Introduction
In this article, we'll explore the concept of 1D moving averages applied to XY position-time 3D matrices. By taking the mean value across specific XY areas over time, we can extract valuable insights and uncover underlying temporal trends. This technique allows us to filter out noise, focus on localized regions, and identify patterns that evolve over time.
By applying the moving average methodology, we aim to highlight trends in XY position-time data and provide a smoothed representation of the original information. This enables us to gain a clearer understanding of how objects or phenomena evolve, detect anomalies, and extract meaningful features.
Throughout this article, we will provide MATLAB examples to demonstrate the calculation of 1D moving averages from the mean values of XY position-time 3D matrices. You'll have the opportunity to adjust parameters, explore different areas of interest, and visualize the results.
Let's Practice ..
In this example, let's consider a 3D matrix that contains information about xy positions and time. We will calculate the 1D moving average by taking the mean value of the specified area across time. Here's the MATLAB code:
% Generate a random 3D matrix of size 50x50x10
rng(1); % Set random seed for reproducibility
matrixData = randn(50, 50, 10);
% Define the area of interest within the matrix
startX = 10; % Starting X-coordinate of the area
endX = 30; % Ending X-coordinate of the area
startY = 15; % Starting Y-coordinate of the area
endY = 35; % Ending Y-coordinate of the area
% Calculate the mean value within the specified area across time
movingAvg = mean(mean(matrixData(startX:endX, startY:endY, :), 1), 2);
% Plot the original data and the moving average
figure;
subplot(2,1,1); plot(matrixData(:), 'b', 'LineWidth', 1.5);
xlabel('Index');
ylabel('Value');
title('Moving Average within Specified Area across Time');
legend('Original Data', 'Moving Average');
subplot(2,1,2);plot(movingAvg(:), 'r', 'LineWidth', 2);
xlabel('Index');
ylabel('Value');
title('Moving Average within Specified Area across Time');
legend('Original Data', 'Moving Average');
In this example, we generate a random 3D matrix using randn for demonstration purposes. The matrix has dimensions 50x50x10, representing xy positions and time.
We define the area of interest within the matrix by specifying the starting and ending coordinates along the xy dimensions: startX, endX, startY, and endY. We consider the entire range of the time dimension.
To calculate the moving average, we use the mean function twice: first, across the rows using mean(..., 1), and then across the columns using mean(..., 2). This gives us the mean value within the specified area across time.
Finally, we plot the original data in blue (top) and the calculated moving average in red (bottom) using the plot function. The x-axis represents the index of the values, and the y-axis represents the value itself. The plot displays the original data along with the moving average within the specified area across time.
Feel free to adjust the area of interest (startX, endX, startY, endY) to suit your specific requirements and explore different regions within the matrix to calculate the moving average.
If you have any further questions or need assistance, please let me know!
Good day !
-asb, founder of myresearchxpress
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