Averaging a curve with itself

I'm trying to average this curve (pixel intensity of a selected object by distance from a point) with itself along the x-axis:

I've tried linear interpolation, which was unsuccessful because I do not have fully unique values in x. However, my x-values also do not always match perfectly between the upper and lower curves, which means that I cannot just average y-coordinate by matching x-values.

What would be the best way to go about doing this? I have attached my code and the relevant .mat file in case that helps.

Answer 1

[Star Strider]

Try this —

% type('membrane_intensity.m')

LD = load('test.mat');
x = LD.cx;
y = LD.c(:,1,1);

[xs,x1] = min(x);
[xe,x2] = max(x);

Lv = ismember(x, x(x1:x2));
Sec{1,:} = [x(Lv) y(Lv)]

Sec = 1×1 cell array
    {608×2 double}

Sec{2,:} = [x(~Lv) y(~Lv)]

Sec = 2×1 cell array
    {608×2 double}
    {555×2 double}

Sec{2} = sortrows(Sec{2})

Sec = 2×1 cell array
    {608×2 double}
    {555×2 double}

[Us1x,ia1,ic1] = unique(Sec{1}(:,1), 'stable');
Sec{1} = Sec{1}(ia1,:)

Sec = 2×1 cell array
    {608×2 double}
    {555×2 double}

[Us2x,ia2,ic2] = unique(Sec{2}(:,1), 'stable');
Sec{2} = Sec{2}(ia2,:)

Sec = 2×1 cell array
    {608×2 double}
    {554×2 double}

figure
plot(Sec{1}(:,1), Sec{1}(:,2))
hold on
plot(Sec{2}(:,1), Sec{2}(:,2))
hold off
title('Before Interpolation')

xv = linspace(xs, xe, 600).';

Seci{1,:} = [xv interp1(Sec{1}(:,1), Sec{1}(:,2), xv)]

Seci = 1×1 cell array
    {600×2 double}

Seci{2,:} = [xv interp1(Sec{2}(:,1), Sec{2}(:,2), xv)]

Seci = 2×1 cell array
    {600×2 double}
    {600×2 double}

ymean = mean([Seci{1}(:,2) Seci{2}(:,2)], 2);

figure
plot(Seci{1}(:,1), Seci{1}(:,2), 'DisplayName','Section #1')
hold on
plot(Seci{2}(:,1), Seci{2}(:,2), 'DisplayName','Section #1')
plot(xv, ymean, '-g', 'DisplayName','Mean')
hold off
title('After Interpolation')
legend('Location','best')

.

[Stephen23]

Simpler without ISMEMBER and SORTROWS:

S = load('test.mat');
Xraw = S.cx;
Yraw = S.c;

[Xmin,Imin] = min(Xraw);
[Xmax,Imax] = max(Xraw);
I1 = Imin:Imax;
I2 = [Imax:numel(Xraw),1:Imin];
[X1,J1] = unique(Xraw(I1));
[X2,J2] = unique(Xraw(I2));
N = 654;
Xnew = linspace(Xmin,Xmax,N);
Ynew = mean([...
    interp1(X1,Yraw(I1(J1)),Xnew);...
    interp1(X2,Yraw(I2(J2)),Xnew)],1);

plot(Xraw,Yraw,Xnew,Ynew)