Multiple Object Tracking Capacity Calculator

Actual separately qualified MOT set size versus all targets-correct fraction threshold piecewise linear inverse, strictly decreasing branch, no extrapolation. Not a model-free universal capacity or independent-object probability correction.

Description

A tracking-capacity criterion depends on the task and definition of successful tracking.

A tracking-capacity criterion depends on the task and definition of successful tracking.^[1]

This tool linearly inverts a supplied strictly decreasing all-targets-correct curve without extrapolating a universal capacity.

When to use Multiple Object Tracking Capacity Calculator

This tool linearly inverts a supplied strictly decreasing all-targets-correct curve without extrapolating a universal capacity.

How to use Multiple Object Tracking Capacity Calculator and how it works

Prepare tracked target set sizes, proportions all targets correct, defined success fraction, using the input definitions and matching units below.
Enter the required fields and run Multiple Object Tracking Capacity Calculator.
Read result.observedInterpolatedTrackingSetSize using the units, signs and ordering explained below.
Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.

Input field	Meaning	Value type	Requirement
actualTrackedTargetSetSizes	Actual Tracked Target Set Sizes. Use the units and matching context stated in the calculation below.	array of number	Required; other constraints below
actualProportionsAllTargetsCorrect	Actual Proportions All Targets Correct. Use the units and matching context stated in the calculation below.	array of number	Required; other constraints below
callerDefinedSuccessFraction	Caller Defined Success Fraction. Use the units and matching context stated in the calculation below.	number	Required; fraction from 0 to 1; finite; other constraints below

Require aligned nonempty integer set sizes 1–1000000 in strictly increasing order and success fractions 0–1 in strictly decreasing order. Require at least two points through the interpolation helper. Reverse both lists to obtain increasing success coordinates, then interpolate set size at the caller criterion within their inclusive range. Return a possibly fractional set size without extrapolation; this is an all-targets-correct convention, not a corrected independent-item capacity.

setSizeAtCriterion=linearInterpolate(reverse(success),reverse(setSize),criterion)

Apply the input ordering, units and branch conditions stated above.

Output field	Meaning	Value type
result	Object containing the calculated or selected fields below.	object
result.observedInterpolatedTrackingSetSize	Possibly fractional set size at the in-range success criterion.	number

json

{
  "input": {
    "actualTrackedTargetSetSizes": [
      2,
      4,
      6
    ],
    "actualProportionsAllTargetsCorrect": [
      0.9,
      0.7,
      0.3
    ],
    "callerDefinedSuccessFraction": 0.5
  },
  "output": {
    "result": {
      "observedInterpolatedTrackingSetSize": 5
    }
  }
}

Limitations and assumptions

The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.

All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.

Alternative or Complementary methods

Use Useful Field of View Calculator for a complementary operation: Useful field of view depends on stimulus presentation, eccentricity and the threshold procedure used by a particular task.

Use Retention Percentage Calculator for a complementary operation: Retention percentage compares retained eligible items with the same initially eligible item set.

References

Multiple Object Tracking Capacity Calculator — tool.io

Similar or alternative tools

Useful Field of View Calculator
Useful field of view depends on stimulus presentation, eccentricity and the threshold procedure used by a particular task.
Retention Percentage Calculator
Retention percentage compares retained eligible items with the same initially eligible item set.