I'm not sure if there is a standard definition of area of 95 confidence in 2D pdf since it like asking what if the shape of 95% of the cake, one can cut in many way provide the remaning is 95%.
Assuming one cut on a level of pdf, here is one way
% Invent some fake 2D pdf
pdf=abs(peaks(100));
pdf=pdf-min(pdf,[],'all');
maxp = max(pdf,[],'all');
minp = 0;
smin = 1;
smax = 0;
spdf = sum(pdf,'all');
starget = 0.95;
sold = NaN;
while true
l = (minp+maxp)/2;
i = find(pdf >= l);
s = sum(pdf(i)) / spdf
if s > starget
minp = l;
else
maxp = l;
end
if s==sold || ... % stuck due to quantification of pixels
abs(smax-smin) < 0.001
break
end
sold = s;
end
close all
figure;
surf(pdf+10)
hold on
contourf(pdf,[l l])
Note that estimation of the integration
%i = find(pdf >= l);
%s = sum(pdf(i)) / spdf
is very crude. One can do much better but a it cumbersome to implement more precise integration.
