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fix formatting errors in glossary
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niksirbi committed Dec 13, 2024
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:::{glossary}

pose estimation
: The process of estimating the positions of body parts (keypoints) in an image
The process of estimating the positions of body parts (keypoints) in an image
or video frame.

pose tracks
: A sequence of pose estimates for an individual or multiple individuals over time.
A sequence of pose estimates for an individual or multiple individuals over time.
Each pose estimate consists of the positions of body parts and associated confidence values.

keypoint
: A body part or feature of interest that is tracked by a
A body part or feature of interest that is tracked by a
{term}`pose estimation` algorithm. Examples include the nose, ears etc.

individual
: An entity that is tracked by a {term}`pose estimation` algorithm.
An entity that is tracked by a {term}`pose estimation` algorithm.
This could be an animal, a person, or an object.

confidence
: A value that indicates the confidence of the machine learning model in the
A value that indicates the confidence of the machine learning model in the
estimated position of a keypoint. In `movement`, this refers to the
point-wise confidence values output by the {term}`pose estimation` software.
: The homonymous data variable in a [movement dataset](target-poses-and-bboxes-dataset) holds

The homonymous data variable in a [movement dataset](target-poses-and-bboxes-dataset) holds
the confidence values for all individuals and keypoints at each timestep.

position
: The estimated location of a {term}`keypoint` in an image or video frame.
The estimated location of a {term}`keypoint` in an image or video frame.
This is typically represented in 2D or 3D Cartesian coordinates.
: The position vector {math}`\vec{r_i}(t)` for keypoint {math}`i` at time {math}`t`
The position vector {math}`\vec{r_i}(t)` for keypoint {math}`i` at time {math}`t`
points from the coordinate system origin to the keypoint's location.
```{math} \vec{r_i}(t) = (x_i(t), y_i(t))
:label: position
:name: eq-position
```
where {math}`x_i(t)`, {math}`y_i(t)` are the coordinates of
keypoint {math}`i` at time {math}`t` (for 3D add {math}`z_i(t)`).
: The homonymous data variable in a [movement dataset](target-poses-and-bboxes-dataset)

The homonymous data variable in a [movement dataset](target-poses-and-bboxes-dataset)
holds the positions of all individuals and keypoints at each timestep.

displacement:
: The change in {term}`position` of a keypoint between two consecutive frames.
The change in {term}`position` of a keypoint between two consecutive frames.
The displacement vector {math}`\vec{d_i}(t)` for keypoint {math}`i` at time
{math}`t` points from the keypoint's position at time {math}`t-1` to its
location at time {math}`t`.
```{math} \vec{d_i}(t) = \vec{r_i}(t) - \vec{r_i}(t-1)
:label: displacement
:name: eq-displacement
```
where {math}`\vec{r_i}(t)` is as defined in {math:numref}`position`.
: The homonymous data variable in a [movement dataset](target-poses-and-bboxes-dataset)
where {math}`\vec{r_i}(t)` is as defined in {math:numref}`eq-position`.

The homonymous data variable in a [movement dataset](target-poses-and-bboxes-dataset)
holds the displacements of all individuals and keypoints at each timestep.
At {math}`t=0`, the displacement is {math}`\vec{0}`.

velocity
: The rate of change of {term}`position` of a keypoint with respect to time.
The rate of change of {term}`position` of a keypoint with respect to time.
The velocity vector {math}`\vec{v_i}(t)` for keypoint {math}`i` at time
{math}`t` is the derivative of the position vector {math}`\vec{r_i}(t)`
with respect to time.
```{math} \vec{v_i}(t) = \frac{d\vec{r_i}(t)}{dt}
:label: velocity
:name: eq-velocity
```
where {math}`\vec{r_i}(t)` is as defined in {math:numref}`position`.
: The homonymous data variable in a [movement dataset](target-poses-and-bboxes-dataset)
where {math}`\vec{r_i}(t)` is as defined in {math:numref}`eq-position`.

The homonymous data variable in a [movement dataset](target-poses-and-bboxes-dataset)
holds the velocities of all individuals and keypoints at each timestep.

acceleration
: The rate of change of {term}`velocity` of a keypoint with respect to time.
The rate of change of {term}`velocity` of a keypoint with respect to time.
The acceleration vector {math}`\vec{a_i}(t)` for keypoint {math}`i` at time
{math}`t` is the derivative of the velocity vector {math}`\vec{v_i}(t)`
with respect to time.
```{math} \vec{a_i}(t) = \frac{d\vec{v_i}(t)}{dt}
:label: acceleration
:name: eq-acceleration
```
where {math}`\vec{v_i}(t)` is as defined in {math:numref}`velocity`.
: The homonymous data variable in a [movement dataset](target-poses-and-bboxes-dataset)
where {math}`\vec{v_i}(t)` is as defined in {math:numref}`eq-velocity`.

The homonymous data variable in a [movement dataset](target-poses-and-bboxes-dataset)
holds the accelerations of all individuals and keypoints at each timestep.

:::

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