# Multi Player Tracking in Ice Hockey with Homographic Projections

Harish Prakash, Jia Cheng Shang, Ken M. Nsiempba, Yuhao Chen, David A. Clausi,
John S. Zelek  Vision and Image Processing Group
University of Waterloo, Ontario, Canada
{harish.prakash, jcshang, kmnsiemp, yuhao.chen1, dclausi, jzelek} @
uwaterloo.ca

###### Abstract

Multi Object Tracking (MOT) in ice hockey pursues the combined task of
localizing and associating players across a given sequence to maintain their
identities. Tracking players from monocular broadcast feeds is an important
computer vision problem offering various downstream analytics and enhanced
viewership experience. However, existing trackers encounter significant
difficulties in dealing with occlusions, blurs, and agile player movements
prevalent in telecast feeds. In this work, we propose a novel tracking
approach by formulating MOT as a bipartite graph matching problem infused with
homography. We disentangle the positional representations of occluded and
overlapping players in broadcast view, by mapping their foot keypoints to an
overhead rink template, and encode these projected positions into the graph
network. This ensures reliable spatial context for consistent player tracking
and unfragmented tracklet prediction. Our results show considerable
improvements in both the _IDsw_ and _IDF1_ metrics on the two available
broadcast ice hockey datasets.

###### Index Terms:

Ice hockey; Tracking; Homography; MPNs.

Figure 1: Other trackers vs Our approach. a) During a significant occlusion
scenario $(t+2)$, other trackers lead to an ID switch error; b) Our method
consistently tracks players before and after occlusion; c) Overhead rink
template used for homography projection; d) Player footpoint coordinates
mapped to the overhead template. At $(t+2)$, there is a clear distinction
between overlapping players from the top view. This information aids our
tracker in maintaining player tracklets.

##  I Introduction

Multi-Object Tracking (MOT) is an important computer vision problem subsuming
several tasks such as object detection, localization, re-identification and
association across a temporal sequence. It is a highly studied and established
problem due to its plethora of applications in robotics, autonomous vehicles,
industrial automation, surveillance, and sports. While most existing MOT
approaches focus exclusively on tracking crowded pedestrians [1, 2, 3], group
dancing [4], and autonomous driving [5], sports tracking is a pivotal task in
vision due to its numerous subsequent applications in game analytics &
statistics, strategic planning, player evaluation, injury prevention, and
crucial game decisions. Player tracking helps save several manual labor hours
and human efforts by automating game understanding and player performance
assessments. With the advent of deep networks[6], several important strides
have been taken to track various sports including soccer [7], handball [8],
basketball [9, 10, 11], and volleyball [12], with public MOT datasets [13, 14]
to support principled evaluations.

Unlike all the aforementioned sports, ice hockey poses unique challenges to
tracking due to its highly _physical_ and _fast-paced_ nature. Specifically
there are three major challenges that exists: (i) the significant occlusion
between two or more players at a given instant within the field-of-view (FoV);
(ii) the non-linear player dynamics due to unpredictable player motion, and;
(iii) blurs and reduced visibility of players due to frequent camera motion.
When faced with these issues, tracking in monocular view increases identity
swaps and tracklet fragmentations. Early attempts at tracking ice hockey
players were pursued using an ensemble of handcrafted methods. Okuma et al.
[15] use Adaboost [16] detection with mixed particle filters [17] for tracking
players from television videos. Cai et al. [18] improve upon [15] by utilizing
the mean-shift algorithm to stabilize player trajectories, and use rink
coordinates (homography) for the particle-filter. However, mixed particle
filters are susceptible to identity switches/losses during mutual occlusions,
background changes, blurs, and lighting effects, which are often found in
hockey. Further, there exists no quantitative evaluation in the above works to
show the efficacy of their models.

Recent approaches using deep networks have shown significant improvements in
the accuracy of tracking hockey players from broadcast feeds. Vats et al. [19]
present a comparison between five different tracking models, fine-tuned on
broadcast ice hockey clips and obtain state-of-the-art results using graphs
with message passing networks (MPN) [20]. They subsequently use this method to
generate tracklets (sequence of player tracks) for player identification &
team recognition [21]. As far as we know, this is the only existing benchmark
for MOT in ice hockey. However, there exists two major limitations in their
approach: first, their model encodes the _bounding box_ attributes of players
as graphical edge embeddings which leads to identity swaps and tracklet
fragmentations. This is because, when there exists heavy occlusion between
players as usually observed in broadcast hockey feeds, their bounding boxes
overlap significantly in the monocular view (Intersection-over-Union (IoU)
$\uparrow$), causing either misassociation of players (identity switch) or a
missed connection (lost tracklet) with previous tracks. Second, their node
embeddings are encoded solely based on player appearance features, which is
ambiguous in hockey due to the fully-covered bulk gear worn by players,
similarly colored team jerseys, blur & lighting effects. With these present
setbacks, we ask the question: _”Given only a monocular broadcast feed, is it
possible to declutter occluded players and track their movements with high
fidelity?”_. Our results show that the answer is Yes.

In this work, we formulate MOT as a link prediction problem in the graph
domain since graphical networks offer a natural way of representing players
and their relationships. The novelty of our approach lies in coupling this
with homography to obtain reliable spatial/positional cues for ice hockey
players. Specifically, we map every frame from broadcast view to an overhead
view (rink template) using an off-the-shelf homography estimator [22], to
obtain the projected footpoints of players in rink coordinates. This yields a
_birds-eye_ effect, reducing the positional ambiguities due to overlapping
players and perspective projection. We encode these projected positions along
with player re-identification features as graph embeddings, and propagate
information through the graph using the message passing network (MPN) [23, 24]
framework. Our model follows the popular _tracking-by-detection_ paradigm and
we show evaluations with both ground-truth detections and off-the-shelf
detector outputs [25], in coherence with the current state-of-the-art (SOTA)
benchmark [19]. Through this approach, our model is able to utilize the
overhead positional information of players as additional cues to track with
consistency during occlusions, blurs, and dynamic player movements.

Our contributions can be summarized as follows:

  * •

We design a simple, yet effective spatio-temporal graphical network and adopt
the MPN framework to track players from broadcast feeds consistently;

  * •

We propose a novel approach based on homography to provide additional
positional information to the graph network during occlusions, blurs and non-
linear movements, and;

  * •

We show significant improvements in the _IDsw_ and _IDF1_ scores on two
available broadcast ice hockey datasets.

##  II Related Works

###  II-A MOT for Pedestrians

Most existing MOT methods [20, 26, 27, 28, 29, 30, 31, 32, 33] focus
exclusively on tracking pedestrians in crowded scenes [1, 2, 3]. Initial
approaches combine Kalman filters [34] and Hungarian method [35] for next
state motion prediction and object associations respectively. Consequent
approaches adopted the two-stage _tracking-by-detection (TBD)_ paradigm where:
first, all objects present in a sequence are detected; and next, their
association features are extracted to link similar objects across frames.
Simple Online and Real-time tracking (SORT) [31] establish a TBD baseline for
MOT, and argue that SOTA associations can only be obtained with traditional
methods [34, 35]. DeepSORT [32] answer SORT’s [31] argument, by embedding
appearance features using a ReID network for association, showing lesser
identity switches and better tracking results on the MOT16 [2] challenge
benchmark. FairMOT [33] combines the detection and ReID steps for Joint
Detection and Tracking (JDT) using an anchor-free detector [36]. Tracktor [29]
frames tracking as a bounding box regression problem, by converting a detector
[25] into a tracker. But, a major limitation with all these methods is their
inability to tackle crowded scenes and declutter occluded pedestrians.
ByteTrack [28] tries to handle occlusion by associating low-confidence targets
too, to retrieve true objects, but fails during significant crowded
(overlapping) situations where the object is heavily obstructed. Sparsetrack
[37] tries to handle occlusion by decomposing dense/crowded pedestrian scenes
into sparse subsets using pseudo-depth map estimation, but incur high
computational costs and significant processing requirements.

###  II-B MOT for Sports

Initial methods in sports utilize Kalman filtering [38, 39] and particle
filters [15, 18] for tracking, but were unable to preserve identities due to
their linear motion model assumptions. Nillius et al. [40] encode player
trajectories into track graphs and use a bayesian framework to predict the
most likely configuration of player paths. Figueroa et al. [41] track players
with multi-cameras by encoding their segmentation blobs as nodes and their
relative distances as edges. With YOLOv2 [42] for detection, Acuna et al. [43]
track basketball players using SORT [31], while Theagarajan et al. [44] track
soccer players using DeepSORT [32]. However, naively extending methods
originally designed for pedestrian tracking to sports is a non-trivial task,
due to the domain-specific challenges in modeling arbitrary player movements,
occlusions, fast camera motions, and perspective projection errors.

###  II-C Tracking with Graphs

Graph-based formulations offer a flexible way to model target movements,
interactions and their relative features. Wang et al. [45] propose a graph-
based MOT framework for joint detection and tracking. MOT neural solver [20]
exploits the network flow formulation of MOT to define a message passing
network for data association. Vats et al. [19] fine-tune the neural solver
architecture on the broadcast ice hockey dataset to create the first tracking
benchmark for hockey. Luna et al. [46] extend the graph domain to multi-camera
tracking, and ReST [47] builds on top with a spatio-temporal network for
online-tracking. Both these algorithms use the intrinsic camera parameters to
map multiple camera views onto a common ground plane for additional positional
cues. But, in our case, we cannot infer camera parameters from broadcast feeds
directly. Therefore, we utilize an off-the-shelf homography model [22] trained
on a top-view rink template, to map each broadcast frame to the overhead rink
coordinates and obtain homographic footpoint coordinates for the graph MPN.

Figure 2: Proposed Approach. a) The general pipeline of our spatio-temporal
graph. b) $G$ denotes the three stages of Graph Initialization, MPN, and
Classification. c) $PP$ denotes the Post-Processing stage where we Prune,
solve graph violations, and assign player IDs

##  III Proposed Method

Given an ice hockey broadcast feed, the objective of our work is to track
multiple players consistently despite prevalent occlusions, blurs, and
arbitrary player movements. We leverage Graphical Neural Networks (GNN) for
this task (due to their efficiency in modeling relationships) to build a
spatio-temporal graph and utilize homography for reliable positional
information. Specifically, we project player foot keypoints onto a common
overhead rink template and encode these projections along with ReID embeddings
[48] as node features and their relative distances as edge features. Since we
cannot obtain camera parameters from broadcast feeds directly, we use an off-
the-shelf homography estimation model [22] specifically designed for ice
hockey, to estimate the homography transformation matrix,
$H\in\mathbb{R}^{3\times 3}$. We utilize the message passing network (MPN)
framework [23, 24] to propagate player features across the entire graph ${G}$,
and update the node and edge embeddings at each message passing step. This
helps our model reason globally over the entire sequence for predicting player
trajectories. We frame the association between two consecutive frames
${f_{i}}$ and ${f_{j}}$ ${s.t\ j>i}$, as a bipartite graph problem, and use a
binary classifier with a sigmoid final layer to output association
probabilities. During inference, we post-process each graph by pruning to
remove low-confidence associations and solve many-to-one violations. Finally,
we assign tracklet IDs to nodes wherein, if the node has a prior connection,
it inherits the same ID or gets assigned a new ID otherwise. (Ref Fig. 2)

###  III-A Problem Formulation

Consider a broadcast hockey sequence (frames) $S_{t}=\\{F_{i}\mid
i=1,2,\ldots,n\\},\ \text{where \ }n=\frac{t}{\Delta t}$; $t$ = total duration
of the sequence, and $\Delta t$ = duration per frame. For each frame $F_{i}$,
assuming that there exists at least one player to track, we have $P_{j}^{i}$
players, where $j>=1$. For each player $P$, the ground truth annotation
includes:

$\\{f^{id},t^{id},x,y,wd,ht,c,x^{proj},y^{proj}\\}$

where $f^{id}$ = frame ID, $t^{id}$ = player ID (only used during training),
$\\{x,y,wd,ht\\}$ = bounding box coordinates, $c$ = annotation confidence
score, and $(x^{proj},y^{proj})$ = homography coordinates for player
footpoints. As per the _tracking-by-detection_ paradigm, player annotations
are detections from an off-the-shelf detector for the inference stage. In our
case, we show both evaluations: first, directly evaluating on the annotated
ground truth which gives the best picture of our tracking performance (Ref.
Section IV-C), and second, inference and evaluation on the detected output
using F-RCNN [25] following the current SOTA [19] benchmark, for a fair
comparison.

We formulate multi-object tracking (MOT) as a bipartite graph matching
problem. We deterministically create one graph per frame in the given
sequence. Each node in this graph points to one player in that frame and the
edges correspond to their relationships with neighboring nodes in other
frames. Let us consider the undirected graph $G_{t}=(V_{t},E_{t})$ with
bidirectional connections, where $V_{t}$ denotes the vertex set and $E_{t}$
denotes the edge set at time $t$. $NodeFeatures(.)$ represents the
concatenation of appearance features and homographic projections of players at
time $t$, and $E_{t}=V_{i}\times V_{j}$ represents a one-one mapping between
vertex sets $v_{i}$ and $v_{j}\ s.t\ i\neq j$, meaning that the mapping is not
within players in the same frame.

Node Formulation Each node $v_{i}\in V_{t}$ represents one unique player $i$
found in $F_{t}$ and contains: frame ID (timestamp)
$f^{id}_{i}\in\mathbb{R}^{1}$, player ID $t^{id}_{i}\in\mathbb{R}^{1}$
(ground-truth, only used for training), bounding box coordinates
$b_{i}=\\{x_{i},y_{i},wd_{i},ht_{i}\\}\in\mathbb{R}^{4}$, ReID appearance
features $r^{id}_{i}\in\mathbb{R}^{512}$ and homographic projection
coordinates $p_{i}=\\{x^{proj}_{i},y^{proj}_{i}\\}\in\mathbb{R}^{2}$.

The ReID features are generated for each node $i$ via an off-the-shelf Re-
Identification network [48], described by:

$r^{id}_{i}=ReID(b_{i}\mid_{crop})$ (1)

where $b_{i}\mid_{crop}$ denotes the cropped bounding box for the $i^{th}$
player. The homographic projections are estimated by projecting the bottom-mid
point ($\sim$foot keypoint) of the bounding box from the monocular broadcast
view. The left footpoint $f_{l}=(x_{i}+\frac{wd_{i}}{2})$ and the right
footpoint $f_{r}=(y_{i}+ht_{i})$ for player $i$ are projected as:

$p_{i}=H_{i}(f_{l},f_{r})$ (2)

with $H_{i}$ being the $3\times 3$ Homography matrix (Ref. Eq. 5)

Edge Formulation Each edge, $e_{ij}\in E_{t}$ is represented as the
interconnection between two players from two distinct frames. It is encoded as
the concatenation of relative appearance $\Delta r^{id}_{ij}$ and positional
$\Delta p_{ij}$ features between the pair of nodes $v_{i}$ and $v_{j}$, where
$e_{ij}=v_{i}\times v_{j},i\neq j$. This can be represented as:

$\Delta r^{id}_{ij}=[\lVert
r^{id}_{i}-r^{id}_{j}\rVert_{1},cosine\\_similarity(r^{id}_{i},r^{id}_{j})]$
(3)

$\Delta p_{ij}=[\lVert p_{i}-p_{j}\rVert_{1},\lVert p_{i}-p_{j}\rVert_{2}]$
(4)

[·,·] denotes the concatenation of Eucledian distance & Cosine Similarity for
$\Delta r^{id}_{ij}$, and Eucledian & Manhattan distance for $\Delta p_{ij}$.
This consideration is inspired from [46] to obtain higher-dimensional
distinctive features.

###  III-B Homographic Projection

Due to the monocular nature of broadcast ice hockey sequences, there exists
high levels of player occlusion and dynamic camera movement effects (blurs,
pans, tilts, zooms). This limits the scope of tracking players consistently
when they’re completely obscured or remain hidden, even if for very short
intervals. To provide the tracker with reliable positional cues in such
scenarios, we propose an approach using homography to warp player positions
from the broadcast video feed onto an common overhead rink template. This
helps reduce the variance in frames present across the sequence due to camera
motion, and provides a pseudo _top-view_ tracking effect to disentangle
overlapping players.

At any given frame $F_{t}$, a player’s $P_{i}$ foot keypoint coordinates
represents their exact point of contact with the ice, which when projected to
the overhead rink plane provides additional positional cues for uncluttered
tracking. For the player $P$ with footpoints $(P_{f_{x}},P_{f_{y}})$ in
broadcast view:

$p_{i}=s\begin{bmatrix}P_{x^{\prime}}\\\ P_{y^{\prime}}\\\
1\end{bmatrix}=H\begin{bmatrix}P_{f_{x}}\\\ P_{f_{y}}\\\
1\end{bmatrix}=\begin{bmatrix}h_{11}&h_{12}&h_{13}\\\ h_{21}&h_{22}&h_{23}\\\
h_{31}&h_{32}&1\\\ \end{bmatrix}\begin{bmatrix}P_{f_{x}}\\\ P_{f_{y}}\\\
1\end{bmatrix}$ (5)

where $p_{i}$ = homographic projection of the $i^{th}$ node,
$(P_{x^{\prime}},P_{y^{\prime}})$ = projected homogenous player footpoints in
the overhead view, $s$ = scale factor, and $H=3\times 3$ homography matrix.

But this is a non-trivial task, since the camera parameters for broadcast
feeds are unknown and thereby, we do not know the values for $H$. Therefore,
we tackle this issue using an off-the-shelf homography-estimator [22] pre-
trained on an ice hockey top-view rink template, to map each broadcast frame
onto the overhead view and obtains its respective homographic projection.

###  III-C Temporal Graph Association

To facilitate association of players across frames, we design a simple
temporal graph network, to correlate player features. Inspired by [47], we
iteratively correlate the learned graph $G_{t-1}^{T}$ at time $t-1$ with the
next graph $G_{t}$ at time $t$ to form a new graph $G_{t}^{T}$. Assuming this
as the $n^{th}$ iteration, each node $v_{t-1}\in G_{t-1}^{T}$ contains
aggregated embeddings from $n-1$ iterations and is connected with the new
nodes $v_{t}\in G_{t}$ to form the new temporal graph $G_{t}^{T}$ at time $t$
(Ref algorithm 1). The edge set thus created can be denoted as:

$e_{t-1,t}=\begin{cases}1,\text{if }v_{i}\times v_{j}\forall\ v_{i}\in
G_{t-1},v_{j}\in G_{t}\\\ 0,\text{otherwise}\end{cases}$

This aggregation of uniterated graphs with learned graphs helps propagate
learned features and assign consistent identities for the same player (Ref
Fig. 2)

Algorithm 1 Model Inference

1:Given g.t $y_{e_{ij}}$, players $P_{k}\in G_{t-1}\oplus G_{t}$, $i=0$ &
$w=2$;

2:for $t=0$ to $(T-1)$ do

3: Initialize $h^{0}_{v_{i}},h^{0}_{v_{j}}$ and $h^{0}_{e_{ij}}$ for
$G_{t-1}\oplus G_{t}$

4: if $i>0$ then

5: Replace $G_{t-1}$ with $G^{learned}_{t}$

6: end if

7: $h^{0}_{v_{i}},h^{0}_{v_{j}}=f^{FE}_{v}(h^{0}_{v_{i}},h^{0}_{v_{j}})$

8: $h^{0}_{e_{ij}}=\it{f}_{e}^{FE}(h^{0}_{e_{ij}})$

9: while $(l\geq L)$ do $\displaystyle\quad
h^{L}_{v_{i}},h^{L}_{v_{j}},h^{L}_{e{{}_{ij}}}=\text{MPN}(G_{t-1}\oplus
G_{t},h^{l-1}_{v_{i}},h^{l-1}_{v_{j}})$
$\hat{y}_{{e}_{ij}}=f^{cls}(h_{e_{ij}}^{L})$

10: end while

11: $G_{t}^{learned}=\text{Post-Processing}(G_{t-1}\oplus
G_{t},\hat{y}_{{e}_{ij}}^{L})$

12: i++;

13:end for

###  III-D Message Passing Network

We adopt the Message Passing Network (MPN) structure as introduced by [24] to
propagate the node and edge information across the graph $G$. Message passing
intuitively helps the graphs learn their neighboring features; each edge
learns about the projection and appearance feature of its neighboring nodes
and each node learns about the geometric features of its neighboring edges. To
begin with, we initialize the node embeddings and edge embeddings as:

$h_{v_{i}}^{(0)}=f_{v}^{FE}([r^{id}_{v_{{}_{i}}},p_{v_{{}_{i}}}])$ (6)
$h_{e_{ij}}^{(0)}=f_{e}^{FE}([\Delta r^{id}_{e_{{}_{ij}}},\Delta
p_{e_{{}_{ij}}}])$ (7)

Note that we add $p$ and $\Delta p$ to both the node and edge features
respectively to propagate homographic (positional) information throughout the
graph. Given these initial embeddings, as standardized by well-established
methods [19, 20, 47, 23, 46], we perform $L$ iterations of edge updates and
node updates as two separate steps.

Edge Update We utilize a learnable multi-layer perceptron (MLP) to perform
edge encoding for $l=\\{1,\ldots,L\\}$ steps using the source and destination
nodes connected by the edge:

$(v\rightarrow e)\ \ \
h_{e_{ij}}^{(l)}=f_{e}^{ME}([h_{v_{i}}^{(l-1)},h_{v_{j}}^{(l-1)},h_{e_{ij}}^{(l-1)}])$
(8)

where, $f_{e}^{ME}$ is the edge encoder. This leads to the sharing of
appearance and projection embeddings from the neighboring nodes
$h_{v_{i}},h_{v_{j}}$ to its connecting edge $h_{e_{ij}}$.

Node Update Similar to Eq. (8), we utilize a learnable MLP to perform node
update for $l=\\{1,\ldots,L\\}$ steps, using the aggregated messages coming
from its neighboring nodes:

$(e\rightarrow v)\ \ \
h_{v_{i}}^{(l)}=\sum_{j\in\mathcal{N}(v_{i})}f_{v}^{ME}([h_{v_{j}}^{(l-1)},h_{e_{ij}}^{(l)}])$
(9)

where, $f_{v}^{ME}$ is the node encoder and $\mathcal{N}(v_{i})$ denotes the
neighboring nodes of $v_{i}$. Note that $f_{v}^{ME}$ and $f_{e}^{ME}$ are two
separate networks with different dimensions, but share the same MLP
architecture (Ref. Table I)

In both the updates, the MLP encodes all the information into a higher-
dimensional feature space. The message passing step $L$ is akin to the
receptive field found in convolutional neural networks [6] and a higher value
of $L$ corresponds to farther propagation of information in the graph, but at
the cost of computation.

Network |  Layer |  Input |  Output
---|---|---|---
$\it{f}^{FE}_{v}(\cdot)$ |  FC+GELU |  515 |  128
|  |  4 |  32
$\it{f}^{FE}_{e}(\cdot)$ |  FC+GELU |  4 |  8
|  |  8 |  6
$\it{f}^{ME}_{v}(\cdot)$ |  FC+GELU |  38 |  64
|  |  64 |  32
$\it{f}^{ME}_{e}(\cdot)$ |  FC+GELU |  70 |  32
|  |  32 |  6
$\it{f}^{cls}(\cdot)$ |  FC+GELU |  6 |  4
|  FC+Sigmoid |  4 |  1
|  |  |
TABLE I: Details of each mlp encoder.
fc - fully connected, gelu activation [49]

Classification We propose to learn the association between nodes as a link
prediction task by framing player tracking as a graph partition problem. That
is, after $L$ iterations, we perform binary classification to predict the edge
probabilities $\hat{y}_{e_{ij}}$ connecting nodes $v_{i}$ and $v_{j}$, as:

$\hat{y}_{e_{ij}}=f^{cls}(h_{e_{ij}})$ (10)

where $f^{cls}$ is a learnable MLP with a sigmoid final layer to output
probabilities. During inference, the edges with low confidence scores (weak
connections) are removed. During training, the binary ground truth labels
$y_{e_{ij}}$ and their corresponding predictions $\hat{y}_{e_{ij}}$ are
compared to find the sigmoid focal loss [50].

###  III-E Post-Processing

We adopt a post-processing step during inference to prune and resolve
violations in our final graphs, and assign consistent tracklet IDs.

Pruning. This is the first step in refining the predicted edge confidence
scores $\hat{y}_{e_{ij}}$ by our classifier. We define a confidence threshold
hyperparameter $\xi$, where:

$\text{Pruned}(\hat{y}_{e_{ij}})=\begin{cases}\hat{y}_{e_{ij}},\ \ \text{if}\
\hat{y}_{e_{ij}}>\xi\\\ 0,\ \ \text{otherwise}\end{cases}$ (11)

This helps eliminate the low-confidence edges and retain only the most
strongest correspondences. For our experiments, we’ve used $\xi=0.9$ to only
retain the most strongest edges. Alongside, similar to [47], we remove many-
to-one edge violations, wherein, there can only exist at most one connection
between two nodes within the connected graphs. This ensures that we represent
each player identity through a unique connected component, since no two
different players can share the same identity at the same time.

Assigning IDs. The final graph contains unique connected components where each
component represents one unique player tracklet. As we iterate temporally, we
assign a new identity when there exists no previous connected components for a
node or propagate the same identity otherwise.

$\text{ID}(h_{v_{j}})=\begin{cases}\text{SameID},\ \text{if}\
h_{v_{j}}=h_{v_{i}};\forall j\in G_{t},i\in G_{t-1}\\\ \text{NewID},\
\text{otherwise}\end{cases}$ (12)

##  IV Implementation Details

This section contains details about datasets used, training scheme, evaluation
metrics and the final results.

###  IV-A Datasets

We experiment our methodology on the two available ice hockey tracking
datasets - first, similar to the current SOTA benchmark [19], we train and
test on the broadcast hockey dataset for a fair comparison; second, we
evaluate on the public VIP Hockey Tracking Dataset (VIP-HTD) [51] to
demonstrate the generalization of our method. Both datasets contain side-of-
the-rink broadcast videos with occlusions, blurs, and challenging player
movements.

Broadcast Tracking Dataset [19] This dataset contains 84 broadcast clips
sampled from 25 NHL games, with an average duration of $\sim$36 seconds per
clip. The dataset has a $1280\times 720p$ resolution (Standard Definition) at
a frame rate of 30fps, with a train:validation:test ratio of 58:13:13. We
follow the same training and testing scheme as [19] for equal comparison, and
show superior results with our method (Ref Table II)

VIP-HTD [51] This _public_ dataset contains 22 broadcast hockey clips sampled
from 8 NHL games, with both 30 & 60Hz frame rates, recorded at $1280\times
720p$ resolution. We perform cross-dataset validation (trained on broadcast
dataset; tested on VIP-HTD) on all the 7 test clips in this dataset to
showcase the generalizability of our method for any given broadcast hockey
feed (Ref Table III)

###  IV-B Training Details.

Given the player bounding boxes and tracklet IDs, we find the footpoint
projection coordinates using an off-the-shelf homography model [22] trained
specifically for NHL ice-hockey rinks. This model is currently the SOTA for
hockey and helps predict highly accurate overhead projections. Next, we
exploit the OSNet architecture [48] as our ReID network for player feature
extraction (Eq. (1)), pre-trained on the ImageNet dataset [52]. We encode the
512-D ReID feature vectors along with the 3-D (homogenous coordinates)
homography features into 32-D node embeddings (Eq. (6)), and the 4-D edge
features (Eq. (7)) into 6-D edge embeddings. We run the MPN for L = 6
iterations and pass the final graph output into our binary classifier for
predicting edge probabilities.

Algorithm 2 Model Training

1:Given g.t $y_{e_{ij}}$, players $P_{k}\in G_{t-1}\oplus G_{t}$ & $w=2$;

2:for $t=1$ to $(T-1)$ do

3: Initialize $h^{0}_{v_{i}},h^{0}_{v_{j}}$ and $h^{0}_{e_{ij}}$ for
$G_{t-1}\oplus G_{t}$

4: $(h^{0}_{v_{i}},h^{0}_{v_{j}})=f^{FE}_{v}(h^{0}_{v_{i}},h^{0}_{v_{j}})$

5: $h^{0}_{e_{ij}}=\it{f}_{e}^{FE}(h^{0}_{e_{ij}})$

6: while l $\leq$ L do:  $\displaystyle
h^{L}_{v_{i}},h^{L}_{v_{j}},h^{L}_{e{{}_{ij}}}=\text{MPN}(G_{t-1}\oplus
G_{t},h^{l-1}_{v_{i}},h^{l-1}_{v_{j}})$
$\hat{y}_{{e}_{ij}}=f^{cls}(h_{e_{ij}}^{L})$

7: end while

8: graph_loss = sigmoid_focal_loss$(\hat{y}_{e_{ij}},y_{e_{ij}})$

9: graph_loss.backward() $\triangleright$ Backpropagation

10: optimizer.step() $\triangleright$ Update parameters

11:end for

During training, we utilize the ground-truth player annotations and calculate
the prediction losses using Focal Loss [50]

$\text{Focal Loss}=\sum_{l}^{L}\sum_{e_{ij}\in G_{t-1}\cup
G_{t}}\mathcal{L}(\hat{y}^{l}_{e_{ij}},y_{e_{ij}})$ (13)

where, $\hat{y}^{l}_{e_{ij}}$ is the edge prediction at iteration $l$ and
$y_{e_{ij}}$ is the ground-truth indicator function:

$\mathds{1}(y_{e_{ij}})=\begin{cases}1,\ \text{if}\ v_{i}=v_{j}\\\ 0,\
\text{otherwise}\end{cases}$ (14)

that is, for every player match, $y_{e_{ij}}$ = 1 else 0. We use Adam
Optimizer [53] without weight decays to update our model parameters. The
learning rate (LR) is initialized at 0.01, with a gradual warmup for the first
10 epochs and a cosine annealing schedule (min. LR = 0.001) thereafter. We
trained our model for 30 epochs with a batch size of 16 on a single NVIDIA
GeForce RTX 4090 GPU with 24 GB RAM, 2.5GHz clock speed, and performed
validation after every 2 training epochs.

Method | MOTA % $\uparrow$ | FP $\downarrow$ | FN $\downarrow$ | IDsw $\downarrow$ | IDF1 $\uparrow$ %
---|---|---|---|---|---
SORT [31] | 92.4 | 2403 | 5826 | 673 | 53.7
DeepSORT [32] | 94.2 | 1881 | 4334 | 528 | 59.3
FairMOT [33] | 91.9 | 1179 | 7568 | 768 | 61.5
Tracktor [29] | 94.4 | 1706 | 4216 | 687 | 56.5
Hockey MOT [19] | 94.5 | 1653 | 4394 | 431 | 62.9
Hockey MOT† [19] | - | - | - | 1056 | 71.8
Ours | 95.4 | 1924 | 4323 | 453 | 71.3
Ours† | - | - | - | 151 | 95.1
TABLE II: Evaluation results on the broadcast ice hockey dataset. † indicates
ground-truth annotations used for evaluation

###  IV-C Evaluation Metrics

Most common evaluation metrics used in popular SOTA tracking methods are the
Multi-Object Tracking Accuracy (MOTA)[54] and IDF1 score [55]. With respect to
our problem context, they can be defined as:

MOT Accuracy: It is calculated as the complement of three distinct errors -

  * •

False Positives (FP): No. of false players detected;

  * •

False Negatives (FN): No. of true players missed;

  * •

Identity Switches (IDsw): No. of identity swaps/re-initializations made for
players within the field-of-view.

$\text{MOTA}=1-\frac{\sum_{t}\text{FN}_{t}+\text{FP}_{t}+\text{IDsw}_{t})}{\sum_{t}\text{GT}_{t}}$
(15)

where, $\text{GT}_{t}$ denotes the ground-truth annotations.

IDF1 Score: It is defined as the ratio of correctly identified players over
the average number of ground-truth and computed identities:

$\text{IDF1}=2\times\frac{{\text{TP}_{id}}}{(2\times{\text{TP}_{id})}+{\text{FP}_{id}}+{\text{FN}_{id}}}$
(16)

where, $\text{TP}_{id},\text{FP}_{id},\text{FN}_{id}$ are True Positive, False
Positive and False Negative player identities respectively. Alternatively,
IDF1 score can also be defined as the harmonic mean of ID Precision and ID
Recall.

NHL teams (clips) | No.of frames | FPS (Hz) | IDsw $\downarrow$ | IDF1 $\uparrow$
---|---|---|---|---
CAR vs. BOS | 2606 | 60 | 115 | 85.4
CAR vs. NYR | 2137 | 60 | 71 | 81.1
CGY vs. DAL | 1330 | 60 | 41 | 77.4
CHI vs. TOR | 1618 | 30 | 152 | 60.3
CNTRL vs. PAC | 1671 | 30 | 136 | 71.7
PIT vs. SJ | 1391 | 30 | 164 | 70.1
STL vs. SJ | 2258 | 60 | 108 | 86.2
Hockey MOT |  |  | 787 | 80.2
CAR vs. BOS | 2606 | 60 | 11 | 89.3
CAR vs. NYR | 2137 | 60 | 7 | 93.1
CGY vs. DAL | 1330 | 60 | 6 | 92.4
CHI vs. TOR | 1618 | 30 | 6 | 90.9
CNTRL vs. PAC | 1671 | 30 | 13 | 90.5
PIT vs. SJ | 1391 | 30 | 7 | 97.4
STL vs. SJ | 2258 | 60 | 7 | 96.3
Ours | 13,011 | - | 60 | 92.84
TABLE III: cross-dataset validation on the public vip-hockey tracking dataset

The FPs and FNs used to calculate MOTA relies solely on the detector’s
quality. Even if the tracker consistently associates players, the MOTA will be
skewed if there exists high FP and FN detections, as they have twice the
weightage of IDsw in MOTA. Since this doesn’t give a clear picture of the
tracker’s association capabilities, we focus only on the IDsw score and the
IDF1 score as the _key_ metrics in player tracking. These metrics are
especially relevant in ice hockey, since they measure how consistently a
player is tracked with respect to his original identity. Therefore, our
primary objective is to have $\downarrow$ IDsw and $\uparrow$ IDF1 score for
consistent player tracking. Our preferred evaluations are directly based on
ground-truth annotations; but, to be consistent with [19] we use similar
detection outputs to show our results.

###  IV-D Results

We report the results of our model’s performance on the test-sets of the
broadcast ice hockey dataset [19] and the public VIP-HTDataset [51]. It is to
be noted that we reproduce the results of our benchmark [19], under similar
hardware and testing conditions as our own method’s evaluations, to avoid any
discrepancies. From Table II during ground-truth evaluations, our model
outperforms the SOTA model by a large 23.3% $\uparrow$ in _IDF1_ score, and
10$\times\downarrow$ in IDsw. This is due to the ability of our model to
handle heavy occlusions and blurs prevalent in these videos. We see similar
trends with the F-RCNN [25] detection inputs, where our model surpasses all
methods by a 8.4%$\uparrow$ in _IDF1_. Our MOT Accuracy is still higher than
all other methods, despite incurring more FPs and FNs due to the ability of
our tracker to recover robustly from mistakes made by the detector. We show
qualitative results for all 7 videos below the reference section. In Table
III, we cross-validate our model on the VIP-HTDataset [51] showing a clear
superiority in both _IDsw_ and _IDF1_ metrics, compared to [19]. This asserts
two important things: (i) our model generalizes well to unseen hockey feeds,
despite of varying environmental conditions; (ii) Our model’s performance
isn’t affected by the $\uparrow$ in frame rate.

##  V Conclusion

We present a novel approach based on the combination of graphical neural
networks and homography to effectively track ice hockey players in broadcast
feeds. We project player footpoints to an overhead rink template to maintain
consistent positional cues, especially during occlusions and blurry
situations. This provides a pseudo ’top-view’ effect to disentangle
overlapping players and maintain their trajectories. Message passing network
(MPN) is used to aggregate player features and model their temporal
relationships, followed by a classifier to predict player association
probabilities. We achieve as significant $\uparrow$ in $IDF1$ and $\downarrow$
in $IDsw$, when compared to both the current SOTA benchmark and a public
tracking dataset. We believe that our work can also benefit various other
sports in the future.

## Acknowledgment

Thanks to Jerrin Bright for helping with the figures and formatting. This work
was supported by Stathletes through the Mitacs Accelerate Program and the
Natural Sciences and Engineering Research Council of Canada (NSERC).

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Supplementary

We present empirical results from experimenting with different network choices
and our reasoning behind the proposed framework. This supplementary includes:
(i) Effect of Homography; (ii) Effect of message passing steps; (iii) Video-
wise quantitative results on the 13-test set videos in broadcast hockey
dataset [19]; (iv) Qualitative tracking results on VIP-HTD and broadcast
hockey dataset.

1\. Effect of Homography

Test video # | Appearance | Homography | IDsw $\downarrow$ | IDF1 $\uparrow$
---|---|---|---|---
| ✓ |  | 31 | 94.8
1 | ✓ | ✓ | 8 | 95.7
| ✓ |  | 37 | 90.7
2 | ✓ | ✓ | 27 | 94.1
| ✓ |  | 19 | 93.5
3 | ✓ | ✓ | 14 | 93.9
| ✓ |  | 13 | 93.8
4 | ✓ | ✓ | 4 | 98.2
| ✓ |  | 53 | 89.2
5 | ✓ | ✓ | 13 | 97.5
| ✓ |  | 25 | 90.0
6 | ✓ | ✓ | 12 | 94.0
| ✓ |  | 28 | 87.9
7 | ✓ | ✓ | 11 | 88.8
| ✓ |  | 35 | 79.0
8 | ✓ | ✓ | 2 | 97.9
| ✓ |  | 16 | 92.8
9 | ✓ | ✓ | 6 | 97.1
| ✓ |  | 25 | 81.5
10 | ✓ | ✓ | 23 | 90.8
| ✓ |  | 25 | 94.1
11 | ✓ | ✓ | 4 | 97.6
| ✓ |  | 23 | 88.2
12 | ✓ | ✓ | 16 | 92.9
| ✓ |  | 10 | 94.9
13 | ✓ | ✓ | 11 | 97.7
TABLE IV: Effect of homography on IDsw and IDF1 scores for the broadcast ice
hockey test-set [19]

From Table IV, it can be observed that only using appearance features
underperforms by a noticeable margin in each listed sequence, while augmenting
it with homography cues boosts the IDF1 score and reduces the number of
incurred IDsw. This empirically validates our core hypothesis that homography
makes tracking better.

Figure 3: No. of message passing steps, $L$ vs. No. of IDsw incurred

2\. No. of message passing steps, $L$

The no. of message passing steps for $L$, analogous to the receptive field of
a CNN is best pronounced at $L=6$ steps in our model. $L<6$ is inadequate to
propagate information across neighboring nodes and edges, leading to lesser
capability (as evident from the $\uparrow$ IDsw), while $L>6$ leads to
possible overfitting on the training data. Thus, $L$ should be treated as an
empirical hyperparameter which is best chosen when observed.

# of message passing steps | IDsw $\downarrow$ | IDF1 $\uparrow$
---|---|---
2 | 173 | 85.5
4 | 51 | 93.4
6 | 27 | 94.1
8 | 34 | 92.2
10 | 42 | 84.7
12 | 107 | 67.4
14 | 388 | 43.3
TABLE V: Effect of message passing steps on IDsw and IDF1 scores for a
randomly chosen sequence from the broadcast hockey dataset [19]

3\. Video-wise quantitative results

Table VI presents a detailed summary of our test results on the 13 test videos
in broadcast ice hockey dataset [19]. Our model achieves SOTA results on all
sequences despite occlusions and camera movements.

Video # | Frames | IDsw $\pm$$\downarrow$ | IDF1 $\pm$$\uparrow$ % | IDsw $\downarrow$ | IDF1 $\uparrow$ %
---|---|---|---|---|---
1 | 1,303 | 85 | 80.7 | 8 | 95.7
2 | 1,210 | 113 | 75.4 | 27 | 94.1
3 | 878 | 114 | 77.0 | 14 | 93.9
4 | 1,033 | 45 | 79.7 | 4 | 98.2
5 | 1,071 | 154 | 54.9 | 13 | 97.5
6 | 1,441 | 81 | 76.1 | 12 | 94.0
7 | 682 | 58 | 63.0 | 11 | 88.8
8 | 1,056 | 50 | 80.7 | 2 | 97.9
9 | 1,497 | 87 | 64.4 | 6 | 97.1
10 | 890 | 54 | 55.9 | 23 | 90.8
11 | 1,109 | 95 | 80.3 | 4 | 97.6
12 | 1,372 | 56 | 72.44 | 16 | 92.9
13 | 795 | 64 | 75.15 | 11 | 97.7
Overall | 14,337 | 1056 | 71.98 | 151 | 95.1
TABLE VI: Sequence-wise results on the 13 test-set videos from broadcast ice
hockey dataset. We evaluate both methods on ground truth annotations. $\pm$
denotes current sota benchmark results Figure 4: Qualitative results for the
VIP-HTD [51] test-set. Our tracker generalizes well to this unseen dataset,
incurring neglible ID switches

4\. Qualitative results

We show qualitative results for our tracker on the 7 games test-set from VIP-
HTD [51]. It can be observed that our tracker generalizes well to unseen, out-
of-distribution (OOD) data incurring less IDsw and excellent IDF1 score (Ref.
Table III), despite varying lighting conditions, jersey colours, and camera
angles. We hope is to further test the generalization capacity of our model
across sports in the future.