Is there a technique to merge two peaks into one peak at the midpoint?

Is it possible to merge two peaks into one through image processing methods or techniques such as matrix averaging or clustering?

What I want is to see a single peak in the middle of that location.

load('data.mat')
figure
subplot 121
imagesc(data);
subplot 122
surf(data);

An additional question is, can I use a CNN to detect the yellow areas and merge them together like I want?

Answer 1

[Mathieu NOE]

hello

maybe this ? (a low tech approach...)

load('data.mat')
[m,n] = size(data);
%% find the two peaks location
MinPeakH = 0.5*max(data,[],'all');
[pks,locs_y,locs_x]=peaks2(data,'MinPeakHeight',MinPeakH); 


% isolate each peak by 2D gaussian filter 
dx = diff(locs_x);
dy = diff(locs_y);
dd = sqrt(dx^2+dy^2);

%Gaussian filter
x = 1:n;
y = 1:m;
sigma = dd/2;

% first peak
x01 = locs_x(1);
y01 = locs_y(1);
[X,Y] = meshgrid(x,y);
g = exp(-((X-x01).^2+(Y-y01).^2)./(2*sigma^2));
data1 = data.*g;

% second peak
x02 = locs_x(2);
y02 = locs_y(2);
[X,Y] = meshgrid(x,y);
g = exp(-((X-x02).^2+(Y-y02).^2)./(2*sigma^2));
data2 = data.*g;


%% re-centering the data to the mid point
% mid point between two peaks
xm = round(mean(locs_x));
ym = round(mean(locs_y));

figure
subplot 131
imagesc(data); hold on
plot(locs_x,locs_y,'+r','markersize',25);
plot(xm,ym,'+k','markersize',25);
subplot 132
imagesc(data1); 
subplot 133
imagesc(data2); 

% shift peak1 data 
sx = xm - x01; % x shift move
sy = ym - y01; % y shift move
data1s = ones(m,n)*min(data,[],'all');
data1s(1+sx:m,1+sy:n) = data1(1:m-sx,1:n-sy);

% shift peak2 data 
sx = -xm + x02; % x shift move
sy = -ym + y02; % y shift move
data2s = ones(m,n)*min(data,[],'all');
data2s(1:m-sx,1:n-sy) = data2(1+sx:m,1+sy:n);

figure
subplot 131
imagesc(data); hold on
plot(locs_x,locs_y,'+r','markersize',25);
plot(xm,ym,'+k','markersize',25);
subplot 132
imagesc(data1s);  hold on
plot(xm,ym,'+k','markersize',25);
subplot 133
imagesc(data2s); hold on
plot(xm,ym,'+k','markersize',25);

% mean of both shifted datas
datas = (data1s+data2s)/2;

figure
subplot 121
imagesc(data); hold on
plot(locs_x,locs_y,'+r','markersize',25);
plot(xm,ym,'+k','markersize',25);
subplot 122
imagesc(datas);  hold on
plot(xm,ym,'+k','markersize',25);