Cell tracking for a large scale (of over 1 million cells) has not yet been achievable within reasonable a time scope with current NN/RNN/Bi-RNN based methods. This individual research conducted by me at Osaka University, ISIR seeks to solve this problem using the Sinkhorn algorithm, and taking inspiration from the MPM method (Hayashida, 2020)

1. Large-scale cell tracking using
an approximated Sinkhorn algorithm
発表者：NANDEDKAR PARTH SHIRISH
1
Department of
Intelligent Media,
Yagi Laboratory

2. Automation of cell image analysis
• Detection and tracking
• Shape, colour and motion analysis
2
Sub-million cells captured by trans-scale-scope [Ichimura+ 2020]
Our Challenge: Efficient large-scale cell tracking
Background

3. Non deep learning based
CancerCellTracker [Li+ 2010], Hungarian
algorithm [Tashita+ 2015], Probabilistic
[Huh+ 2011], Particle Filter [Fujimoto+ 2020]
+ Does not require huge training
data
- Tracking by global association
is time consuming
Deep learning-based
MPM [Hayashida+ 2020], CellNucleiTracker [Chen+
2019], Deep MOT [Xu+ 2020]
+ Better accuracies in detection
and tracking
- Require huge training data by
manual annotation
Related Work
3
[Hayashida+ 2020] [Chen+ 2019] [Li+ 2010]

4. Efficient large-scale cell tracking
• Non-deep learning-based approach
(i.e., huge training data is unnecessary)
• Tracking by global association
 Hungarian algorithm
 Sinkhorn algorithm
 Approximate Sinkhorn algorithm (proposed)
4
Objective

5. Pipeline
5
Detection: 2D blob detection by Laplacian of Gaussian filter
Tracking (association): Approximated Sinkhorn algorithm
Tracking (association)
Detection
Input cell image

6. Association by Hungarian Algorithm
• Association for sets of cells in adjacent frames t-1 and t
by minimal transportation cost
• Time complexity: 𝑂(𝑁3) 𝑁: #cells
6
Cost matrix
(Dissimilarity of positions,
sizes, intensities, etc.)
1
3
2
2
3
1
1 2 3
1 5 1 3
2 2 6 1
3 5 6 2
Frame t-1
Frame t
Hungarian
algorithm
Cell
ID
at
t-1
Cell ID at t
1 2 3
1 0 1 0
2 1 0 0
3 0 0 1
Association result
1: Associated
0: Not associated
2
3
1
Frame t
1
3
2
Frame t-1

7. Association by Sinkhorn Algorithm
• Fast approximation for Hungarian algorithm by iterative
update of affinity matrix K
• Time complexity: 𝑂(𝑁2) 𝑁: #cells
7
Sinkhorn Algorithm
Affinity matrix K
Cost matrix C
Bottleneck: Iterative
matrix multiplication

8. Limiting Association Candidates
• Division into small patches
• Association candidates: cells in adjacent 9 patches
8
Cell of interest
Matching cells are
in this patches
#Matching candidate: k <<N

9. Association by Aproximated Sinkhorn Algorithm
• Fast approximation for Sinkhorn algorithm by
sparse affinity matrix K
• Time complexity: 𝑂(𝑘𝑁) 𝑁: #cells
9
Sinkhorn Algorithm
Cost matrix C
Faster multiplication
by sparse matrix
Affinity matrix K
Sparse affinity
matrix K

10. • Data
• Fluorescent images of malnourished Dictyostelium cells
captured by trans-scale-scope [Ichimura+ 2020]
• Evaluation items
• Computational time for association per frame
over various #cells
• Tracking accuracy over 50 ground-truth tracklets
• Comparison
• Sinkhorn algorithm
• Approximated Sinkhorn algorithm (proposed)
10
Experiments: Setup

11. Experiments: Computational Time
11
Sinkhorn - 𝑂(𝑛2
)
Approximated Sinkhorn − 𝑂(𝑘𝑛)

12. Tracking Accuracy
12
IDS (ID Switches): Number of times a trajectory changes
its matched ground-truth identity, in the sample size.
Recall:
𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑙𝑦 𝑚𝑎𝑡𝑐ℎ𝑒𝑑 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛𝑠
𝐺𝑟𝑜𝑢𝑛𝑑 𝑡𝑟𝑢𝑡ℎ 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛𝑠
Precision:
𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑙𝑦 𝑚𝑎𝑡𝑐ℎ𝑒𝑑 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛𝑠
𝑇𝑜𝑡𝑎𝑙 𝑟𝑒𝑠𝑢𝑙𝑡 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛𝑠

13. Summary and Future Work
13
• Efficient large-scale cell tracking by approximated
Sinkhorn algorithm
• Sparse affinity matrix by limiting matching candidates
• Linear time complexity
• Future work
• Extension to association at the tracklet level
• Speeding up detection process 13
Cost matrix C Sparse affinity matrix K