Tracking

Tracking connects objects or particles frame-to-frame (or volume-to-volume in 3D) over time-lapse sequences.

A binary object typically has a different object ID in consecutive frames. Tracking nodes assign a new track ID to objects in such way that objects keep that ID over the whole time-lapse.

Therefore, tracking is necessary when investigating single object behavior over time.

There are two distinct tracking nodes:

Track Objects that takes a binary layer as input and connects binary objects that overlap frame-to-frame.
Track Particles that takes a table with objects as input and connects objects as they fit the motion model while minimizing global error frame-to-frame. The table must contain time and position of each object. This is useful when objects can be reduced to points of mass: particles.

Both nodes output a table that has track ID assigned to objects that are part of a track.

In order to see tracked objects in the preview they must be accumulated using Accumulate Tracks.

Object Position

Convenience measurement nodes for calculating the time and position of each object. The same measurement can be done using ordinary Measure object.

Time & Center

It produces a table where every row corresponds to an object (input A - Binary).

The node measures Time and Center for each object (together with default book keeping columns):

loop indexes for book keeping (one-based),
object entity and id for book keeping,
Time [s] acquisition time assigned to each objects and
Center calibrated X and Y (and Z if 3D) coordinate.

Parameters

Input

A (Binary)

Output

R (Table)

Control

See also: Object Position (group)

Time & CenterAbs

It produces a table where every row corresponds to an object (input A - Binary).

The node measures Time and CenterAbs for each object (together with default book keeping columns):

loop indexes for book keeping (one-based),
object entity and id for book keeping,
Time [s] acquisition time assigned to each objects and
CenterAbs stage calibrated X and Y (and Z if 3D) coordinate.

Parameters

Input

A (Binary)

Output

R (Table)

Control

See also: Object Position (group)

Time & Centroid

It produces a table where every row corresponds to an object (input A - Binary).

The node measures Time and Center for each object (together with default book keeping columns):

loop indexes for book keeping (one-based),
object entity and id for book keeping,
Time [s] acquisition time assigned to each objects and
Centroid calibrated X and Y (and Z if 3D) coordinate.

Parameters

Input

A (Binary)
B (Channel)

Output

R (Table)

Control

See also: Object Position (group)

Time & CentroidAbs

It produces a table where every row corresponds to an object (input A - Binary).

The node measures Time and CentroidAbs for each object (together with default book keeping columns):

loop indexes for book keeping (one-based),
object entity and id for book keeping,
Time [s] acquisition time assigned to each objects and
CentroidAbs stage calibrated X and Y (and Z if 3D) coordinate.

Parameters

Input

A (Binary)
B (Channel)

Output

R (Table)

Control

See also: Object Position (group)

Tracking

Track Objects

The node takes objects (input A - Binary) and connects them based on their frame-to-frame overlap area. When there are more candidates (more objects in one frame overlap with an object on the other) the one with the biggest overlap is chosen.

The node returns a table with following columns:

loop indexes for book keeping (one-based),
object entity and ID for book keeping,
TrackId acquisition time assigned to each objects.

Parameters

Input

A (Binary)

Output

R (Table)

Control

PreviewMode (Number)
PreviewModeFrameCount (Number)

Track Particles

Advanced

The node takes particles represented by time and position (input A - Table) and connects them based on predicted position. Every particle is assigned a cost based on the distance from the predicted point. The algorithm minimizes the sum of the costs in each frame-to-frame linking step.

There are two models implemented:

Random motion model predicts the particle at the same place and
Constant speed model predicts the next position using Kalman filter and current position and velocity.

The algorithm is inspired by the Robust single-particle tracking in live-cell time-lapse sequences paper by Jaqaman, K. et al. published in Nature Methods 2008 Vol. 5 No. 8.published in Nature Methods 2008 Vol. 5 No. 8.

Parameters:

Source time and position columns define particle positions,
Motion model is either Random motion or Constant speed,
Stdev multiplication factor is the relative cut-off distance; the bigger the number more objects are allowed to compete for continuation of a track,
Maximum speed/distance is absolute cut-off ; the bigger the distance more objects are allowed to compete for continuation of a track,
Close gaps defines how many gaps can be in the track and
Distinguishing feature and its cut-off lets the user specify a column that may help the algorithm to discriminate between objects.

Particle tracking dialog — Particle tracking settings

The node returns a table with following columns:

loop indexes for book keeping (one-based),
object entity and ID for book keeping,
Time [s] acquisition time as defined in the settings dialog,
Position X and Y (and Z if 3D) coordinate of the position defined in the settings dialog and
TrackId ID of the track the object belongs to or empty if there is none.

Algorithm overview

1. Frame-to-frame linking

The algorithm works with a set of active tracks. Initially - in the first frame each object is set to be an active track. Then the algorithm goes through all frames in time and tries to extend the track. An object not fitting to any track may initiate a new active track (if ignore new tracks is unchecked) at any time as well. At a given frame, each track can be linked to at most one object. If there is no suitable link a gap is introduced. In case that Gap Closing is disabled, the track is terminated and no longer active for further linking. If gaps are allowed the track remains active. It can link until the gap length reaches the threshold which terminates it.

The goal of linking is to find the best correspondence between active tracks so far and objects in the current frame. A probability for each possible link (active track with object) together with a probability of track ending is calculated. The result is the solution with globally (over all possibilities: linking, gap closing, track ending and new track starting) highest probability.

The probability of a link is the likelihood that the track will extend through the given object. As each track is built a Kalman filter is applied and its prediction and error estimate are used to calculate a multidimensional Gaussian probability distribution function for a given frame. From this function it is possible calculate the probability that any object links with the given track.

The probability of non-linking (i.e. track termination) is given by user as a multiplication factor of Standard deviation. The lower the factor the smaller the linking area becomes and the probability of non-linking increases. The Standard Deviation is calculated for each track and time-point. With increasing object speeds the Standard deviation increases as well. This criterion is relative.

Additionally, user can set an absolute maximum speed, which eliminates impossible links right away.

Splitting or merging is not possible.

2. Distinguishing feature

Some “distinguishing” object feature may be selected to be included into probability calculation. Feature that is selected should have the ability to distinguish between objects that form distinct tracks. Maximum change per second may be set for every feature as a restriction. Infinity means that the feature is not restricted.

Parameters

Input

A (Table)

Output

R (Table)

Control

xColumn (Text)
yColumn (Text)
tColumn (Text)
fColumn (Text)
motionModel (Number)
stdevFactor (Number)
maxSpeed (Number)
maxGap (Number)
maxF (Number)
PreviewMode (Number)
PreviewModeFrameCount (Number)

Tracks

An object track or trajectory (schematically shown in the picture) is a sequence of segments that connects successive object positions $P_{i}$ . Each object position has a time value $t_{i}$ associated with it.

The tracking overlay shows track IDs and the track itself.

Accumulate Tracks

2D/3D

Accumulates the tracked objects over whole time-lapse. It filters out objects that are not part of any track and optionally removes objects that are in tracks shorter than specified number. It also groups the records by track IDs.

Parameters:

Min. segment count optionally filters the tracks based on their length.
Apply only on segment count in preview is an optimization for GA3 preview ; when checked the preview runs only on the number of frames specified.

Accumulate tracks dialog — Accumulate tracks settings

Accumulated tracks — Accumulated tacks results

The tracking nodes don’t accumulate their output. It means that the table contains objects for only one frame or volume. This is handy for easy addition of other measurement features by just adding the columns instead of having to use a more complex Join records node.

Parameters

Input

A (Table)

Output

R (Table)

Control

MinSegmentCount (Number)
PreviewMode (Number)
PreviewModeFrameCount (Number)

MSD

2D/3D

Advanced

The node calculates Mean Squared Displacement (MSD) over accumulated tracks.

Parameters define the source columns for the calculation.

The node returns a table containing one row for every track $Δ t$ segment and following columns:

object entity for book keeping,
TrackId,
ΔTime [s] is calibrated $Δ t$ ,
MSD [µm²] is mean squared displacement over $Δ t$ track segments,
Stdev [µm²] is standard deviation of squared displacements over $Δ t$ track segments,
Count number $Δ t$ track segments.

For each track it computes the MSDs as a function of the time lag $Δ t$ .

MSD is the standard statistic to investigate diffusion. In the case of free diffusion, the slope of the MSD is equal to the diffusion coefficient $D$ .

Parameters

Input

A (Table)

Output

R (Table)

Control

TrackId (Text)
Time (Text)
PositionX (Text)
PositionY (Text)
PositionZ (Text)

Tracking Features

Tracking features measure dynamic properties of objects:

at any given point in time $t_{i}$ (Feature Derivative and Motion Features) or
as aggregates for the whole track (Track Features).

Feature Derivative

2D/3D

Advanced

The node measures any selected feature rate of change.

F^{'} = \frac{Δ F}{Δ t}

Parameters

Input

A (Table)

Output

R (Table)

Control

Time (Text)
Feature (Text)
NewColumnName (Text)
Unit (Text)

Motion Features

2D/3D

Advanced

Motion features measure dynamic properties of tracked objects at any given point in time $t_{i}$ .

Motion features dialog — Motion features settings

Tracks must be accumulated using Accumulate Tracks.

Parameters

Input

A (Table)

Output

R (Table)

Control

Time (Text)
PositionX (Text)
PositionY (Text)
PositionZ (Text)
FeatureModel (ListModel)

Track Features

2D/3D

Advanced

Track features measure aggregated dynamic properties for whole tracks.

Track features dialog — Track features settings

Tracks must be accumulated using Accumulate Tracks.

Parameters

Input

A (Table)

Output

R (Table)

Control

Time (Text)
PositionX (Text)
PositionY (Text)
PositionZ (Text)
FeatureModel (ListModel)

Results

Export Tracking

2D/3D

Advanced

Parameters

Input

A (Table)

Output

R (Table)

Control

NIS.ai Measurement features