There are multiple methods to select the center of the oval where density is maximum. One of the methods is just by counting the points at each pixel (of any threshold), and subsequently get the approx center of the oval. Once you get the optimum center of the oval (or circle), you can iterate the size of oval (or circle) to get the optimum length of the oval which covers the most dense area.
Just for the simplicity, I have taken circle instaead of oval. But I think this would be a good starting point for you to develop your thought process so that you can extend this code to oval.
clc;clear;close all;
load(['clean_data.mat'])
t = linspace(0,2*pi,5000);
theta = deg2rad(90); % vertical ellipse
threshold=10;
U_vec_array=[min(Uvec):threshold:max(Uvec)];
V_vec_array=[min(Vvec):threshold:max(Vvec)];
size_dist= arrayfun(@(u) arrayfun(@(v) size(find(Uvec>u & Uvec<=u+threshold & Vvec>v & Vvec<=v+threshold),1),...
V_vec_array), U_vec_array, 'uni', 0);
size_dist_matrix=cat(1,size_dist{:});
[uvec_max,vvec_max]=find(size_dist_matrix==max(size_dist_matrix(:)))
U0=U_vec_array(uvec_max);
V0=V_vec_array(vvec_max);
% Iterating over diff radius
for radius = 5:5:20
a = radius; b = radius; % major and minor radii
xv = U0 + a*cos(t)*cos(theta) - b*sin(t)*sin(theta);
yv = V0 + b*sin(t)*cos(theta) + a*cos(t)*sin(theta);
[in,on] = inpolygon(Uvec,Vvec,xv,yv); % Points inside and on oval
sprintf('Number of points lies in the circle of center (%d, %d), and radius %d is %d:', U0, V0, radius, size(Uvec(in),1))
end
