hilbertCurve

Convert 2D data to 1D data and back easily by applying Hilbert curve transformation

The benefit of Hilbert curve transformation is that the 1D data can be downsampled or upsampled without worrying about whether the 2D coordinate of the data point changes. Hilbert curve is designed in such a way that the absolute index of the data point does not matter; only the relative index compared to the whole data size matters.

Consists of three files:

hilbertCurve takes in 2D data and outputs it as 1D data.
hilbertCurveRev takes in 1D data and outputs it as 2D data.
hilbertCurveExample gives examples of using the functions.

Example:

% toy data
rowLen = 256;
data = zeros(rowLen,rowLen);
for x = 1:rowLen
for y = 1:rowLen
data(x,y) = exp(-(0.125/rowLen)*((x-(rowLen+1)/2)^2+(y-(rowLen+1)/2)^2));
end
end

% transform to hilbert curve
transData = hilbertCurve(data);

% reduce dimensionality
reduceRatio = 16; % has to be power of 4
transData = downsample(transData,reduceRatio);

%%%%% this is where you would place any of your analysis scripts %%%%%

% reverse transform to 2D
twoDimData = hilbertCurveRev(transData);

% plot
figure('Position',[100 100 1000 400]);
subplot(1,2,1);
imagesc(data,[0 1]);
subplot(1,2,2);
imagesc(twoDimData,[0 1]);