Nonlinear filtering using lookup tables
A = bwlookup(BW,lut)
gpuarrayA = bwlookup(gpuarrayBW,lut)
performs
a 2-by-2 or 3-by-3 nonlinear neighborhood filtering operation on binary
or grayscale image A
= bwlookup(BW
,lut
)BW
and returns the results
in output image A
. The neighborhood processing
determines an integer index value used to access values in lookup
table lut
. The fetched lut
value
becomes the pixel value in output image A at the targeted position.
A
is the same size as BW
A
is the same data type as lut
performs
the filtering operation on a GPU. The input image and output image
are gpuarrayA
= bwlookup(gpuarrayBW
,lut
)gpuArray
s. lut
can be
a numeric or gpuArray
vector. This syntax requires
the Parallel Computing Toolbox™.
The first step in each iteration of the filtering operation
performed by bwlookup
entails computing the index
into
vector lut
based on the binary pixel pattern
of the neighborhood matrix on image BW
. The value
in lut
accessed at index
, lut(index)
,
is inserted into output image A
at the targeted
pixel location. This results in image A
being
the same data type as vector lut
.
Since there is a 1-to-1 correspondence in targeted pixel locations,
image A is the same size as image BW
. If the
targeted pixel location is on an edge of image BW
and
if any part of the 2-by-2 or 3-by-3 neighborhood matrix extends beyond
the image edge, then these non-image locations are padded with 0 in
order to perform the filtering operation.
The following figures show the mapping from binary 0 and 1 patterns
in the neighborhood matrices to its binary representation. Adding
1 to the binary representation yields index
which
is used to access lut
.
For 2-by-2 neighborhoods, length(lut)
is
16. There are four pixels in each neighborhood, and two possible states
for each pixel, so the total number of permutations is 2^{4} =
16.
To illustrate, this example shows how the pixel pattern in a
2-by-2 matrix determines which entry in lut
is
placed in the targeted pixel location.
Create random 16-element lut
vector
containing uint8
data.
scurr = rng; % save current random number generator seed state rng('default') % always generate same set of random numbers lut = uint8( round( 255*rand(16,1) ) ) % generate lut rng(scurr); % restore
lut = 208 231 32 233 161 25 71 139 244 246 40 248 244 124 204 36
Create a 2-by-2 image and assume for this example
that the targeted pixel location is location BW(1,1)
.
BW = [1 0; 0 1]
BW = 1 0 0 1
By referring to the color coded mapping figure above,
the binary representation for this 2-by-2 neighborhood can be computed
as shown in the code snippet below. The logical 1 at BW(1,1)
corresponds
to blue in the figure which maps to the Least Signficant Bit (LSB)
at position 0 in the 4-bit binary representation (,2^{0}=
1). The logical 1 at BW(2,2)
is red which maps
to the Most Significant Bit (MSB) at position 3 in the 4-bit binary
representation (2^{3}= 8) .
% BW(1,1): blue square; sets bit position 0 on right % BW(2,2): red square; sets bit position 3 on left binNot = '1 0 0 1'; % binary representation of 2x2 neighborhood matrix X = bin2dec( binNot ); % convert from binary to decimal index = X + 1 % add 1 to compute index value for uint8 vector lut A11 = lut(index) % value at A(1,1)
index = 10 A11 = 246
The above calculation predicts that output image A
should contain the value 246 at targeted position A(1,1)
.
A = bwlookup(BW,lut) % perform filtering
A = 246 32 161 231
A(1,1)
does in fact equal 246.
Note:
For a more robust way to perform image erosion, see function |
For 3-by-3 neighborhoods, length(lut)
is
512. There are nine pixels in each neighborhood, and two possible
states for each pixel, so the total number of permutations is 2^{9} =
512.
The process for computing the binary representation of 3-by-3 neighborhood processing is the same as shown above for 2-by-2 neighborhoods.