Ive been looking at implementing GLCM within MATLAB using graycomatrix. There are two arguments that I have discovered (NumLevels and GrayLimits) but in in my research and implementation they seem to achieve the same result.
GrayLimits specified bins between a range set [low high], causing a restricted set of gray levels.
NumLevels declares the number of gray levels in an image.
Could someone please explain the difference between these two arguments, as I don't understand why there would be two arguments that achieve the same result.
From the documentation:
'GrayLimits': Range used scaling input image into gray levels, specified as a two-element vector [low high]. If N is the number of gray levels (see parameter 'NumLevels') to use for scaling, the range [low high] is divided into N equal width bins and values in a bin get mapped to a single gray level.
'NumLevels': Number of gray levels, specified as an integer.
Thus the first parameter sets the input gray level range to be used (defaults to the min and max values in the image), and the second parameter sets the number of unique gray levels considered (and thus the size of the output matrix, defaults to 8, or 2 for binary images).
For example:
>> graycomatrix(img,'NumLevels',8,'GrayLimits',[0,255])
ans =
17687 1587 81 31 7 0 0 0
1498 7347 1566 399 105 8 0 0
62 1690 3891 1546 298 38 1 0
12 335 1645 4388 1320 145 4 0
2 76 305 1349 4894 959 18 0
0 16 40 135 965 7567 415 0
0 0 0 2 15 421 2410 0
0 0 0 0 0 0 0 0
>> graycomatrix(img,'NumLevels',8,'GrayLimits',[0,127])
ans =
1 9 0 0 0 0 0 0
7 17670 1431 156 50 31 23 15
1 1369 3765 970 350 142 84 92
0 128 1037 1575 750 324 169 167
0 46 361 836 1218 747 335 260
0 16 163 330 772 1154 741 547
0 10 74 150 370 787 1353 1208
0 4 67 136 294 539 1247 21199
>> graycomatrix(img,'NumLevels',4,'GrayLimits',[0,255])
ans =
28119 2077 120 0
2099 11470 1801 5
94 1829 14385 433
0 2 436 2410
As you can see, these parameters modify the output in different ways:
In the first case above, the range [0,255] was mapped to columns/rows 1-8, putting 32 different input grey values into each.
In the second case, the smaller range [0,127] was mapped to 8 indices, putting 16 different input grey values into each, and putting the remaining grey values 128-255 into the 8th index.
In the third case, the range [0,255] was mapped to 4 indices, putting 64 different input grey values into each.
Related
I'm trying to perform some simple logic on a table but I'd like to verify that the columns exists prior to doing so as a validation step. My data consists of standard table names though they are not always present in each data source.
While the following seems to work (just validating AAA at present) I need to expand to ensure that PRI_AAA (and eventually many other variables) is present as well.
t: $[`AAA in cols `t; temp: update AAA_VAL: AAA*AAA_PRICE from t;()]
Two part question
This seems quite tedious for each variable (imagine AAA-ZZZ inputs and their derivatives). Is there a clever way to leverage a dictionary (or table) to see if a number of variables exists or insert a place holder column of zeros if they do not?
Similarly, can we store a formula or instructions to to apply within a dictionary (or table) to validate and return a calculation (i.e. BBB_VAL: BBB*BBB_PRICE.) Some calculations would be dependent on others (i.e. BBB_Tax_Basis = BBB_VAL - BBB_COSTS costs for example so there could be iterative issues.
Thank in advance!
A functional update may be the best way to achieve this if your intention is to update many columns of a table in a similar fashion.
func:{[t;x]
if[not x in cols t;t:![t;();0b;(enlist x)!enlist 0]];
:$[x in cols t;
![t;();0b;(enlist`$string[x],"_VAL")!enlist(*;x;`$string[x],"_PRICE")];
t;
];
};
This function will update t with *_VAL columns for any column you pass as an argument, while first also adding a zero column for any missing columns passed as an argument.
q)t:([]AAA:10?100;BBB:10?100;CCC:10?100;AAA_PRICE:10*10?10;BBB_PRICE:10*10?10;CCC_PRICE:10*10?10;DDD_PRICE:10*10?10)
q)func/[t;`AAA`BBB`CCC`DDD]
AAA BBB CCC AAA_PRICE BBB_PRICE CCC_PRICE DDD_PRICE AAA_VAL BBB_VAL CCC_VAL DDD DDD_VAL
---------------------------------------------------------------------------------------
70 28 89 10 90 0 0 700 2520 0 0 0
39 17 97 50 90 40 10 1950 1530 3880 0 0
76 11 11 0 0 50 10 0 0 550 0 0
26 55 99 20 60 80 90 520 3300 7920 0 0
91 51 3 30 20 0 60 2730 1020 0 0 0
83 81 7 70 60 40 90 5810 4860 280 0 0
76 68 98 40 80 90 70 3040 5440 8820 0 0
88 96 30 70 0 80 80 6160 0 2400 0 0
4 61 2 70 90 0 40 280 5490 0 0 0
56 70 15 0 50 30 30 0 3500 450 0 0
As you've already mentioned, to cover point 2, a dictionary of functions might be the best way to go.
q)dict:raze{(enlist`$string[x],"_VAL")!enlist(*;x;`$string[x],"_PRICE")}each`AAA`BBB`DDD
q)dict
AAA_VAL| * `AAA `AAA_PRICE
BBB_VAL| * `BBB `BBB_PRICE
DDD_VAL| * `DDD `DDD_PRICE
And then a slightly modified function...
func:{[dict;t;x]
if[not x in cols t;t:![t;();0b;(enlist x)!enlist 0]];
:$[x in cols t;
![t;();0b;(enlist`$string[x],"_VAL")!enlist(dict`$string[x],"_VAL")];
t;
];
};
yields a similar result.
q)func[dict]/[t;`AAA`BBB`DDD]
AAA BBB CCC AAA_PRICE BBB_PRICE CCC_PRICE DDD_PRICE AAA_VAL BBB_VAL DDD DDD_VAL
-------------------------------------------------------------------------------
70 28 89 10 90 0 0 700 2520 0 0
39 17 97 50 90 40 10 1950 1530 0 0
76 11 11 0 0 50 10 0 0 0 0
26 55 99 20 60 80 90 520 3300 0 0
91 51 3 30 20 0 60 2730 1020 0 0
83 81 7 70 60 40 90 5810 4860 0 0
76 68 98 40 80 90 70 3040 5440 0 0
88 96 30 70 0 80 80 6160 0 0 0
4 61 2 70 90 0 40 280 5490 0 0
56 70 15 0 50 30 30 0 3500 0 0
Here's another approach which handles dependent/cascading calculations and also figures out which calculations are possible or not depending on the available columns in the table.
q)show map:`AAA_VAL`BBB_VAL`AAA_RevenueP`AAA_RevenueM`BBB_Other!((*;`AAA;`AAA_PRICE);(*;`BBB;`BBB_PRICE);(+;`AAA_Revenue;`AAA_VAL);(%;`AAA_RevenueP;1e6);(reciprocal;`BBB_VAL));
AAA_VAL | (*;`AAA;`AAA_PRICE)
BBB_VAL | (*;`BBB;`BBB_PRICE)
AAA_RevenueP| (+;`AAA_Revenue;`AAA_VAL)
AAA_RevenueM| (%;`AAA_RevenueP;1000000f)
BBB_Other | (%:;`BBB_VAL)
func:{c:{$[0h=type y;.z.s[x]each y;-11h<>type y;y;y in key x;.z.s[x]each x y;y]}[y]''[y];
![x;();0b;where[{all in[;cols x]r where -11h=type each r:(raze/)y}[x]each c]#c]};
q)t:([] AAA:1 2 3;AAA_PRICE:1 2 3f;AAA_Revenue:10 20 30;BBB:4 5 6);
q)func[t;map]
AAA AAA_PRICE AAA_Revenue BBB AAA_VAL AAA_RevenueP AAA_RevenueM
---------------------------------------------------------------
1 1 10 4 1 11 1.1e-05
2 2 20 5 4 24 2.4e-05
3 3 30 6 9 39 3.9e-05
/if the right columns are there
q)t:([] AAA:1 2 3;AAA_PRICE:1 2 3f;AAA_Revenue:10 20 30;BBB:4 5 6;BBB_PRICE:4 5 6f);
q)func[t;map]
AAA AAA_PRICE AAA_Revenue BBB BBB_PRICE AAA_VAL BBB_VAL AAA_RevenueP AAA_RevenueM BBB_Other
--------------------------------------------------------------------------------------------
1 1 10 4 4 1 16 11 1.1e-05 0.0625
2 2 20 5 5 4 25 24 2.4e-05 0.04
3 3 30 6 6 9 36 39 3.9e-05 0.02777778
The only caveat is that your map can't have the same column name as both the key and in the value of your map, aka cannot re-use column names. And it's assumed all symbols in your map are column names (not global variables) though it could be extended to cover that
EDIT: if you have a large number of column maps then it will be easier to define it in a more vertical fashion like so:
map:(!). flip(
(`AAA_VAL; (*;`AAA;`AAA_PRICE));
(`BBB_VAL; (*;`BBB;`BBB_PRICE));
(`AAA_RevenueP;(+;`AAA_Revenue;`AAA_VAL));
(`AAA_RevenueM;(%;`AAA_RevenueP;1e6));
(`BBB_Other; (reciprocal;`BBB_VAL))
);
I have a csv file with experiment results that goes like this:
64 4 8 1 1 2 1 ttt 62391 4055430 333 0.0001 10 161 108 288 0
64 4 8 1 1 2 1 ttt 60966 3962810 322 0.0001 10 164 112 295 0
64 4 8 1 1 2 1 ttt 61530 3999475 325 0.0001 10 162 112 291 0
64 4 8 1 1 2 1 ttt 61430 4054428 332 0.0001 10 158 110 286 0
64 4 8 1 1 2 1 ttt 63891 4152938 339 0.0001 9 149 109 274 0
64 4 32 1 1 2 1 ttt 63699 4204182 345 0.0001 4 43 179 240 0
64 4 32 1 1 2 1 ttt 63326 4116218 336 0.0001 4 45 183 248 0
64 4 32 1 1 2 1 ttt 62654 4135211 340 0.0001 4 48 178 248 0
64 4 32 1 1 2 1 ttt 63192 4107506 339 0.0001 4 49 175 245 0
64 4 32 1 1 2 1 ttt 62707 4138666 345 0.0001 4 46 179 245 0
64 4 64 1 1 2 1 ttt 60968 3962929 323 0.0001 4 46 191 256 0
64 4 64 1 1 2 1 ttt 58765 3819787 305 0.0001 4 50 196 267 0
64 4 64 1 1 2 1 ttt 58946 3831499 308 0.0001 5 52 187 260 0
64 4 64 1 1 2 1 ttt 60646 3942047 321 0.0001 4 47 187 254 0
64 4 64 1 1 2 1 ttt 59723 3882044 311 0.0001 4 46 201 269 0
64 8 8 1 1 2 1 ttt 63414 4185382 382 0.0001 33 517 109 643 0
64 8 8 1 1 2 1 ttt 62429 4057899 372 0.0001 33 538 110 667 0
64 8 8 1 1 2 1 ttt 60622 3940452 384 0.0001 33 556 115 689 0
64 8 8 1 1 2 1 ttt 64433 4188192 369 0.0001 33 519 110 644 0
My goal is to be able to plot various combinations (choose which, in different charts) of the columns before the "ttt", with the average and standard deviation of the columns (choose which) after "ttt" (by grouping them by the before "ttt" columns).
Is this possible in GNUPlot and if yes how? If not, do you have any alternate suggestions regarding my problem?
Here is a completely revised and more general version.
Since you want to filter by 3 columns you need to have 3 properties to distinguish the data in the plot. This would be for example color, x-position and pointtype. What the script basically does:
Generates random data for testing (take your file instead)
$Data looks like this:
8 64 57773 0
4 32 64721 2
8 32 56757 1
4 16 56226 2
8 8 56055 1
8 64 59874 0
8 32 58733 0
4 16 55525 2
8 32 58869 0
8 64 64470 0
4 32 60930 1
8 64 57073 2
...
the variables ColX, ColC, ColP, and ColS define which columns are taken for x-position, color, pointtype and statistics.
find unique values of ColX, ColC, ColP, (check help smooth frequency) and put them to datablocks $ColX, $ColC, and $ColP.
put the unique values to arrays ArrX, ArrC, ArrP
loop all possible combinations and do statistics on ColS and put it to $Data2. Add 3 columns at the beginning for color, x-position and pointtype.
$Data2 looks like this:
1 1 1 0 8 4 61639.4 2788.4
1 1 2 0 8 8 59282.1 2740.2
1 2 1 0 16 4 59372.3 2808.6
1 2 2 0 16 8 60502.3 2825.0
1 3 1 0 32 4 59850.7 2603.8
1 3 2 0 32 8 60617.7 1979.8
1 4 1 0 64 4 60399.4 3273.6
1 4 2 0 64 8 59930.7 2919.8
2 1 1 1 8 4 59172.6 2288.2
2 1 2 1 8 8 58992.2 2888.0
2 2 1 1 16 4 59350.1 2364.6
2 2 2 1 16 8 61034.0 2368.5
2 3 1 1 32 4 59920.8 2867.6
2 3 2 1 32 8 59711.9 3464.2
2 4 1 1 64 4 60936.7 3439.7
2 4 2 1 64 8 61078.7 2349.3
3 1 1 2 8 4 58976.0 2376.3
3 1 2 2 8 8 61731.5 1635.7
3 2 1 2 16 4 58276.0 2101.7
3 2 2 2 16 8 58594.5 3358.5
3 3 1 2 32 4 60471.5 3737.6
3 3 2 2 32 8 59909.1 2024.0
3 4 1 2 64 4 62044.2 1446.7
3 4 2 2 64 8 60454.0 3215.1
Finally, plot the data. I couldn't figure out how plotting style with yerror works properly together with variable pointtypes. So, instead I split it into two plot commands with vectors and with points. The third one keyentry is just to get an empty line in the legend and the forth one is to get the pointtype into the legend.
I hope you can figure out all the other details and adapt it to your data.
Code:
### grouped statistics on filtered (unsorted) data
reset session
set colorsequence classic
# generate some random test data
rand1(n) = 2**(int(rand(0)*2)+2) # values 4,8
rand2(n) = 2**(int(rand(0)*4)+3) # values 8,16,32,64
rand3(n) = int(rand(0)*10000)+55000 # values 55000 to 65000
rand4(n) = int(rand(0)*3) # values 0,1,2
set print $Data
do for [i=1:200] {
print sprintf("% 3d% 4d% 7d% 3d", rand1(0), rand2(0), rand3(0), rand4(0))
}
set print
print $Data # (just for test purpose)
ColX = 2 # column for x
ColC = 4 # column for color
ColP = 1 # column for pointtype
ColS = 3 # column for statistics
# get unique values of the columns
set table $ColX
plot $Data u (column(ColX)) smooth freq
unset table
set table $ColC
plot $Data u (column(ColC)) smooth freq
unset table
set table $ColP
plot $Data u (column(ColP)) smooth freq
unset table
# put unique values into arrays
set table $Dummy
array ArrX[|$ColX|-6] # gnuplot creates 6 extra lines
array ArrC[|$ColC|-6]
array ArrP[|$ColP|-6]
plot $ColX u (ArrX[$0+1]=$1)
plot $ColC u (ArrC[$0+1]=$1)
plot $ColP u (ArrP[$0+1]=$1)
unset table
print ArrX, ArrC, ArrP # just for test purpose
# define filter function
Filter(c,x,p) = ArrX[x]==column(ColX) && ArrC[c]==column(ColC) && \
ArrP[p]==column(ColP) ? column(ColS) : NaN
# loop all values and do statistics, write data into $Data2
set print $Data2
do for [c=1:|ArrC|] {
do for [x=1:|ArrX|] {
do for [p=1:|ArrP|] {
undef var STATS*
stats $Data u (Filter(c,x,p)) nooutput
if (exists('STATS_mean') && exists('STATS_stddev')) {
print sprintf("% 3d% 3d% 3d% 3d% 3d% 3d% 9.1f % 7.1f", c, x, p, ArrC[c], ArrX[x], ArrP[p], STATS_mean, STATS_stddev)
}
}
}
print ""; print ""
}
set print
# print $Data2 # just for testing purpose
set xlabel sprintf("Column %d", ColX)
set ylabel sprintf("Column %d", ColS)
set xrange[0.5:|ArrX|+1]
set xtics () # remove all xtics
do for [x=1:|ArrX|] { set xtics add (sprintf("%d",ArrX[x]) x)} # set xtics "manually"
# function for x position and offsets,
# actually not dependent on 'n' but to shorten plot command
# columns in $Data2: 1=color, 2=x, 3=pointtype
width = 0.5 # float number!
step = width/(|ArrC|-1)
PosX(n) = column(2) - width/2.0 + step*(column(1)-1) + (column(3)-1)*step*0.3
plot \
for [c=1:|ArrC|] $Data2 u (PosX(0)):($7-$8):(0):(2*$8) index c-1 w vectors \
heads size 0.04,90 lw 2 lc c ti sprintf("%g",ArrC[c]),\
for [c=1:|ArrC|] '' u (PosX(0)):7:($3*2+4):(c) index c-1 w p ps 1.5 pt var lc var not, \
keyentry w p ps 0 ti "\n", \
for [p=1:|ArrP|] '' u (0):(NaN) w p pt p*2+4 ps 1.5 lc rgb "black" ti sprintf("%g",ArrP[p])
### end of code
Result:
I do not think gnuplot can produce exactly what you are asking for in a single plot command. I will show you two alternatives in the hope that one or both is a useful starting point.
Alternative 1: standard boxplot
spacing = 1.0
width = 0.25
unset key
set xlabel "Column 3"
set ylabel "Column 9"
plot 'data' using (spacing):9:(width):3 with boxplot lw 2
This collects points based on the value in column 3 and for each such value it produces a boxplot. This is a widely used method of showing the distribution of point values in a category, but it is a quartile analysis not a display of mean + standard deviation.
Alternative 2: calculate mean and standard deviation for categories known in advance
The boxplot analysis has the advantage that you do not need to know in advance what values may be present in column 3. Gnuplot can calculate mean and standard deviation based on a column 3 value, but you need to specify in advance what that value is. Here is a set of commands tailored to the specific example file you provided. It calculates, but does not plot, the requested categorical mean and standard deviation. You can use these numbers to construct a plot, but that will require additional commands. You could, for example, save the values for each category in a new file, or array, or datablock and then go back and plot these together.
col3entry = "8 32 64"
do for [i in col3entry] {
stats "data" using ($3 == real(i) ? $9 : NaN) name "Condition".i nooutput
print i, ": ", value("Condition".i."_mean"), value("Condition".i."_stddev")
}
output:
8: 62345.1111111111 1259.34784220021
32: 63115.6 392.552977316438
64: 59809.6 881.583711283279
I have this matrix:
A = [92 92 92 91 91 91 146 146 146 0
0 0 112 112 112 127 127 127 35 35
16 16 121 121 121 55 55 55 148 148
0 0 0 96 96 0 0 0 0 0
0 16 16 16 140 140 140 0 0 0]
How can I replace consecutive zero value with shuffled consecutive value from matrix B?
B = [3 3 3 5 5 6 6 2 2 2 7 7 7]
The required result is some matrix like this:
A = [92 92 92 91 91 91 146 146 146 0
6 6 112 112 112 127 127 127 35 35
16 16 121 121 121 55 55 55 148 148
7 7 7 96 96 5 5 3 3 3
0 16 16 16 140 140 140 2 2 2]
You simply can do it like this:
[M,N]=size(A);
for i=1:M
for j=1:N
if A(i,j)==0
A(i,j)=B(i+j);
end
end
end
If I understand it correctly from what you've described, your solution is going to need the following steps:
Loop over the rows of your matrix, e.g. for row = 1:size(A, 1)
Loop over the elements of each row, identify where each run of zeroes starts and store the indices and the length of the run. For example you might end up with a matrix like: consecutiveZeroes = [ 2 1 2 ; 4 1 3 ; 4 6 5 ; 5 8 3 ] indicating that you have a run at (2, 1) of length 2, a run at (4, 1) of length 3, a run at (4, 6) of length 5, and a run at (5, 8) of length 3.
Now loop over the elements of B counting up how many elements there are of each value. For example you might store this as replacementValues = [ 3 3 ; 2 5 ; 2 6 ; 3 2 ; 3 7 ] meaning three 3's, two 5's, two 6's etc.
Now take a row from your consecutiveZeroes matrix and randomly choose a row of replacementValues that specifies the same number of elements, replace the zeroes in A with the values from replacementValues, and delete the row from replacementValues to show that you've used it.
If there isn't a row in replacementValues that describes a long enough run of values to replace one of your runs of zeroes, find a combination of two or more rows from replacementValues that will work.
You can't do this with just a single pass through the matrix, because presumably you could have a matrix A like [ 15 7 0 0 0 0 0 0 3 ; 2 0 0 0 5 0 0 0 9 ] and a vector B like [ 2 2 2 3 3 3 7 7 5 5 5 5 ], where you can only achieve what you want if you use the four 5's and two 7's and not the three 2's and three 3's to substitute for the run of six zeroes, because you have to leave the 2's and 3's for the two runs of three zeroes in the next row. The easiest approach if efficiency is not critical would probably be to run the algorithm multiple times trying different random combinations until you get one that works - but you'll need to decide how many times to try before giving up in case the input data actually has no solution.
If you get stuck on any of these steps I suggest asking a new, more specific question.
I had two arrays, (data1 is a header array of strings and data2 is the data array of numbers)
data1 = {'#','Area','C Xp','C Yp','Length','B #','R','L','Ch','E1 Xp','E1 Yp','E2 Xp','E2 Yp'};
data2 = [1 939 -397 586 99 2 2 0 -1 -450 588 -352 572
2 1185 -287 294 145 2 1 1 0 -317 359 -235 244
3 592 -242 486 77 3 2 1 0 -278 488 -202 477
4 818 -144 480 60 2 0 2 1 -181 488 -135 451
5 377 -23 -443 37 1 0 1 0 -42 -459 -12 -460
6 923 32 -234 67 1 0 0 0 -3 -260 60 -212
7 812 150 -148 54 1 0 1 0 136 -130 169 -161
8 5968 428 432 402 3 3 0 -1 224 468 622 356
9 617 714 13 63 1 0 1 0 687 35 702 -22
csvwrite('file.xlsx', data1, 0, 0);
csvwrite('file.xlsx', data2, 0, 1);
My first problem is data1 prints to the spreadsheet as an array of chars (example: '#','A','r','e','... each in their own cells). How do I get it to print as the strings I am passing?
My second problem is when I csvwrite data2, data1's info is erased or overwritten. How can I write both to the same file?
Hidden away in the Tips section of the csvwrite documentation:
csvwrite does not accept cell arrays for the input matrix M. To export a cell array that contains only numeric data, use cell2mat to convert the cell array to a numeric matrix before calling csvwrite. To export cell arrays with mixed alphabetic and numeric data, where each cell contains a single element, you can create an Excel® spreadsheet (if your system has Excel installed) using xlswrite. For all other cases, you must use low-level export functions to write your data. For more information, see Export Cell Array to Text File in the MATLAB® Data Import and Export documentation.
I'd say, use xlswrite.
If you can't use xlswrite, it looks like you are stuck doing it manually as described on the page, Export Cell Array to Text File. Something along the lines of:
% write headers
fid = fopen('test.csv','w');
fprintf(fid,'%s,',data1{:});
fprintf(fid,'\n');
% write data...
fprintf(fid,[repmat('%d,',1,numel(data1)) '\n'],data2);
fclose(fid)
I have a matrix in MATLAB. I want to check the 4-connected neighbours (left, right, top, bottom) for every element. If the current element is less than any of the neighbours then we set it to zero otherwise it will keep its value. It can easily be done with loop, but it is very expensive as I have thousands of these matrices.
You might recognize it as nonmaxima suppression after edge detection.
If you have the image processing toolbox, you can do this with a morpological dilation to find local maxima and suppress all other elements.
array = magic(6); %# make some data
msk = [0 1 0;1 0 1;0 1 0]; %# make a 4-neighbour mask
%# dilation will replace the center pixel with the
%# maximum of its neighbors
maxNeighbour = imdilate(array,msk);
%# set pix to zero if less than neighbors
array(array<maxNeighbour) = 0;
array =
35 0 0 26 0 0
0 32 0 0 0 25
31 0 0 0 27 0
0 0 0 0 0 0
30 0 34 0 0 16
0 36 0 0 18 0
edited to use the same data as #gnovice, and to fix the code
One way to do this is with the function NLFILTER from the Image Processing Toolbox, which applies a given function to each M-by-N block of a matrix:
>> A = magic(6) %# A sample matrix
A =
35 1 6 26 19 24
3 32 7 21 23 25
31 9 2 22 27 20
8 28 33 17 10 15
30 5 34 12 14 16
4 36 29 13 18 11
>> B = nlfilter(A,[3 3],#(b) b(5)*all(b(5) >= b([2 4 6 8])))
B =
35 0 0 26 0 0
0 32 0 0 0 25
31 0 0 0 27 0
0 0 0 0 0 0
30 0 34 0 0 16
0 36 0 0 18 0
The above code defines an anonymous function which uses linear indexing to get the center element of a 3-by-3 submatrix b(5) and compare it to its 4-connected neighbors b([2 4 6 8]). The value in the center element is multiplied by the logical result returned by the function ALL, which is 1 when the center element is larger than all of its nearest neighbors and 0 otherwise.
If you don't have access to the Image Processing Toolbox, another way to accomplish this is by constructing four matrices representing the top, right, bottom and left first differences for each point and then searching for corresponding elements in all four matrices that are non-negative (i.e. the element exceeds all of its neighbours).
Here's the idea broken down...
Generate some test data:
>> sizeA = 3;
A = randi(255, sizeA)
A =
254 131 94
135 10 124
105 191 84
Pad the borders with zero-elements:
>> A2 = zeros(sizeA+2) * -Inf;
A2(2:end-1,2:end-1) = A
A2 =
0 0 0 0 0
0 254 131 94 0
0 135 10 124 0
0 105 191 84 0
0 0 0 0 0
Construct the four first-difference matrices:
>> leftDiff = A2(2:end-1,2:end-1) - A2(2:end-1,1:end-2)
leftDiff =
254 -123 -37
135 -125 114
105 86 -107
>> topDiff = A2(2:end-1,2:end-1) - A2(1:end-2,2:end-1)
topDiff =
254 131 94
-119 -121 30
-30 181 -40
>> rightDiff = A2(2:end-1,2:end-1) - A2(2:end-1,3:end)
rightDiff =
123 37 94
125 -114 124
-86 107 84
>> bottomDiff = A2(2:end-1,2:end-1) - A2(3:end,2:end-1)
bottomDiff =
119 121 -30
30 -181 40
105 191 84
Find the elements that exceed all of the neighbours:
indexKeep = find(leftDiff >= 0 & topDiff >= 0 & rightDiff >= 0 & bottomDiff >= 0)
Create the resulting matrix:
>> B = zeros(sizeA);
B(indexKeep) = A(indexKeep)
B =
254 0 0
0 0 124
0 191 0
After wrapping this all into a function and testing it on 1000 random 100x100 matrices, the algorithm appears to be quite fast:
>> tic;
for ii = 1:1000
A = randi(255, 100);
B = test(A);
end; toc
Elapsed time is 0.861121 seconds.