How to calculate the number of points in each rectangular grid cell

I possess 10,000 data points corresponding to each value of x and y, and I intend to determine the count of (x, y) points falling within distinct grid cells. To achieve this, I partition the x-y plane into a meshgrid, subsequently tallying the occurrence of points within each cell. This process involves calculating the frequency of points present in each individual cell.

Below is the code I have formulated to carry out this procedure:

x_hit = transpose(x(end,:)); %x data

y_hit = transpose(y(end,:)); % y data

x_values = linspace(0,1 , 100);

y_values = linspace(5, 14, 100);

% Create a grid of x and y values

[x_grid, y_grid] = meshgrid(x_values, y_values);

cell_counts = zeros(length(x_values), length(y_values));

% Iterate through each trajectory

for i = 1:length(x_hit)

x_pos = x_hit(i);

y_pos = y_hit(i);

% Find the indices of the cell in the grid

x_cell = find(x_values <= x_pos, 1, 'last');

y_cell = find(y_values <= y_pos, 1, 'last');

% Increment the cell count

cell_counts(x_cell, y_cell) = cell_counts(x_cell, y_cell) + 1;

end

The purpose of "cell_counts" is to calculate the quantity of points within each cell. However, I am uncertain whether the code is functioning correctly for my specific issue, as the anticipated outcome has not been achieved. Could someone please assess whether the aforementioned code is suitable for my task? Alternatively, is there an alternative method that could be utilized?

The total counts of points in cells should be 10,000.

Answer 1

[Star Strider]

Perhaps the histcounts2 function could make this easier.

EDIT — (8 Aug 2023 at 15:49)

Added this example —

x_hit = 0.5+randn(1E4,1)/3;                                     % Missing Data
y_hit = randn(1E4,1)+10;                                        % Missing Data

x_values = linspace(0,1 , 100);
y_values = linspace(5, 14, 100);
% Create a grid of x and y values
[x_grid, y_grid] = meshgrid(x_values, y_values);
cell_counts = zeros(length(x_values), length(y_values));

N = histcounts2(x_hit, y_hit, x_values, y_values);              % Use 'histcounts2'

figure
b = bar3(N);
for k = 1:length(b)
    zdata = b(k).ZData;
    b(k).CData = zdata;
    b(k).FaceColor = 'interp';
end
xticklabels(x_values)
yticklabels(y_values)
colormap(turbo)
colorbar
xlabel('x\_values')
ylabel('y\_values')
zlabel('Counts')

.

[Sagar Karmakar]

Hi @Star Strider Thanks for your answer but perhaps this does not work for my data set. Here is my data set....

I aim to determine the count of (x, y) points within individual grid cells. This will allow me to compute the frequency density P for each cell. Subsequently, I intend to create a contour plot of P in the x-y plane.

The challenge with the code provided in the initial question is that although it effectively tallies the points within each cell, the resulting contour plot visualization does not accurately represent high points of P (from the data sets clearly, P should be high at some points)

Thank you!

[Star Strider]

Win11 crashed again for some sort of ‘azure’ and ‘autopilot’ (expletives deleted). I’m going Linux.

That aside, there is not much in your data.

This is the best I can do with them —

LD1 = load('x_hit.mat');
LD2 = load('y_hit.mat');

x_hit = LD1.x_hit;
y_hit = LD2.y_hit;

% x_hit = 0.5+randn(1E4,1)/3;                                     % Missing Data
% y_hit = randn(1E4,1)+10;                                        % Missing Data

x_values = linspace(0,1 , 100);
y_values = linspace(5, 14, 100);
% Create a grid of x and y values
[x_grid, y_grid] = meshgrid(x_values, y_values);
cell_counts = zeros(length(x_values), length(y_values));

[N,Xedg,Yedg] = histcounts2(x_hit, y_hit, x_values, y_values);              % Use 'histcounts2'

Nsz = size(N)

Nsz = 1×2

99 99

idx = find(N>0);
Xvalue = x_grid(idx);
Yvalue = y_grid(idx);
Cell_Counts = N(idx);
Cell_Freq = Cell_Counts/sum(Cell_Counts);

CountsTable = table(Xvalue, Yvalue, Cell_Counts, Cell_Freq)

CountsTable = 17×4 table
    Xvalue     Yvalue    Cell_Counts    Cell_Freq
    _______    ______    ___________    _________

    0.25253    11.727          1         0.0002  
    0.26263    11.636        104         0.0208  
    0.42424    10.818          1         0.0002  
    0.43434    10.727        189         0.0378  
    0.44444    10.636        429         0.0858  
    0.45455    10.545         18         0.0036  
    0.90909    12.364          5          0.001  
    0.90909    12.455        279         0.0558  
    0.90909    12.545        335          0.067  
    0.90909    12.636          6         0.0012  
    0.91919    12.273         18         0.0036  
    0.91919    12.364       1639         0.3278  
    0.91919    12.455       1738         0.3476  
    0.91919    12.545         24         0.0048  
    0.92929    12.273        106         0.0212  
    0.92929    12.364        106         0.0212  

figure
b = bar3(N);
for k = 1:length(b)
    zdata = b(k).ZData;
    b(k).CData = zdata;
    b(k).FaceColor = 'interp';
end
Ax = gca;
% Ax.YDir = 'reverse';
xticks(0:20:100)
xt = xticks;
yt = yticks;
xticklabels(linspace(min(x_values), max(x_values),numel(xt)))
yticklabels(linspace(min(y_values), max(y_values),numel(yt)))
colormap(turbo)
colorbar
xlabel('x\_values')
ylabel('y\_values')
zlabel('Counts')

[x_mtx,y_mtx] = ndgrid(x_values(1:end-1), y_values(1:end-1));
z_mtx = griddata(x_mtx(:), y_mtx(:), N(:), x_mtx, y_mtx);

figure
contour(x_mtx, y_mtx, log(z_mtx+0.01))
grid
colormap(turbo)
colorbar
xlabel('X')
ylabel('Y')
title('Contour Plot of  2-D Histogram Data (Logarithmic)')

figure
surfc(x_mtx, y_mtx, z_mtx+0.01, 'EdgeColor','interp')
grid
colormap(turbo)
colorbar
Ax = gca;
Ax.ZScale = 'log';
xlabel('X')
ylabel('Y')
zlabel('Counts')
title('Surface Plot of  2-D Histogram Data')
grid('on')

It is necessary to take the logarithms of the offset counts to plot the smaller cell count values.

.