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Use Kalman Filter for Object Tracking

This example shows how to use the vision.KalmanFilter object and configureKalmanFilter function to track objects.

This example is a function with its main body at the top and helper routines in the form of nested functions.

function kalmanFilterForTracking


The Kalman filter has many uses, including applications in control, navigation, computer vision, and time series econometrics. This example illustrates how to use the Kalman filter for tracking objects and focuses on three important features:

  • Prediction of object's future location

  • Reduction of noise introduced by inaccurate detections

  • Facilitating the process of association of multiple objects to their tracks

Challenges of Object Tracking

Before showing the use of Kalman filter, let us first examine the challenges of tracking an object in a video. The following video shows a green ball moving from left to right on the floor.


The white region over the ball highlights the pixels detected using vision.ForegroundDetector, which separates moving objects from the background. The background subtraction only finds a portion of the ball because of the low contrast between the ball and the floor. In other words, the detection process is not ideal and introduces noise.

To easily visualize the entire object trajectory, we overlay all video frames onto a single image. The "+" marks indicate the centroids computed using blob analysis.


Two issues can be observed:

  1. The region's center is usually different from the ball's center. In other words, there is an error in the measurement of the ball's location.

  2. The location of the ball is not available when it is occluded by the box, i.e. the measurement is missing.

Both of these challenges can be addressed by using the Kalman filter.

Track a Single Object Using Kalman Filter

Using the video which was seen earlier, the trackSingleObject function shows you how to:

  • Create vision.KalmanFilter by using configureKalmanFilter

  • Use predict and correct methods in a sequence to eliminate noise present in the tracking system

  • Use predict method by itself to estimate ball's location when it is occluded by the box

The selection of the Kalman filter parameters can be challenging. The configureKalmanFilter function helps simplify this problem. More details about this can be found further in the example.

The trackSingleObject function includes nested helper functions. The following top-level variables are used to transfer the data between the nested functions.

frame            = [];  % A video frame
detectedLocation = [];  % The detected location
trackedLocation  = [];  % The tracked location
label            = '';  % Label for the ball
utilities        = [];  % Utilities used to process the video

The procedure for tracking a single object is shown below.

function trackSingleObject(param)
  % Create utilities used for reading video, detecting moving objects,
  % and displaying the results.
  utilities = createUtilities(param);

  isTrackInitialized = false;
  while hasFrame(utilities.videoReader)
    frame = readFrame(utilities.videoReader);

    % Detect the ball.
    [detectedLocation, isObjectDetected] = detectObject(frame);

    if ~isTrackInitialized
      if isObjectDetected
        % Initialize a track by creating a Kalman filter when the ball is
        % detected for the first time.
        initialLocation = computeInitialLocation(param, detectedLocation);
        kalmanFilter = configureKalmanFilter(param.motionModel, ...
          initialLocation, param.initialEstimateError, ...
          param.motionNoise, param.measurementNoise);

        isTrackInitialized = true;
        trackedLocation = correct(kalmanFilter, detectedLocation);
        label = 'Initial';
        trackedLocation = [];
        label = '';

      % Use the Kalman filter to track the ball.
      if isObjectDetected % The ball was detected.
        % Reduce the measurement noise by calling predict followed by
        % correct.
        trackedLocation = correct(kalmanFilter, detectedLocation);
        label = 'Corrected';
      else % The ball was missing.
        % Predict the ball's location.
        trackedLocation = predict(kalmanFilter);
        label = 'Predicted';

  end % while


There are two distinct scenarios that the Kalman filter addresses:

  • When the ball is detected, the Kalman filter first predicts its state at the current video frame, and then uses the newly detected object location to correct its state. This produces a filtered location.

  • When the ball is missing, the Kalman filter solely relies on its previous state to predict the ball's current location.

You can see the ball's trajectory by overlaying all video frames.

param = getDefaultParameters();  % get Kalman configuration that works well
                                 % for this example

trackSingleObject(param);  % visualize the results

Explore Kalman Filter Configuration Options

Configuring the Kalman filter can be very challenging. Besides basic understanding of the Kalman filter, it often requires experimentation in order to come up with a set of suitable configuration parameters. The trackSingleObject function, defined above, helps you to explore the various configuration options offered by the configureKalmanFilter function.

The configureKalmanFilter function returns a Kalman filter object. You must provide five input arguments.

kalmanFilter = configureKalmanFilter(MotionModel, InitialLocation,
         InitialEstimateError, MotionNoise, MeasurementNoise)

The MotionModel setting must correspond to the physical characteristics of the object's motion. You can set it to either a constant velocity or constant acceleration model. The following example illustrates the consequences of making a sub-optimal choice.

param = getDefaultParameters();         % get parameters that work well
param.motionModel = 'ConstantVelocity'; % switch from ConstantAcceleration
                                        % to ConstantVelocity
% After switching motion models, drop noise specification entries
% corresponding to acceleration.
param.initialEstimateError = param.initialEstimateError(1:2);
param.motionNoise          = param.motionNoise(1:2);

trackSingleObject(param); % visualize the results

Notice that the ball emerged in a spot that is quite different from the predicted location. From the time when the ball was released, it was subject to constant deceleration due to resistance from the carpet. Therefore, constant acceleration model was a better choice. If you kept the constant velocity model, the tracking results would be sub-optimal no matter what you selected for the other values.

Typically, you would set the InitialLocation input to the location where the object was first detected. You would also set the InitialEstimateError vector to large values since the initial state may be very noisy given that it is derived from a single detection. The following figure demonstrates the effect of misconfiguring these parameters.

param = getDefaultParameters();  % get parameters that work well
param.initialLocation = [0, 0];  % location that's not based on an actual detection
param.initialEstimateError = 100*ones(1,3); % use relatively small values

trackSingleObject(param); % visualize the results

With the misconfigured parameters, it took a few steps before the locations returned by the Kalman filter align with the actual trajectory of the object.

The values for MeasurementNoise should be selected based on the detector's accuracy. Set the measurement noise to larger values for a less accurate detector. The following example illustrates the noisy detections of a misconfigured segmentation threshold. Increasing the measurement noise causes the Kalman filter to rely more on its internal state rather than the incoming measurements, and thus compensates for the detection noise.

param = getDefaultParameters();
param.segmentationThreshold = 0.0005; % smaller value resulting in noisy detections
param.measurementNoise      = 12500;  % increase the value to compensate
                                      % for the increase in measurement noise

trackSingleObject(param); % visualize the results

Typically objects do not move with constant acceleration or constant velocity. You use the MotionNoise to specify the amount of deviation from the ideal motion model. When you increase the motion noise, the Kalman filter relies more heavily on the incoming measurements than on its internal state. Try experimenting with MotionNoise parameter to learn more about its effects.

Now that you are familiar with how to use the Kalman filter and how to configure it, the next section will help you learn how it can be used for multiple object tracking.

Note: In order to simplify the configuration process in the above examples, we used the configureKalmanFilter function. This function makes several assumptions. See the function's documentation for details. If you require greater level of control over the configuration process, you can use the vision.KalmanFilter object directly.

Track Multiple Objects Using Kalman Filter

Tracking multiple objects poses several additional challenges:

  • Multiple detections must be associated with the correct tracks

  • You must handle new objects appearing in a scene

  • Object identity must be maintained when multiple objects merge into a single detection

The vision.KalmanFilter object together with the assignDetectionsToTracks function can help to solve the problems of

  • Assigning detections to tracks

  • Determining whether or not a detection corresponds to a new object, in other words, track creation

  • Just as in the case of an occluded single object, prediction can be used to help separate objects that are close to each other

To learn more about using Kalman filter to track multiple objects, see the example titled Motion-Based Multiple Object Tracking.

Utility Functions Used in the Example

Utility functions were used for detecting the objects and displaying the results. This section illustrates how the example implemented these functions.

Get default parameters for creating Kalman filter and for segmenting the ball.

function param = getDefaultParameters
  param.motionModel           = 'ConstantAcceleration';
  param.initialLocation       = 'Same as first detection';
  param.initialEstimateError  = 1E5 * ones(1, 3);
  param.motionNoise           = [25, 10, 1];
  param.measurementNoise      = 25;
  param.segmentationThreshold = 0.05;

Detect and annotate the ball in the video.

function showDetections()
  param = getDefaultParameters();
  utilities = createUtilities(param);
  trackedLocation = [];

  idx = 0;
  while hasFrame(utilities.videoReader)
    frame = readFrame(utilities.videoReader);
    detectedLocation = detectObject(frame);
    % Show the detection result for the current video frame.

    % To highlight the effects of the measurement noise, show the detection
    % results for the 40th frame in a separate figure.
    idx = idx + 1;
    if idx == 40
      combinedImage = max(repmat(utilities.foregroundMask, [1,1,3]), im2single(frame));
      figure, imshow(combinedImage);
  end % while

  % Close the window which was used to show individual video frame.

Detect the ball in the current video frame.

function [detection, isObjectDetected] = detectObject(frame)
  grayImage = im2gray(im2single(frame));
  utilities.foregroundMask = step(utilities.foregroundDetector, grayImage);
  detection = step(utilities.blobAnalyzer, utilities.foregroundMask);
  if isempty(detection)
    isObjectDetected = false;
    % To simplify the tracking process, only use the first detected object.
    detection = detection(1, :);
    isObjectDetected = true;

Show the current detection and tracking results.

function annotateTrackedObject()
  % Combine the foreground mask with the current video frame in order to
  % show the detection result.
  combinedImage = max(repmat(utilities.foregroundMask, [1,1,3]), im2single(frame));

  if ~isempty(trackedLocation)
    shape = 'circle';
    region = trackedLocation;
    region(:, 3) = 5;
    combinedImage = insertObjectAnnotation(combinedImage, shape, ...
      region, {label}, 'AnnotationColor', 'red');
  step(utilities.videoPlayer, combinedImage);

Show trajectory of the ball by overlaying all video frames on top of each other.

function showTrajectory
  % Close the window which was used to show individual video frame.

  % Create a figure to show the processing results for all video frames.
  figure; imshow(utilities.accumulatedImage/2+0.5); hold on;
  plot(utilities.accumulatedDetections(:,1), ...
    utilities.accumulatedDetections(:,2), 'k+');

  if ~isempty(utilities.accumulatedTrackings)
    plot(utilities.accumulatedTrackings(:,1), ...
      utilities.accumulatedTrackings(:,2), 'r-o');
    legend('Detection', 'Tracking');

Accumulate video frames, detected locations, and tracked locations to show the trajectory of the ball.

function accumulateResults()
  utilities.accumulatedImage      = max(utilities.accumulatedImage, frame);
  utilities.accumulatedDetections ...
    = [utilities.accumulatedDetections; detectedLocation];
  utilities.accumulatedTrackings  ...
    = [utilities.accumulatedTrackings; trackedLocation];

For illustration purposes, select the initial location used by the Kalman filter.

function loc = computeInitialLocation(param, detectedLocation)
  if strcmp(param.initialLocation, 'Same as first detection')
    loc = detectedLocation;
    loc = param.initialLocation;

Create utilities for reading video, detecting moving objects, and displaying the results.

function utilities = createUtilities(param)
  % Create System objects for reading video, displaying video, extracting
  % foreground, and analyzing connected components.
  utilities.videoReader = VideoReader('singleball.mp4');
  utilities.videoPlayer = vision.VideoPlayer('Position', [100,100,500,400]);
  utilities.foregroundDetector = vision.ForegroundDetector(...
    'NumTrainingFrames', 10, 'InitialVariance', param.segmentationThreshold);
  utilities.blobAnalyzer = vision.BlobAnalysis('AreaOutputPort', false, ...
    'MinimumBlobArea', 70, 'CentroidOutputPort', true);

  utilities.accumulatedImage      = 0;
  utilities.accumulatedDetections = zeros(0, 2);
  utilities.accumulatedTrackings  = zeros(0, 2);