matlabalignmentoverlapcurvessequence-alignment

Aligning curves along the horizontal direction


I have some 'n' experimental curves for the same experimental conditions. Due to the inherent thermal drift in the system, the data sets are not exactly aligned with each other. I am looking for a robust algorithm that would align the data-curves for me.

This is what I tried so far:

x = linspace(1,100,1000);
y = tanh(0.09*x) ; figure; plot(x,y)
y1 = tanh(0.09*(x+10)) ; hold on; plot(x,y1)
y2 = tanh(0.09*(x-10)) ; hold on; plot(x,y2)

The curves look like this:

enter image description here

and this is what I would like to get:

Expected output

(Here I have aligned the curves y1 and y2 on top of the curve y)


I thought cross-correlation might help me align the data. So I tried:

[cc,lag] = xcorr(y,y1,'none');
[~,ind] = max(cc);
sh = lag(ind);

But this gave me sh=0.

Is there a better way of doing this?


Solution

  • Here's my idea on how to approach this, using "reverse" interpolation (reverse in the sense that usually we want to find y values that correspond to some x, but here it's the other way around):

    function q51282667
    %% Generate data:
    x = linspace(1,100,1000);
    y{1} = tanh(0.09*x) ; 
    y{2} = tanh(0.09*(x+10));
    y{3} = tanh(0.09*(x-10));
    % ^ y,y1,y2 are not necessarily the same length so I used a cell and not a numeric array
    
    %% Find alignment:
    % Establish a baseline: the curve with the largest vertical extent:
    [~,mxi] = sort(cellfun(@max,y) - cellfun(@min,y), 'descend');
    % Reverse interpolation using y-values:
    ny = numel(y);
    deltaX = zeros(ny,1);
    for indY = 1:ny
      deltaX(indY) = interp1(y{mxi(1)}, x, y{indY}(1)) - x(1);
    end
    
    %% Plot:
    % Original:
    figure(); plot(x, y{1}, x, y{2}, x, y{3}); % this is the same as your example
    % Shifted:
    figure(); plot(x + deltaX(mxi(1)), y{mxi(1)}, ...
                   x + deltaX(mxi(2)), y{mxi(2)}, ...
                   x + deltaX(mxi(3)), y{mxi(3)});
    

    resulting in:

    deltaX = 
    
      10.0000063787562
      20.0000993310027
      0
    

    and:

    Desired output