Agreed terminology

• default (cartesian) coordinate system:
  • origin top left of the image,
  • x-axis is positive across columns (pointing right),
  • y-axis resulting from the right hand rule; i.e., positive across rows (pointing down).
    This convention matches DLC, napari and most image processing tools.
• position vector for keypoint i at time t: vector from the origin of the coordinate system to keypoint i $$\vec{r_i}(t) = (x_i(t), y_i(t))$$
• velocity vector for keypoint i at time t: instant velocity of keypoint i at time t $$\vec{v_i}(t) = (\dot{x}_i(t), \dot{y}_i(t))$$
• acceleration vector for keypoint i at time t: instant acceleration of keypoint i at time t $$\vec{a_i}(t) = (\ddot{x}_i(t), \ddot{y}_i(t))$$
• displacement vector for keypoint i at time t: vector representing the displacement of a keypoint i with respect to its position at the previous frame t-1 $$\vec{d_i}(t) = (x_i(t) - x_i(t-1), y_i(t) - y_i(t-1))$$

FWIW, here's a post on the coordinate system we adopt in SLEAP (center pixel-aligned):

talmolab/sleap#1640 (comment)

This is the same as OpenCV too.

Thanks @talmo, this is super useful!

also include/link to the concept of movement dataset

and the concept of bounding boxes (and tracked bounding boxes)

Definitions for "forward vector", "head direction vector", "heading"

@sfmig on zulip :

Note that as Niko said above, vectors in movement are free vectors, that is , their point of application is not fixed and they are just defined by their magnitude and direction. The magnitude and direction can be expressed by the x-y coordinates of the tip of the vector (assumed to be applied at the origin), or by the polar coordinates rho, phi.

As pointed out by @lochhh we should also clarify any movement specific terms that we use for convenience, such as "motion tracks".
From PR #352:

In the context of movement, we refer to these trajectories as tracks: we use pose tracks to refer to the trajectories of a set of keypoints, bounding boxes' tracks to refer to the trajectories of bounding boxes' centroids, or motion tracks in the more general case.

From the meeting with Mikkel:

• image coord system: make it clear in the glossary that this is the default and how it is defined (including, pixel-centred clarification).
• add a schematic of the right-hand rule in the glossary, something similar to Freya Holmer's nice schematic but further simplified.
• add a schematic of polar coordinates in the glossary.
• add pinhole camera schematic, showing the image coord system, the camera coord system, and the world coord system.
• if we implement a "transform to top-right / top-left / bottom-right / bottom-left" coordinate systems, we need to clarify what we mean in the glossary.