Feature Track Length

easyPROBundle Adjustment for SfMSfMCV: Structure from Motion and SLAM

Count how many cameras observe a particular 3D point.

In Structure from Motion, a track is the set of 2D observations of a single 3D point across multiple images. The track length is the number of images where the point is observed.

Longer tracks are valuable because:

More observations lead to better triangulation accuracy
They provide more constraints for bundle adjustment
They help verify the correctness of feature matching

Typically, we filter out points with very short tracks (e.g., < 3) as they may be noise or outliers.

Example

Input

track_length([True, True, False, True, False])

Output

Reasoning

visibility has one entry per camera, in camera order: entry $i$ says whether the 3D point was detected and matched in image $i$ . Here there are 5 cameras.
The track is the set of cameras that see the point: cameras 0, 1 and 3. Cameras 2 and 4 contribute nothing, because the point was not observed there (occluded, out of frame, or the match was rejected).
Writing $v_i = 1$ for a visible camera and $v_i = 0$ otherwise, the track length is $L = \sum_{i=0}^{4} v_i = 1 + 1 + 0 + 1 + 0 = 3$ .
The output 3 is a plain integer count, not a list of camera indices. It can range from $0$ (no camera sees the point) up to the number of cameras.
Notice that the order of the cameras does not matter, only how many are visible. With the usual "at least 3 views" filter this point just survives.

Constraints

visibility: list of boolean values, one per camera
Return count of True values (cameras that see the point)

Learn this in

Multi-View Geometry3D Computer Vision

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Concept primerPREVIEW

Background Knowledge

In Structure from Motion (SfM), a 3D point in the scene is reconstructed from its 2D projections (feature detections) across multiple images. Each time a feature detector finds the same physical point in a new image and the matcher links it consistently to previous views, that 2D detection becomes another observation of the same 3D point. The collection of all such observations for one 3D point is called a track.

Formally, a track is a set of tuples like $($ \text{camera_id} $, x, y)$ that all correspond to the same underlying 3D point. The track length is just the number of distinct cameras (or images) in that set. Longer tracks give better geometry: more views mean more constraints on the 3D point position and camera poses, which helps triangulation and bundle adjustment to be more stable and accurate. Very short tracks (e.g., appearing in only 1–2 images) are often unreliable or unhelpful and are commonly filtered out.

Algorithm/Approach

At an algorithmic level, this problem is simply counting how many cameras observe a given 3D point. In coding-interview terms, this usually reduces to one of these patterns:

If the input already groups observations by 3D point (e.g., a list of camera indices per point), then:
The track length = size of that list (or the size of the set, if duplicates are possible).
If the input is a flat list of observations (e.g., pairs/triples containing point ID and camera ID), then:
Group by point ID, then count unique camera IDs per group.

So the core approach is: aggregate all observations belonging to the same 3D point and then count how many cameras are involved.

Step-by-Step Strategy

Assume you are given all observations for a single 3D point, or you first isolate them from a larger dataset:

Identify the observations of the target 3D point

If input is already “for this point, here are its cameras”, you are done with this step.
If input is global, filter observations where point_id == target_point_id.

Extract camera identifiers

From each observation, take the camera_id (or image index).

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solution.py

Python 3.13

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