How linearly do people walk?
MOT is one of the most widely used evaluation datasets for object tracking. MOT17 is now 6+ years old, and while the benchmark has newer versions like MOT20, even the older MOT17 is also still used as a key SOTA benchmark:
And yet the ground truth is piecewise linear. Sort of.
Note: You can check out the code for this project here: https://github.com/smrfeld/mot-linearity
Let’s grab a few of the ground truth (GT) trajectories from the MOT17 dataset, and plot them. In the following figure, we show the initial and final bounding boxes, as well as the trajectory of the top-left and bottom-right points.
There are a lot of linear pieces here! For example between x=[1300,1350], or x=[1400,1440].
Is it an outlier?
It doesn’t look like this is outliers — it looks like the trajectories are at least somewhat piecewise linear.
Let’s find out!
But we need a way to measure linearity. We have a time series consisting of points that we think are piecewise linear. How can we tell if a section is a linear one?
Between two points, there is only one line, so we need to look at 3 points. Between three points, there are two line segments connecting the three points. If the three points lie in a line, the slopes of the two line segments will be the…