I am looking for a \'good\' way to find a matrix (pattern) in a larger matrix (arbitrary number of dimensions).
Example:
total = rand(3,4,5);
sub = t
Here is low-performance, but (supposedly) arbitrary dimensional function. It uses find
to create a list of (linear) indices of potential matching positions in total
and then just checks if the appropriately sized subblock of total
matches sub
.
function loc = matrixFind(total, sub)
%matrixFind find position of array in another array
% initialize result
loc = [];
% pre-check: do all elements of sub exist in total?
elements_in_both = intersect(sub(:), total(:));
if numel(elements_in_both) < numel(unique(sub))
% if not, return nothing
return
end
% select a pivot element
% Improvement: use least common element in total for less iterations
pivot_element = sub(1);
% determine linear index of all occurences of pivot_elemnent in total
starting_positions = find(total == pivot_element);
% prepare cell arrays for variable length subscript vectors
[subscripts, subscript_ranges] = deal(cell([1, ndims(total)]));
for k = 1:length(starting_positions)
% fill subscript vector for starting position
[subscripts{:}] = ind2sub(size(total), starting_positions(k));
% add offsets according to size of sub per dimension
for m = 1:length(subscripts)
subscript_ranges{m} = subscripts{m}:subscripts{m} + size(sub, m) - 1;
end
% is subblock of total equal to sub
if isequal(total(subscript_ranges{:}), sub)
loc = [loc; cell2mat(subscripts)]; %#ok<AGROW>
end
end
end
This is based on doing all possible shifts of the original matrix total
and comparing the upper-leftmost-etc sub-matrix of the shifted total
with the sought pattern subs
. Shifts are generated using strings, and are applied using circshift
.
Most of the work is done vectorized. Only one level of loops is used.
The function finds all matchings, not just the first. For example:
>> total = ones(3,4,5,6);
>> sub = ones(3,3,5,6);
>> matrixFind(total, sub)
ans =
1 1 1 1
1 2 1 1
Here is the function:
function sol = matrixFind(total, sub)
nd = ndims(total);
sizt = size(total).';
max_sizt = max(sizt);
sizs = [ size(sub) ones(1,nd-ndims(sub)) ].'; % in case there are
% trailing singletons
if any(sizs>sizt)
error('Incorrect dimensions')
end
allowed_shift = (sizt-sizs);
max_allowed_shift = max(allowed_shift);
if max_allowed_shift>0
shifts = dec2base(0:(max_allowed_shift+1)^nd-1,max_allowed_shift+1).'-'0';
filter = all(bsxfun(@le,shifts,allowed_shift));
shifts = shifts(:,filter); % possible shifts of matrix "total", along
% all dimensions
else
shifts = zeros(nd,1);
end
for dim = 1:nd
d{dim} = 1:sizt(dim); % vectors with subindices per dimension
end
g = cell(1,nd);
[g{:}] = ndgrid(d{:}); % grid of subindices per dimension
gc = cat(nd+1,g{:}); % concatenated grid
accept = repmat(permute(sizs,[2:nd+1 1]), [sizt; 1]); % acceptable values
% of subindices in order to compare with matrix "sub"
ind_filter = find(all(gc<=accept,nd+1));
sol = [];
for shift = shifts
total_shifted = circshift(total,-shift);
if all(total_shifted(ind_filter)==sub(:))
sol = [ sol; shift.'+1 ];
end
end
For an arbitrary number of dimensions, you might try convn
.
C = convn(total,reshape(sub(end:-1:1),size(sub)),'valid'); % flip dimensions of sub to be correlation
[~,indmax] = max(C(:));
% thanks to Eitan T for the next line
cc = cell(1,ndims(total)); [cc{:}] = ind2sub(size(C),indmax); subs = [cc{:}]
Thanks to Eitan T for the suggestion to use comma-separated lists for a generalized ind2sub.
Finally, you should test the result with isequal
because this is not a normalized cross correlation, meaning that larger numbers in a local subregion will inflate the correlation value potentially giving false positives. If your total
matrix is very inhomogeneous with regions of large values, you might need to search other maxima in C
.