The document discusses an efficient approach for large-scale cell tracking using an approximated Sinkhorn algorithm that minimizes the need for extensive training data. It compares this non-deep learning-based method with existing algorithms, highlighting its faster time complexity and improved tracking efficiency. Future work includes extending the method for tracklet-level association and enhancing the detection process.

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