, 2,11,  53, 239,1018];

%disperse from the right outside fourth line:

[0, 0, 0,  0, 2, 11,  53, 239];

%disperse from the right outside fifth line:

[0, 0, 0,  0,   0,  2, 11, 53];

%disperse from the right outside sixth line:

[0, 0, 0,  0,   0,   0, 2, 11];

%disperse from the right outside seventh:

[0, 0, 0,  0,   0,   0,  0, 2];

%disperse from the right outside eigth line and beyond:

[0, 0, 0,  0,   0,   0,  0, 0];

 

a =

 

           2          11          53         239        1018        4001       13379       27041

           0           2          11          53         239        1018        4001       13379

           0           0           2          11          53         239        1018        4001

           0           0           0           2          11          53         239        1018

           0           0           0           0           2          11          53         239

           0           0           0           0           0           2          11          53

           0           0           0           0           0           0           2          11

           0           0           0           0           0           0           0           2

           0           0           0           0           0           0           0           0

          

  sum(a,1)  =[2,13,66,305,1323,5324,18703,45744]

 

  the sum is quite close to the observed: [3,14,68,307,1324,5327,18706,45748].

 

  

 
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The next question is, how the padding was defined for the pixels outside the box but at upper left/right and lower left/right?

Construct a tif image with the most upper right pixel as 64455 and a 5X5 square in the middle as 64455:

a = zeros(100,100);

a(48:52,48:52) = 64455;

a(100,100) = 64455;

imwrite(uint16(a),'D:\ TestImarisPadding.tif ');

 

open image with imaris and do a Gaussian filter with parameter as 0.67um. Under the 0.67um, each pixels will be dispersed into a 5x5 diamond.

It is likely that the pixel at the corner was used for padding for these area.

If so, then extend the upper right most pixel to upside, to right side, and to upper right corner,

and after filtering, this patch together contribute to the pixel intensity at that corner.

 

To test it, make a square at least 5 X 5 with intensity 64455, and do Gaussian filtering,

then the pixel at the corner of 5x5 should be equal to the pixel at the upper right most corner of the entire image.

 

This is the result:

Corner of 5x5 square: 41578.

Corner of entire image: 41581.

 

The 3-dimension stack should be the same padding option, and with another layer of operation that the corner extension for eight corner of stack should be the replication of that eight corner.

 

 
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