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Distances#

Predefined distances

Distance #

Bases: ABC

Abstract class representing a distance.

Subclasses must implement the method get_distances

Source code in norfair/distances.py 
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class Distance(ABC):
    """
    Abstract class representing a distance.

    Subclasses must implement the method `get_distances`
    """

    @abstractmethod
    def get_distances(
        self,
        objects: Sequence["TrackedObject"],
        candidates: Optional[Union[List["Detection"], List["TrackedObject"]]],
    ) -> np.ndarray:
        """
        Method that calculates the distances between new candidates and objects.

        Parameters
        ----------
        objects : Sequence[TrackedObject]
            Sequence of [TrackedObject][norfair.tracker.TrackedObject] to be compared with potential [Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]
            candidates.
        candidates : Union[List[Detection], List[TrackedObject]], optional
            List of candidates ([Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]) to be compared to [TrackedObject][norfair.tracker.TrackedObject].

        Returns
        -------
        np.ndarray
            A matrix containing the distances between objects and candidates.
        """

get_distances(objects, candidates) abstractmethod #

Method that calculates the distances between new candidates and objects.

Parameters:

Name Type Description Default
objects Sequence[TrackedObject]

Sequence of TrackedObject to be compared with potential Detection or TrackedObject candidates.

 required
candidates Union[List[Detection], List[TrackedObject]], optional

List of candidates (Detection or TrackedObject) to be compared to TrackedObject.

 required

Returns:

Type Description
np.ndarray

A matrix containing the distances between objects and candidates.
Source code in norfair/distances.py 
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@abstractmethod
def get_distances(
    self,
    objects: Sequence["TrackedObject"],
    candidates: Optional[Union[List["Detection"], List["TrackedObject"]]],
) -> np.ndarray:
    """
    Method that calculates the distances between new candidates and objects.

    Parameters
    ----------
    objects : Sequence[TrackedObject]
        Sequence of [TrackedObject][norfair.tracker.TrackedObject] to be compared with potential [Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]
        candidates.
    candidates : Union[List[Detection], List[TrackedObject]], optional
        List of candidates ([Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]) to be compared to [TrackedObject][norfair.tracker.TrackedObject].

    Returns
    -------
    np.ndarray
        A matrix containing the distances between objects and candidates.
    """

ScalarDistance #

Bases: Distance

ScalarDistance class represents a distance that is calculated pointwise.

Parameters:

Name Type Description Default
distance_function Union[Callable[[Detection, TrackedObject], float], Callable[[TrackedObject, TrackedObject], float]]

Distance function used to determine the pointwise distance between new candidates and objects. This function should take 2 input arguments, the first being a Union[Detection, TrackedObject], and the second TrackedObject. It has to return a float with the distance it calculates.

 required
Source code in norfair/distances.py 
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class ScalarDistance(Distance):
    """
    ScalarDistance class represents a distance that is calculated pointwise.

    Parameters
    ----------
    distance_function : Union[Callable[["Detection", "TrackedObject"], float], Callable[["TrackedObject", "TrackedObject"], float]]
        Distance function used to determine the pointwise distance between new candidates and objects.
        This function should take 2 input arguments, the first being a `Union[Detection, TrackedObject]`,
        and the second [TrackedObject][norfair.tracker.TrackedObject]. It has to return a `float` with the distance it calculates.
    """

    def __init__(
        self,
        distance_function: Union[
            Callable[["Detection", "TrackedObject"], float],
            Callable[["TrackedObject", "TrackedObject"], float],
        ],
    ):
        self.distance_function = distance_function

    def get_distances(
        self,
        objects: Sequence["TrackedObject"],
        candidates: Optional[Union[List["Detection"], List["TrackedObject"]]],
    ) -> np.ndarray:
        """
        Method that calculates the distances between new candidates and objects.

        Parameters
        ----------
        objects : Sequence[TrackedObject]
            Sequence of [TrackedObject][norfair.tracker.TrackedObject] to be compared with potential [Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]
            candidates.
        candidates : Union[List[Detection], List[TrackedObject]], optional
            List of candidates ([Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]) to be compared to [TrackedObject][norfair.tracker.TrackedObject].

        Returns
        -------
        np.ndarray
            A matrix containing the distances between objects and candidates.
        """
        distance_matrix = np.full(
            (len(candidates), len(objects)),
            fill_value=np.inf,
            dtype=np.float32,
        )
        if not objects or not candidates:
            return distance_matrix
        for c, candidate in enumerate(candidates):
            for o, obj in enumerate(objects):
                if candidate.label != obj.label:
                    if (candidate.label is None) or (obj.label is None):
                        print("\nThere are detections with and without label!")
                    continue
                distance = self.distance_function(candidate, obj)
                distance_matrix[c, o] = distance
        return distance_matrix

get_distances(objects, candidates) #

Method that calculates the distances between new candidates and objects.

Parameters:

Name Type Description Default
objects Sequence[TrackedObject]

Sequence of TrackedObject to be compared with potential Detection or TrackedObject candidates.

 required
candidates Union[List[Detection], List[TrackedObject]], optional

List of candidates (Detection or TrackedObject) to be compared to TrackedObject.

 required

Returns:

Type Description
np.ndarray

A matrix containing the distances between objects and candidates.
Source code in norfair/distances.py 
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def get_distances(
    self,
    objects: Sequence["TrackedObject"],
    candidates: Optional[Union[List["Detection"], List["TrackedObject"]]],
) -> np.ndarray:
    """
    Method that calculates the distances between new candidates and objects.

    Parameters
    ----------
    objects : Sequence[TrackedObject]
        Sequence of [TrackedObject][norfair.tracker.TrackedObject] to be compared with potential [Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]
        candidates.
    candidates : Union[List[Detection], List[TrackedObject]], optional
        List of candidates ([Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]) to be compared to [TrackedObject][norfair.tracker.TrackedObject].

    Returns
    -------
    np.ndarray
        A matrix containing the distances between objects and candidates.
    """
    distance_matrix = np.full(
        (len(candidates), len(objects)),
        fill_value=np.inf,
        dtype=np.float32,
    )
    if not objects or not candidates:
        return distance_matrix
    for c, candidate in enumerate(candidates):
        for o, obj in enumerate(objects):
            if candidate.label != obj.label:
                if (candidate.label is None) or (obj.label is None):
                    print("\nThere are detections with and without label!")
                continue
            distance = self.distance_function(candidate, obj)
            distance_matrix[c, o] = distance
    return distance_matrix

VectorizedDistance #

Bases: Distance

VectorizedDistance class represents a distance that is calculated in a vectorized way. This means that instead of going through every pair and explicitly calculating its distance, VectorizedDistance uses the entire vectors to compare to each other in a single operation.

Parameters:

Name Type Description Default
distance_function Callable[[np.ndarray, np.ndarray], np.ndarray]

Distance function used to determine the distances between new candidates and objects. This function should take 2 input arguments, the first being a np.ndarray and the second np.ndarray. It has to return a np.ndarray with the distance matrix it calculates.

 required
Source code in norfair/distances.py 
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class VectorizedDistance(Distance):
    """
    VectorizedDistance class represents a distance that is calculated in a vectorized way. This means
    that instead of going through every pair and explicitly calculating its distance, VectorizedDistance
    uses the entire vectors to compare to each other in a single operation.

    Parameters
    ----------
    distance_function : Callable[[np.ndarray, np.ndarray], np.ndarray]
        Distance function used to determine the distances between new candidates and objects.
        This function should take 2 input arguments, the first being a `np.ndarray` and the second
        `np.ndarray`. It has to return a `np.ndarray` with the distance matrix it calculates.
    """

    def __init__(
        self,
        distance_function: Callable[[np.ndarray, np.ndarray], np.ndarray],
    ):
        self.distance_function = distance_function

    def get_distances(
        self,
        objects: Sequence["TrackedObject"],
        candidates: Optional[Union[List["Detection"], List["TrackedObject"]]],
    ) -> np.ndarray:
        """
        Method that calculates the distances between new candidates and objects.

        Parameters
        ----------
        objects : Sequence[TrackedObject]
            Sequence of [TrackedObject][norfair.tracker.TrackedObject] to be compared with potential [Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]
            candidates.
        candidates : Union[List[Detection], List[TrackedObject]], optional
            List of candidates ([Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]) to be compared to [TrackedObject][norfair.tracker.TrackedObject].

        Returns
        -------
        np.ndarray
            A matrix containing the distances between objects and candidates.
        """
        distance_matrix = np.full(
            (len(candidates), len(objects)),
            fill_value=np.inf,
            dtype=np.float32,
        )
        if not objects or not candidates:
            return distance_matrix

        object_labels = np.array([o.label for o in objects]).astype(str)
        candidate_labels = np.array([c.label for c in candidates]).astype(str)

        # iterate over labels that are present both in objects and detections
        for label in np.intersect1d(
            np.unique(object_labels), np.unique(candidate_labels)
        ):
            # generate masks of the subset of object and detections for this label
            obj_mask = object_labels == label
            cand_mask = candidate_labels == label

            stacked_objects = []
            for o in objects:
                if str(o.label) == label:
                    stacked_objects.append(o.estimate.ravel())
            stacked_objects = np.stack(stacked_objects)

            stacked_candidates = []
            for c in candidates:
                if str(c.label) == label:
                    if "Detection" in str(type(c)):
                        stacked_candidates.append(c.points.ravel())
                    else:
                        stacked_candidates.append(c.estimate.ravel())
            stacked_candidates = np.stack(stacked_candidates)

            # calculate the pairwise distances between objects and candidates with this label
            # and assign the result to the correct positions inside distance_matrix
            distance_matrix[np.ix_(cand_mask, obj_mask)] = self._compute_distance(
                stacked_candidates, stacked_objects
            )

        return distance_matrix

    def _compute_distance(
        self, stacked_candidates: np.ndarray, stacked_objects: np.ndarray
    ) -> np.ndarray:
        """
        Method that computes the pairwise distances between new candidates and objects.
        It is intended to use the entire vectors to compare to each other in a single operation.

        Parameters
        ----------
        stacked_candidates : np.ndarray
            np.ndarray containing a stack of candidates to be compared with the stacked_objects.
        stacked_objects : np.ndarray
            np.ndarray containing a stack of objects to be compared with the stacked_objects.

        Returns
        -------
        np.ndarray
            A matrix containing the distances between objects and candidates.
        """
        return self.distance_function(stacked_candidates, stacked_objects)

get_distances(objects, candidates) #

Method that calculates the distances between new candidates and objects.

Parameters:

Name Type Description Default
objects Sequence[TrackedObject]

Sequence of TrackedObject to be compared with potential Detection or TrackedObject candidates.

 required
candidates Union[List[Detection], List[TrackedObject]], optional

List of candidates (Detection or TrackedObject) to be compared to TrackedObject.

 required

Returns:

Type Description
np.ndarray

A matrix containing the distances between objects and candidates.
Source code in norfair/distances.py 
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def get_distances(
    self,
    objects: Sequence["TrackedObject"],
    candidates: Optional[Union[List["Detection"], List["TrackedObject"]]],
) -> np.ndarray:
    """
    Method that calculates the distances between new candidates and objects.

    Parameters
    ----------
    objects : Sequence[TrackedObject]
        Sequence of [TrackedObject][norfair.tracker.TrackedObject] to be compared with potential [Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]
        candidates.
    candidates : Union[List[Detection], List[TrackedObject]], optional
        List of candidates ([Detection][norfair.tracker.Detection] or [TrackedObject][norfair.tracker.TrackedObject]) to be compared to [TrackedObject][norfair.tracker.TrackedObject].

    Returns
    -------
    np.ndarray
        A matrix containing the distances between objects and candidates.
    """
    distance_matrix = np.full(
        (len(candidates), len(objects)),
        fill_value=np.inf,
        dtype=np.float32,
    )
    if not objects or not candidates:
        return distance_matrix

    object_labels = np.array([o.label for o in objects]).astype(str)
    candidate_labels = np.array([c.label for c in candidates]).astype(str)

    # iterate over labels that are present both in objects and detections
    for label in np.intersect1d(
        np.unique(object_labels), np.unique(candidate_labels)
    ):
        # generate masks of the subset of object and detections for this label
        obj_mask = object_labels == label
        cand_mask = candidate_labels == label

        stacked_objects = []
        for o in objects:
            if str(o.label) == label:
                stacked_objects.append(o.estimate.ravel())
        stacked_objects = np.stack(stacked_objects)

        stacked_candidates = []
        for c in candidates:
            if str(c.label) == label:
                if "Detection" in str(type(c)):
                    stacked_candidates.append(c.points.ravel())
                else:
                    stacked_candidates.append(c.estimate.ravel())
        stacked_candidates = np.stack(stacked_candidates)

        # calculate the pairwise distances between objects and candidates with this label
        # and assign the result to the correct positions inside distance_matrix
        distance_matrix[np.ix_(cand_mask, obj_mask)] = self._compute_distance(
            stacked_candidates, stacked_objects
        )

    return distance_matrix

ScipyDistance #

Bases: VectorizedDistance

ScipyDistance class extends VectorizedDistance for the use of Scipy's vectorized distances.

This class uses scipy.spatial.distance.cdist to calculate distances between two np.ndarray.

Parameters:

Name Type Description Default
metric str, optional

Defines the specific Scipy metric to use to calculate the pairwise distances between new candidates and objects.

 'euclidean'

Other kwargs are passed through to cdist

See Also#

scipy.spatial.distance.cdist

Source code in norfair/distances.py 
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class ScipyDistance(VectorizedDistance):
    """
    ScipyDistance class extends VectorizedDistance for the use of Scipy's vectorized distances.

    This class uses `scipy.spatial.distance.cdist` to calculate distances between two `np.ndarray`.

    Parameters
    ----------
    metric : str, optional
        Defines the specific Scipy metric to use to calculate the pairwise distances between
        new candidates and objects.

    Other kwargs are passed through to cdist

    See Also
    --------
    [`scipy.spatial.distance.cdist`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.distance.cdist.html)
    """

    def __init__(self, metric: str = "euclidean", **kwargs):
        self.metric = metric
        super().__init__(distance_function=partial(cdist, metric=self.metric, **kwargs))

frobenius(detection, tracked_object) #

Frobernius norm on the difference of the points in detection and the estimates in tracked_object.

The Frobenius distance and norm are given by:

\[ d_f(a, b) = ||a - b||_F \]
\[ ||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2} \]

Parameters:

Name Type Description Default
detection Detection

A detection.

 required
tracked_object TrackedObject

A tracked object.

 required

Returns:

Type Description
float

The distance.

See Also#

np.linalg.norm

Source code in norfair/distances.py 
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def frobenius(detection: "Detection", tracked_object: "TrackedObject") -> float:
    """
    Frobernius norm on the difference of the points in detection and the estimates in tracked_object.

    The Frobenius distance and norm are given by:

    $$
    d_f(a, b) = ||a - b||_F
    $$

    $$
    ||A||_F = [\\sum_{i,j} abs(a_{i,j})^2]^{1/2}
    $$

    Parameters
    ----------
    detection : Detection
        A detection.
    tracked_object : TrackedObject
        A tracked object.

    Returns
    -------
    float
        The distance.

    See Also
    --------
    [`np.linalg.norm`](https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html)
    """
    return np.linalg.norm(detection.points - tracked_object.estimate)

mean_euclidean(detection, tracked_object) #

Average euclidean distance between the points in detection and estimates in tracked_object.

\[ d(a, b) = \frac{\sum_{i=0}^N ||a_i - b_i||_2}{N} \]

Parameters:

Name Type Description Default
detection Detection

A detection.

 required
tracked_object TrackedObject

A tracked object

 required

Returns:

Type Description
float

The distance.

See Also#

np.linalg.norm

Source code in norfair/distances.py 
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def mean_euclidean(detection: "Detection", tracked_object: "TrackedObject") -> float:
    """
    Average euclidean distance between the points in detection and estimates in tracked_object.

    $$
    d(a, b) = \\frac{\\sum_{i=0}^N ||a_i - b_i||_2}{N}
    $$

    Parameters
    ----------
    detection : Detection
        A detection.
    tracked_object : TrackedObject
        A tracked object

    Returns
    -------
    float
        The distance.

    See Also
    --------
    [`np.linalg.norm`](https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html)
    """
    return np.linalg.norm(detection.points - tracked_object.estimate, axis=1).mean()

mean_manhattan(detection, tracked_object) #

Average manhattan distance between the points in detection and the estimates in tracked_object

Given by:

\[ d(a, b) = \frac{\sum_{i=0}^N ||a_i - b_i||_1}{N} \]

Where \(||a||_1\) is the manhattan norm.

Parameters:

Name Type Description Default
detection Detection

A detection.

 required
tracked_object TrackedObject

a tracked object.

 required

Returns:

Type Description
float

The distance.

See Also#

np.linalg.norm

Source code in norfair/distances.py 
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def mean_manhattan(detection: "Detection", tracked_object: "TrackedObject") -> float:
    """
    Average manhattan distance between the points in detection and the estimates in tracked_object

    Given by:

    $$
    d(a, b) = \\frac{\\sum_{i=0}^N ||a_i - b_i||_1}{N}
    $$

    Where $||a||_1$ is the manhattan norm.

    Parameters
    ----------
    detection : Detection
        A detection.
    tracked_object : TrackedObject
        a tracked object.

    Returns
    -------
    float
        The distance.

    See Also
    --------
    [`np.linalg.norm`](https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html)
    """
    return np.linalg.norm(
        detection.points - tracked_object.estimate, ord=1, axis=1
    ).mean()

iou(candidates, objects) #

Calculate IoU between two sets of bounding boxes. Both sets of boxes are expected to be in [x_min, y_min, x_max, y_max] format.

Normal IoU is 1 when the boxes are the same and 0 when they don't overlap, to transform that into a distance that makes sense we return 1 - iou.

Parameters:

Name Type Description Default
candidates numpy.ndarray

(N, 4) numpy.ndarray containing candidates bounding boxes.

 required
objects numpy.ndarray

(K, 4) numpy.ndarray containing objects bounding boxes.

 required

Returns:

Type Description
numpy.ndarray

(N, K) numpy.ndarray of 1 - iou between candidates and objects.
Source code in norfair/distances.py 
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def iou(candidates: np.ndarray, objects: np.ndarray) -> np.ndarray:
    """
    Calculate IoU between two sets of bounding boxes. Both sets of boxes are expected
    to be in `[x_min, y_min, x_max, y_max]` format.

    Normal IoU is 1 when the boxes are the same and 0 when they don't overlap,
    to transform that into a distance that makes sense we return `1 - iou`.

    Parameters
    ----------
    candidates : numpy.ndarray
        (N, 4) numpy.ndarray containing candidates bounding boxes.
    objects : numpy.ndarray
        (K, 4) numpy.ndarray containing objects bounding boxes.

    Returns
    -------
    numpy.ndarray
        (N, K) numpy.ndarray of `1 - iou` between candidates and objects.
    """
    _validate_bboxes(candidates)

    area_candidates = _boxes_area(candidates.T)
    area_objects = _boxes_area(objects.T)

    top_left = np.maximum(candidates[:, None, :2], objects[:, :2])
    bottom_right = np.minimum(candidates[:, None, 2:], objects[:, 2:])

    area_intersection = np.prod(
        np.clip(bottom_right - top_left, a_min=0, a_max=None), 2
    )
    return 1 - area_intersection / (
        area_candidates[:, None] + area_objects - area_intersection
    )

get_distance_by_name(name) #

Select a distance by name.

Parameters:

Name Type Description Default
name str

A string defining the metric to get.

 required

Returns:

Type Description
Distance

The distance object.
Source code in norfair/distances.py 
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def get_distance_by_name(name: str) -> Distance:
    """
    Select a distance by name.

    Parameters
    ----------
    name : str
        A string defining the metric to get.

    Returns
    -------
    Distance
        The distance object.
    """

    if name in _SCALAR_DISTANCE_FUNCTIONS:
        warning(
            "You are using a scalar distance function. If you want to speed up the"
            " tracking process please consider using a vectorized distance function"
            f" such as {AVAILABLE_VECTORIZED_DISTANCES}."
        )
        distance = _SCALAR_DISTANCE_FUNCTIONS[name]
        distance_function = ScalarDistance(distance)
    elif name in _SCIPY_DISTANCE_FUNCTIONS:
        distance_function = ScipyDistance(name)
    elif name in _VECTORIZED_DISTANCE_FUNCTIONS:
        if name == "iou_opt":
            warning("iou_opt is deprecated, use iou instead")
        distance = _VECTORIZED_DISTANCE_FUNCTIONS[name]
        distance_function = VectorizedDistance(distance)
    else:
        raise ValueError(
            f"Invalid distance '{name}', expecting one of"
            f" {list(_SCALAR_DISTANCE_FUNCTIONS.keys()) + AVAILABLE_VECTORIZED_DISTANCES}"
        )

    return distance_function

create_keypoints_voting_distance(keypoint_distance_threshold, detection_threshold) #

Construct a keypoint voting distance function configured with the thresholds.

Count how many points in a detection match the with a tracked_object. A match is considered when distance between the points is < keypoint_distance_threshold and the score of the last_detection of the tracked_object is > detection_threshold. Notice the if multiple points are tracked, the ith point in detection can only match the ith point in the tracked object.

Distance is 1 if no point matches and approximates 0 as more points are matched.

Parameters:

Name Type Description Default
keypoint_distance_threshold float

Points closer than this threshold are considered a match.

 required
detection_threshold float

Detections and objects with score lower than this threshold are ignored.

 required

Returns:

Type Description
Callable

The distance funtion that must be passed to the Tracker.
Source code in norfair/distances.py 
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def create_keypoints_voting_distance(
    keypoint_distance_threshold: float, detection_threshold: float
) -> Callable[["Detection", "TrackedObject"], float]:
    """
    Construct a keypoint voting distance function configured with the thresholds.

    Count how many points in a detection match the with a tracked_object.
    A match is considered when distance between the points is < `keypoint_distance_threshold`
    and the score of the last_detection of the tracked_object is > `detection_threshold`.
    Notice the if multiple points are tracked, the ith point in detection can only match the ith
    point in the tracked object.

    Distance is 1 if no point matches and approximates 0 as more points are matched.

    Parameters
    ----------
    keypoint_distance_threshold: float
        Points closer than this threshold are considered a match.
    detection_threshold: float
        Detections and objects with score lower than this threshold are ignored.

    Returns
    -------
    Callable
        The distance funtion that must be passed to the Tracker.
    """

    def keypoints_voting_distance(
        detection: "Detection", tracked_object: "TrackedObject"
    ) -> float:
        distances = np.linalg.norm(detection.points - tracked_object.estimate, axis=1)
        match_num = np.count_nonzero(
            (distances < keypoint_distance_threshold)
            * (detection.scores > detection_threshold)
            * (tracked_object.last_detection.scores > detection_threshold)
        )
        return 1 / (1 + match_num)

    return keypoints_voting_distance

create_normalized_mean_euclidean_distance(height, width) #

Construct a normalized mean euclidean distance function configured with the max height and width.

The result distance is bound to [0, 1] where 1 indicates oposite corners of the image.

Parameters:

Name Type Description Default
height int

Height of the image.

 required
width int

Width of the image.

 required

Returns:

Type Description
Callable

The distance funtion that must be passed to the Tracker.
Source code in norfair/distances.py 
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def create_normalized_mean_euclidean_distance(
    height: int, width: int
) -> Callable[["Detection", "TrackedObject"], float]:
    """
    Construct a normalized mean euclidean distance function configured with the max height and width.

    The result distance is bound to [0, 1] where 1 indicates oposite corners of the image.

    Parameters
    ----------
    height: int
        Height of the image.
    width: int
        Width of the image.

    Returns
    -------
    Callable
        The distance funtion that must be passed to the Tracker.
    """

    def normalized__mean_euclidean_distance(
        detection: "Detection", tracked_object: "TrackedObject"
    ) -> float:
        """Normalized mean euclidean distance"""
        # calculate distances and normalized it by width and height
        difference = (detection.points - tracked_object.estimate).astype(float)
        difference[:, 0] /= width
        difference[:, 1] /= height

        # calculate eucledean distance and average
        return np.linalg.norm(difference, axis=1).mean()

    return normalized__mean_euclidean_distance