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5.4 Block Processing

In a convolution operation, a finite size filter is scanned over a data array. At each position, a sum of the point-by-point products of the filter samples with the corresponding data samples is calculated. The operator neighborhood is defined by the geometry of the filter. Block processing is a generalization of convolution. The mathematical operators need not be multiplication and addition, and the neighborhoods do not need to overlap. The data operators that lend themselves to this kind of processing are typically called area operators. The processes that can be carried out by area operators include, in addition to convolution and correlation, data resampling, morphological operators, block transforms, noise filtering, and more.

BlockProcessing function.

This loads the package.
In[1]:=
Here we create a small data array.
In[2]:=
Out[2]//MatrixForm=Out[2]//MatrixForm=
Here we apply some arbitrary function f to each 2×2 non-overlapping block of array arr.
In[3]:=
Out[3]=Out[3]=
In practice, the dimensions of the original data array need not be an integer multiple of the block size. Therefore, as in convolution and correlation, padding is used to extend the original data array to ensure that all border samples are processed in exactly the same way as any interior samples. Padding is accomplished with option PaddingMethod, the values being the function names of any of the methods described in Section 4.4.

BlockProcessing options.

This demonstrates the use of a sliding window and zero-padding.
In[4]:=
Out[4]=Out[4]=
Here we use BlockProcessing to return the median pixel value within a 3×3 sliding window using the example books image.
In[5]:=
In[6]:=
Out[6]=Out[6]=


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