Question 5 of 6: Application — Cell Tracking

Question 5: Application — Cell Tracking (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A per-frame detection function returning $(x,y,p)$ triples (position + confidence), a 1-minute frame interval, a maximum inter-frame displacement of 20 px (one cell diameter), and detections that can be false positives (spurious, typically low $p$) or false negatives (a real cell missed).

Find. A tracking system that returns, for every currently-detected cell, its trajectory across all past frames in which it was present, robust to the stated detector imperfections.

Approach. Because the detector already supplies a confidence score, filter out low-confidence (likely spurious) detections BEFORE attempting to associate anything across frames, then solve the remaining association problem with a bounded-radius nearest-centroid search, using the stated maximum-displacement bound to disambiguate ordinary motion from cell division.

1. Filter by confidence. Discard every detection with $p$ below a fixed threshold (e.g. $p\ge0.5$) BEFORE any temporal reasoning, since a spurious detection has no real trajectory to join and would otherwise corrupt the association step; this directly reuses the confidence score find_cells already provides rather than inventing a separate spurious-detection filter.
2. Associate by nearest centroid within the motion bound. For every surviving detection in frame $t$, search frame $t{+}1$ for every surviving detection within the stated maximum displacement (20 px). Because the bound is physically stated (one cell diameter per minute), this search radius is not a tuning parameter to guess — it follows directly from the problem statement.
3. Classify each match by count. Exactly one candidate within range $\Rightarrow$ ordinary tracked motion (append the new position to that cell's trajectory). Zero candidates within range $\Rightarrow$ the cell was lost (moved out of frame, or missed by the detector that frame) — log it as lost rather than forcing an incorrect match to a distant, unrelated detection. Two or more candidates within range of one frame-$t$ detection is the signature of division: record a division event at that location and start a new trajectory for each daughter.
4. Handle a missed detection (false negative) gracefully. If a tracked cell has zero candidates in frame $t{+}1$ but reappears within the motion bound of its LAST known position in frame $t{+}2$, treat that as a one-frame detector miss rather than a genuine loss (interpolate the missing frame's position) — distinguishing a true exit/occlusion from a transient detector failure without ever needing to re-run find_cells itself.

The pipeline filters detections by confidence (threshold $p\ge0.5$) so that spurious low-confidence detections are dropped, tracks a cell that moves by less than the 20 px bound as a single one-to-one match, and flags a cell that splits into two daughters both within the search radius of the parent's centroid as a one-to-two division event. Detections more than 20 px apart are reported as "lost" rather than forced into a spurious long-range match.