Assigning values in neighborhood of local maxima’s to the value of local maxima based on varying window width (non symmetric window width) - matlab

Question

This question is an extension of my previous question with some new issues so I thought to make a new query. I hope it is ok.
https://stackoverflow.com/questions/46054811/changing-the-values-in-the-neighbourhood-of-local-maxima-to-the-local-maxima/46055833#46055833
Query:
Where I find local maxima. I want to make a window and assign the values depending upon window size to the neighbors the value of local maxima.
Problem: (I want my window size to change as in my original signal I have different behavior around local maxima’s.) For example in 8th window local maxima is at 34th location but I have assigned the values on the left of 34th location the value of local maxima.
In short I want to have varying and controllable window width.
Please have a look at the attached picture to get an idea of output what I want.
I hope it will give some good idea.
I want to have varying and non symmetric means not same at every local maxima window width .
I have also attached a code for nlfilter which is doing exactly what I want to do means it makes window and assign values to local maximas within that window width but I need to have flexible and changeable window width.
Is it possible to have varying window width or is there some other way possible to do that.
enter image description here
Code:
t = 1:35 ;
Y = [1 3 13 6 2 7 5 4 2 4 1 0 1 2 3 5 0 0 1 0 0 2 3 6 7 0 0 8 0 1 1 2 3 4 2];
n = 2;
[p l] = findpeaks(Y);
locations = zeros(size(Y));
locations(l) = true;
locations = conv(locations, ones(1, 2*n+1), 'same') > 0;
X = -inf(size(Y)); % create temporary
X(l) = Y(l); % copy the local maxima
X = nlfilter(X, [1 2*n+1 ], #(x) max(x)); %replace all values with it local maxima
X(l) = Y(l); % ensure local maxima are not changed
Y(locations) = X(locations); % copy filtered temporary to output
figure(1)
hold on
plot(t,Y,'r')
t = 1:35 ;
Y = [1 3 13 6 2 7 5 4 2 4 1 0 1 2 3 5 0 0 1 0 0 2 3 6 7 0 0 8 0 1 1 2 3 4 2];
plot(t,Y,'b')
hold off
I shall be grateful to you for your valuable replies.
Further Explanation:
Please have a look at the pictures attached.
2nd picture is a part of original signal with local maximas mentioned as green dots.
In 1st pictures the red lines shows the region which I want to assign the value of local maxima. Green Dot is local maxima . So you will see that if I apply window with fixed width it will not work because the points before local maxima are less than after local maxima.
The reason for placing 1 outside in example is same that there are few points before local maxima which I want to flat as compared to after local maxima.
The same is the case with other windows like last window 8 I have local maxima on 34th location but why I have chosen large values before it is only due to the values I want to assign the values of local maxima .

Answer 1

You can define a criterion that starting form a peak and going to the both sides we compute variance of neighbors of the peak and we increase the radius of the neighborhood until variance of neighboring elements becomes greater than a predefined threshold.
Here idx_peaks is position of peaks and peaks is value of peaks. After applying the threshold you can get number of elements before and after position of each peak n_before and n_after. Then you can find indices of neighborhood and assign values to them.
Y = [1 3 13 6 2 7 5 4 2 4 1 0 1 2 3 5 0 0 1 0 0 2 3 6 7 0 0 8 0 1 1 2 3 4 2];
idx_peaks = [3 6 10 16 19 25 28 34];
peaks = [13 7 4 5 1 7 8 4];
threshold = 2;
cumvar = #(a)cumsum(a(:).^2)./(1:numel(a)).'-(cumsum(a(:))./(1:numel(a)).').^2;
categ = zeros(numel(Y),1);
categ(idx_peaks)=1;
forward_categ = cumsum(categ(idx_peaks(1):end));
n_after = accumarray(forward_categ,Y(idx_peaks(1):end),[],#(x)sum(cumvar(x)<threshold)-1).';
backward_categ = cumsum(flipud(categ(1:idx_peaks(end))));
n_before = flipud(accumarray(backward_categ,fliplr(Y(1:idx_peaks(end))),[],#(x)sum(cumvar(x)<threshold)-1)).';
lo = idx_peaks-n_before;
up = idx_peaks+n_after;
val = repelem(peaks,up-lo+1);
index=cumsum(accumarray(cumsum([1;up(:)-lo(:)+1]),[lo(:);0]-[0;up(:)]-1)+1);
index= index(1:end-1);
Y(index) = val
Here is the result when setting the threshold to 2 :
Y=
[1 3 13 6 2 7 4 4 4 4 4 4 1 5 5 5 1 1 1 1 1 1 1 7 7 0 0 8 4 4 4 4 4 4 4]