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Metrics for multiple object tracker benchmarking.

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The py-motmetrics library provides a Python implementation of metrics for benchmarking multiple object trackers (MOT).

While benchmarking single object trackers is rather straightforward, measuring the performance of multiple object trackers needs careful design as multiple correspondence constellations can arise (see image below). A variety of methods have been proposed in the past and while there is no general agreement on a single method, the methods of [1,2,3,4] have received considerable attention in recent years. py-motmetrics implements these metrics.

Pictures courtesy of Bernardin, Keni, and Rainer Stiefelhagen [1]

In particular py-motmetrics supports CLEAR-MOT[1,2] metrics and ID[4] metrics. Both metrics attempt to find a minimum cost assignment between ground truth objects and predictions. However, while CLEAR-MOT solves the assignment problem on a local per-frame basis, ID-MEASURE solves the bipartite graph matching by finding the minimum cost of objects and predictions over all frames. This blog-post by Ergys illustrates the differences in more detail.

Features at a glance

  • Variety of metrics
    Provides MOTA, MOTP, track quality measures, global ID measures and more. The results are comparable with the popular MOTChallenge benchmarks (*1).
  • Distance agnostic
    Supports Euclidean, Intersection over Union and other distances measures.
  • Complete event history
    Tracks all relevant per-frame events suchs as correspondences, misses, false alarms and switches.
  • Flexible solver backend
    Support for switching minimum assignment cost solvers. Supports scipy, ortools, munkres out of the box. Auto-tunes solver selection based on availability and problem size.
  • Easy to extend
    Events and summaries are utilizing pandas for data structures and analysis. New metrics can reuse already computed values from depending metrics.


py-motmetrics implements the following metrics. The metrics have been aligned with what is reported by MOTChallenge benchmarks.

import motmetrics as mm
# List all default metrics
mh = mm.metrics.create()
Name Description
num_frames Total number of frames.
num_matches Total number matches.
num_switches Total number of track switches.
num_false_positives Total number of false positives (false-alarms).
num_misses Total number of misses.
num_detections Total number of detected objects including matches and switches.
num_objects Total number of unique object appearances over all frames.
num_predictions Total number of unique prediction appearances over all frames.
num_unique_objects Total number of unique object ids encountered.
mostly_tracked Number of objects tracked for at least 80 percent of lifespan.
partially_tracked Number of objects tracked between 20 and 80 percent of lifespan.
mostly_lost Number of objects tracked less than 20 percent of lifespan.
num_fragmentations Total number of switches from tracked to not tracked.
motp Multiple object tracker precision.
mota Multiple object tracker accuracy.
precision Number of detected objects over sum of detected and false positives.
recall Number of detections over number of objects.
idfp ID measures: Number of false positive matches after global min-cost matching.
idfn ID measures: Number of false negatives matches after global min-cost matching.
idtp ID measures: Number of true positives matches after global min-cost matching.
idp ID measures: global min-cost precision.
idr ID measures: global min-cost recall.
idf1 ID measures: global min-cost F1 score.
obj_frequencies pd.Series Total number of occurrences of individual objects over all frames.
pred_frequencies pd.Series Total number of occurrences of individual predictions over all frames.
track_ratios pd.Series Ratio of assigned to total appearance count per unique object id.
id_global_assignment dict ID measures: Global min-cost assignment for ID measures.

MOTChallenge compatibility

py-motmetrics produces results compatible with popular MOTChallenge benchmarks (*1). Below are two results taken from MOTChallenge Matlab devkit corresponding to the results of the CEM tracker on the training set of the 2015 MOT 2DMark.

 IDF1  IDP  IDR| Rcll  Prcn   FAR| GT  MT  PT  ML|   FP    FN  IDs   FM| MOTA  MOTP MOTAL
 55.8 73.0 45.1| 58.2  94.1  0.18|  8   1   6   1|   13   150    7    7| 52.6  72.3  54.3

 IDF1  IDP  IDR| Rcll  Prcn   FAR| GT  MT  PT  ML|   FP    FN  IDs   FM| MOTA  MOTP MOTAL
 64.5 82.0 53.1| 60.9  94.0  0.25| 10   5   4   1|   45   452    7    6| 56.4  65.4  56.9

In comparison to py-motmetrics

                IDF1   IDP   IDR  Rcll  Prcn GT MT PT ML FP  FN IDs  FM  MOTA  MOTP
TUD-Campus     55.8% 73.0% 45.1% 58.2% 94.1%  8  1  6  1 13 150   7   7 52.6% 0.277
TUD-Stadtmitte 64.5% 82.0% 53.1% 60.9% 94.0% 10  5  4  1 45 452   7   6 56.4% 0.346

(*1) Besides naming conventions, the only obvious differences are

  • Metric FAR is missing. This metric is given implicitly and can be recovered by FalsePos / Frames * 100.
  • Metric MOTP seems to be off. To convert compute (1 - MOTP) * 100. MOTChallenge benchmarks compute MOTP as percentage, while py-motmetrics sticks to the original definition of average distance over number of assigned objects [1].

You can compare tracker results to ground truth in MOTChallenge format by

python -m motmetrics.apps.eval_motchallenge --help

For MOT16/17, you can run

python -m motmetrics.apps.evaluateTracking --help


To install latest development version of py-motmetrics (usually a bit more recent than PyPi below)

pip install git+

Install via PyPi

To install py-motmetrics use pip

pip install motmetrics

Python 3.5/3.6/3.9 and numpy, pandas and scipy is required. If no binary packages are available for your platform and building source packages fails, you might want to try a distribution like Conda (see below) to install dependencies.

Alternatively for developing, clone or fork this repository and install in editing mode.

pip install -e <path/to/>

Install via Conda

In case you are using Conda, a simple way to run py-motmetrics is to create a virtual environment with all the necessary dependencies

conda env create -f environment.yml
> activate motmetrics-env

Then activate / source the motmetrics-env and install py-motmetrics and run the tests.

activate motmetrics-env
pip install .

In case you already have an environment you install the dependencies from within your environment by

conda install --file requirements.txt
pip install .


Populating the accumulator

import motmetrics as mm
import numpy as np

# Create an accumulator that will be updated during each frame
acc = mm.MOTAccumulator(auto_id=True)

# Call update once for per frame. For now, assume distances between
# frame objects / hypotheses are given.
    [1, 2],                     # Ground truth objects in this frame
    [1, 2, 3],                  # Detector hypotheses in this frame
        [0.1, np.nan, 0.3],     # Distances from object 1 to hypotheses 1, 2, 3
        [0.5,  0.2,   0.3]      # Distances from object 2 to hypotheses 1, 2, 3

The code above updates an event accumulator with data from a single frame. Here we assume that pairwise object / hypothesis distances have already been computed. Note np.nan inside the distance matrix. It signals that object 1 cannot be paired with hypothesis 2. To inspect the current event history simple print the events associated with the accumulator.

print( # a pandas DataFrame containing all events

                Type  OId HId    D
FrameId Event
0       0        RAW    1   1  0.1
        1        RAW    1   2  NaN
        2        RAW    1   3  0.3
        3        RAW    2   1  0.5
        4        RAW    2   2  0.2
        5        RAW    2   3  0.3
        6      MATCH    1   1  0.1
        7      MATCH    2   2  0.2
        8         FP  NaN   3  NaN

The above data frame contains RAW and MOT events. To obtain just MOT events type

print(acc.mot_events) # a pandas DataFrame containing MOT only events

                Type  OId HId    D
FrameId Event
0       6      MATCH    1   1  0.1
        7      MATCH    2   2  0.2
        8         FP  NaN   3  NaN

Meaning object 1 was matched to hypothesis 1 with distance 0.1. Similarily, object 2 was matched to hypothesis 2 with distance 0.2. Hypothesis 3 could not be matched to any remaining object and generated a false positive (FP). Possible assignments are computed by minimizing the total assignment distance (Kuhn-Munkres algorithm).

Continuing from above

frameid = acc.update(
    [1, 2],

        Type OId  HId    D
2      MATCH   1    1  0.2
3       MISS   2  NaN  NaN

While object 1 was matched, object 2 couldn't be matched because no hypotheses are left to pair with.

frameid = acc.update(
    [1, 2],
    [1, 3],
        [0.6, 0.2],
        [0.1, 0.6]

         Type OId HId    D
4       MATCH   1   1  0.6
5      SWITCH   2   3  0.6

Object 2 is now tracked by hypothesis 3 leading to a track switch. Note, although a pairing (1, 3) with cost less than 0.6 is possible, the algorithm prefers prefers to continue track assignments from past frames which is a property of MOT metrics.

Computing metrics

Once the accumulator has been populated you can compute and display metrics. Continuing the example from above

mh = mm.metrics.create()
summary = mh.compute(acc, metrics=['num_frames', 'mota', 'motp'], name='acc')

     num_frames  mota  motp
acc           3   0.5  0.34

Computing metrics for multiple accumulators or accumulator views is also possible

summary = mh.compute_many(
    metrics=['num_frames', 'mota', 'motp'],
    names=['full', 'part'])

      num_frames  mota      motp
full           3   0.5  0.340000
part           2   0.5  0.166667

Finally, you may want to reformat column names and how column values are displayed.

strsummary =
    formatters={'mota' : '{:.2%}'.format},
    namemap={'mota': 'MOTA', 'motp' : 'MOTP'}

      num_frames   MOTA      MOTP
full           3 50.00%  0.340000
part           2 50.00%  0.166667

For MOTChallenge py-motmetrics provides predefined metric selectors, formatters and metric names, so that the result looks alike what is provided via their Matlab devkit.

summary = mh.compute_many(
    names=['full', 'part'])

strsummary =

      IDF1   IDP   IDR  Rcll  Prcn GT MT PT ML FP FN IDs  FM  MOTA  MOTP
full 83.3% 83.3% 83.3% 83.3% 83.3%  2  1  1  0  1  1   1   1 50.0% 0.340
part 75.0% 75.0% 75.0% 75.0% 75.0%  2  1  1  0  1  1   0   0 50.0% 0.167

In order to generate an overall summary that computes the metrics jointly over all accumulators add generate_overall=True as follows

summary = mh.compute_many(
    names=['full', 'part'],

strsummary =

         IDF1   IDP   IDR  Rcll  Prcn GT MT PT ML FP FN IDs  FM  MOTA  MOTP
full    83.3% 83.3% 83.3% 83.3% 83.3%  2  1  1  0  1  1   1   1 50.0% 0.340
part    75.0% 75.0% 75.0% 75.0% 75.0%  2  1  1  0  1  1   0   0 50.0% 0.167
OVERALL 80.0% 80.0% 80.0% 80.0% 80.0%  4  2  2  0  2  2   1   1 50.0% 0.275

Computing distances

Up until this point we assumed the pairwise object/hypothesis distances to be known. Usually this is not the case. You are mostly given either rectangles or points (centroids) of related objects. To compute a distance matrix from them you can use motmetrics.distance module as shown below.

Euclidean norm squared on points

# Object related points
o = np.array([
    [1., 2],
    [2., 2],
    [3., 2],

# Hypothesis related points
h = np.array([
    [0., 0],
    [1., 1],

C = mm.distances.norm2squared_matrix(o, h, max_d2=5.)

[[  5.   1.]
 [ nan   2.]
 [ nan   5.]]

Intersection over union norm for 2D rectangles

a = np.array([
    [0, 0, 1, 2],    # Format X, Y, Width, Height
    [0, 0, 0.8, 1.5],

b = np.array([
    [0, 0, 1, 2],
    [0, 0, 1, 1],
    [0.1, 0.2, 2, 2],
mm.distances.iou_matrix(a, b, max_iou=0.5)

[[ 0.          0.5                nan]
 [ 0.4         0.42857143         nan]]

Solver backends

For large datasets solving the minimum cost assignment becomes the dominant runtime part. py-motmetrics therefore supports these solvers out of the box

A comparison for different sized matrices is shown below (taken from here)

Please note that the x-axis is scaled logarithmically. Missing bars indicate excessive runtime or errors in returned result.

By default py-motmetrics will try to find a LAP solver in the order of the list above. In order to temporarly replace the default solver use

costs = ...
mysolver = lambda x: ... # solver code that returns pairings

with lap.set_default_solver(mysolver):

Running tests

py-motmetrics uses the pytest framework. To run the tests, simply cd into the source directly and run pytest.


  1. Bernardin, Keni, and Rainer Stiefelhagen. "Evaluating multiple object tracking performance: the CLEAR MOT metrics." EURASIP Journal on Image and Video Processing 2008.1 (2008): 1-10.
  2. Milan, Anton, et al. "Mot16: A benchmark for multi-object tracking." arXiv preprint arXiv:1603.00831 (2016).
  3. Li, Yuan, Chang Huang, and Ram Nevatia. "Learning to associate: Hybridboosted multi-target tracker for crowded scene." Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on. IEEE, 2009.
  4. Performance Measures and a Data Set for Multi-Target, Multi-Camera Tracking. E. Ristani, F. Solera, R. S. Zou, R. Cucchiara and C. Tomasi. ECCV 2016 Workshop on Benchmarking Multi-Target Tracking.


Update ground truth and test data:

/data/train directory should contain MOT 2D 2015 Ground Truth files. /data/test directory should contain your results.

You can check usage and directory listing at

Build Image

docker build -t desired-image-name -f Dockerfile .

Run Image

docker run desired-image-name

(credits to christosavg)


MIT License

Copyright (c) 2017-2022 Christoph Heindl
Copyright (c) 2018 Toka
Copyright (c) 2019-2022 Jack Valmadre

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.


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