comparison_plot.m

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% =========================================================================== %
%> @brief create a comparison plot
%>
%> this function creates a modified bland-altman plot from two vectors. the plot
%>  is saved to a file or displayed.
%>
%> @param gt_vec vector with the ground truth values
%> @param meas_vec vector with the measured values
%> @param i_step vector with the step indices
%> @param filename filename of the plot
%> @param options options for the plot
%> - "title" (default: "Bland-Altman plot") title of the plot
%> - "legend" (default: false) show a legend
%> - "compare_ptps" (default: false) compare the PTPs
%> - "ptp_vec" vector with the PTP numbers (only if "compare_ptps" is true)
%>
%> @retval mu mean of the differences (cm)
%> @retval sigma standard deviation of the differences (cm)
%> @retval mse mean squared error of the differences (cm^2)
%>
%> @copyright see the file @ref LICENSE in the root directory of the repository
% =========================================================================== %
function [mu, sigma, mse] = comparison_plot(gt_vec, meas_vec, i_step, filename, options)
 
arguments
    gt_vec (:,1) double
    meas_vec (:,1) double
    i_step (:,1) double
    filename (1,:) string
    options.title (1,:) char = "Bland-Altman plot"
    options.legend (1,1) logical = true
    options.compare_ptps (1,1) logical = false
    options.ptp_vec (:,1) categorical = categorical()
end
 
if options.compare_ptps
    assert(~isempty(options.ptp_vec), "The PTP vector must be provided")
end
 
% remove NaN values
assert(all(isnan(gt_vec) == isnan(meas_vec)), "The vectors must have the same NaN values")
i_step = i_step(~isnan(gt_vec));
gt_vec = gt_vec(~isnan(gt_vec));
meas_vec = meas_vec(~isnan(meas_vec));
if options.compare_ptps
    options.ptp_vec = options.ptp_vec(~isnan(gt_vec));
end
 
% check vector sizes
assert(length(gt_vec) == length(meas_vec), "The vectors must have the same length")
assert(length(gt_vec) == length(i_step), "The vectors must have the same length")
if options.compare_ptps
    assert(length(gt_vec) == length(options.ptp_vec), "The vectors must have the same length")
end
 
% convert to cm
gt_vec = gt_vec * 100;
meas_vec = meas_vec * 100;
 
% calculate the difference
diff_vec = gt_vec - meas_vec;
 
% calculate accuracy matrics
n = length(gt_vec);
mu = mean(diff_vec); % cm
mse = mean(diff_vec.^2); % cm^2
sigma = std(diff_vec); % cm
me = rmse(gt_vec, meas_vec); % cm
mu_rel = mean(diff_vec ./ gt_vec) * 100; % %
sigma_rel = std(diff_vec ./ gt_vec) * 100; % %
me_rel = rmse(gt_vec, meas_vec) / mean(gt_vec) * 100; % %
 
% create the plot
fig = figure(Visible="off", InnerPosition=[0,0,1920,1080]);
 
% bland altman part (absolute values)
subplot(2,2,1)
scatter(gt_vec, diff_vec, "filled", 'SizeData', 5)
hold on
yline(mean(diff_vec), "r", "LineWidth", 1.5)
yline(mean(diff_vec) + 1.96 * std(diff_vec), "r--", "LineWidth", 1.5)
yline(mean(diff_vec) - 1.96 * std(diff_vec), "r--", "LineWidth", 1.5)
xlabel("Ground Truth [cm]")
ylabel("Difference (VICON - IMU) [cm]")
title(sprintf("n = %d, \\mu = %.2f cm, \\sigma = %.2f cm, RMSE = %.2f cm", ...
    n, mu, sigma, me))
grid on
if options.legend
    legend("VICON - IMU", "Ground Truth", "95% CI", "Location", "best")
end
 
% bland altman part (relative values)
subplot(2,2,2)
scatter(gt_vec, diff_vec ./ gt_vec, "filled", 'SizeData', 5)
hold on
yline(mean(diff_vec ./ gt_vec), "r", "LineWidth", 1.5)
yline(mean(diff_vec ./ gt_vec) + 1.96 * std(diff_vec ./ gt_vec), "r--", "LineWidth", 1.5)
yline(mean(diff_vec ./ gt_vec) - 1.96 * std(diff_vec ./ gt_vec), "r--", "LineWidth", 1.5)
xlabel("Ground Truth [cm]")
ylabel("Relative Difference (VICON - IMU) [%]")
title(sprintf("n = %d, \\mu_{rel} = %.2f %%, \\sigma_{rel} = %.2f %%, RMSE_{rel} = %.2f %%", ...
    n, mu_rel, sigma_rel, me_rel), "Interpreter","tex")
grid on
if options.legend
    legend("VICON - IMU", "Ground Truth", "95% CI", "Location", "best")
end
 
% Q-Q plot (only if ptp comparison is disabled)
if ~options.compare_ptps
    subplot(2,2,3)
    qqplot(gt_vec, diff_vec)
    xlabel("Ground Truth [cm]")
    ylabel("Difference (VICON - IMU) [cm]")
    title("Q-Q plot")
    grid on
end
 
% boxplot per PTP (only if ptp comparison is enabled)
if options.compare_ptps
    subplot(2,2,3)
    boxplot(diff_vec, options.ptp_vec, 'Notch', true)
    xlabel("PTP")
    ylabel("Difference (VICON - IMU) [cm]")
    title("Boxplot per PTP")
    grid on
end
 
% error vs step (spearman correlation plot between error and step index)
% calculate the correlation
r = corr(diff_vec, i_step, Type="Spearman");
[p,S] = polyfit(diff_vec, i_step, 1);
[fit, delta] = polyval(p, diff_vec, S);
 
%sort the data
[diff_vec, idx] = sort(diff_vec);
i_step = i_step(idx);
fit = fit(idx);
delta = delta(idx);
 
% plot
subplot(2,2,4)
scatter(diff_vec, i_step, "filled", 'SizeData', 5)
hold on
plot(diff_vec, fit, 'r', 'LineWidth', 0.75)
xlabel("Difference (VICON - IMU) [cm]")
ylabel("Step Index")
title(sprintf("Error vs Step Index, r = %.2f", r))
grid on
 
% figure title
sgtitle(options.title)
 
saveas(fig, filename)
close(fig)
 
end