─░├žeri─če ge├ž

Referans i├žin ultralytics/trackers/utils/kalman_filter.py

Not

Bu dosya https://github.com/ultralytics/ultralytics/blob/main/ ultralytics/trackers/utils/kalman_filter .py adresinde mevcuttur. Bir sorun tespit ederseniz l├╝tfen bir ├çekme ─░ste─či ­čŤá´ŞĆ ile katk─▒da bulunarak d├╝zeltilmesine yard─▒mc─▒ olun. Te┼čekk├╝rler ­čÖĆ!



ultralytics.trackers.utils.kalman_filter.KalmanFilterXYAH

Bytetrack i├žin. G├Âr├╝nt├╝ uzay─▒nda s─▒n─▒rlay─▒c─▒ kutular─▒ izlemek i├žin basit bir Kalman filtresi.

8 boyutlu durum uzay─▒ (x, y, a, h, vx, vy, va, vh) s─▒n─▒rlay─▒c─▒ kutu merkez konumunu (x, y), en-boy a oran─▒, h y├╝ksekli─či ve bunlar─▒n ilgili h─▒zlar─▒.

Nesne hareketi sabit h─▒z modelini takip eder. S─▒n─▒rlay─▒c─▒ kutu konumu (x, y, a, h) do─črudan olarak al─▒n─▒r durum uzay─▒n─▒n g├Âzlemlenmesi (do─črusal g├Âzlem modeli).

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
class KalmanFilterXYAH:
    """
    For bytetrack. A simple Kalman filter for tracking bounding boxes in image space.

    The 8-dimensional state space (x, y, a, h, vx, vy, va, vh) contains the bounding box center position (x, y), aspect
    ratio a, height h, and their respective velocities.

    Object motion follows a constant velocity model. The bounding box location (x, y, a, h) is taken as direct
    observation of the state space (linear observation model).
    """

    def __init__(self):
        """Initialize Kalman filter model matrices with motion and observation uncertainty weights."""
        ndim, dt = 4, 1.0

        # Create Kalman filter model matrices
        self._motion_mat = np.eye(2 * ndim, 2 * ndim)
        for i in range(ndim):
            self._motion_mat[i, ndim + i] = dt
        self._update_mat = np.eye(ndim, 2 * ndim)

        # Motion and observation uncertainty are chosen relative to the current state estimate. These weights control
        # the amount of uncertainty in the model.
        self._std_weight_position = 1.0 / 20
        self._std_weight_velocity = 1.0 / 160

    def initiate(self, measurement: np.ndarray) -> tuple:
        """
        Create track from unassociated measurement.

        Args:
            measurement (ndarray): Bounding box coordinates (x, y, a, h) with center position (x, y), aspect ratio a,
                and height h.

        Returns:
            (tuple[ndarray, ndarray]): Returns the mean vector (8 dimensional) and covariance matrix (8x8 dimensional)
                of the new track. Unobserved velocities are initialized to 0 mean.
        """
        mean_pos = measurement
        mean_vel = np.zeros_like(mean_pos)
        mean = np.r_[mean_pos, mean_vel]

        std = [
            2 * self._std_weight_position * measurement[3],
            2 * self._std_weight_position * measurement[3],
            1e-2,
            2 * self._std_weight_position * measurement[3],
            10 * self._std_weight_velocity * measurement[3],
            10 * self._std_weight_velocity * measurement[3],
            1e-5,
            10 * self._std_weight_velocity * measurement[3],
        ]
        covariance = np.diag(np.square(std))
        return mean, covariance

    def predict(self, mean: np.ndarray, covariance: np.ndarray) -> tuple:
        """
        Run Kalman filter prediction step.

        Args:
            mean (ndarray): The 8 dimensional mean vector of the object state at the previous time step.
            covariance (ndarray): The 8x8 dimensional covariance matrix of the object state at the previous time step.

        Returns:
            (tuple[ndarray, ndarray]): Returns the mean vector and covariance matrix of the predicted state. Unobserved
                velocities are initialized to 0 mean.
        """
        std_pos = [
            self._std_weight_position * mean[3],
            self._std_weight_position * mean[3],
            1e-2,
            self._std_weight_position * mean[3],
        ]
        std_vel = [
            self._std_weight_velocity * mean[3],
            self._std_weight_velocity * mean[3],
            1e-5,
            self._std_weight_velocity * mean[3],
        ]
        motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))

        mean = np.dot(mean, self._motion_mat.T)
        covariance = np.linalg.multi_dot((self._motion_mat, covariance, self._motion_mat.T)) + motion_cov

        return mean, covariance

    def project(self, mean: np.ndarray, covariance: np.ndarray) -> tuple:
        """
        Project state distribution to measurement space.

        Args:
            mean (ndarray): The state's mean vector (8 dimensional array).
            covariance (ndarray): The state's covariance matrix (8x8 dimensional).

        Returns:
            (tuple[ndarray, ndarray]): Returns the projected mean and covariance matrix of the given state estimate.
        """
        std = [
            self._std_weight_position * mean[3],
            self._std_weight_position * mean[3],
            1e-1,
            self._std_weight_position * mean[3],
        ]
        innovation_cov = np.diag(np.square(std))

        mean = np.dot(self._update_mat, mean)
        covariance = np.linalg.multi_dot((self._update_mat, covariance, self._update_mat.T))
        return mean, covariance + innovation_cov

    def multi_predict(self, mean: np.ndarray, covariance: np.ndarray) -> tuple:
        """
        Run Kalman filter prediction step (Vectorized version).

        Args:
            mean (ndarray): The Nx8 dimensional mean matrix of the object states at the previous time step.
            covariance (ndarray): The Nx8x8 covariance matrix of the object states at the previous time step.

        Returns:
            (tuple[ndarray, ndarray]): Returns the mean vector and covariance matrix of the predicted state. Unobserved
                velocities are initialized to 0 mean.
        """
        std_pos = [
            self._std_weight_position * mean[:, 3],
            self._std_weight_position * mean[:, 3],
            1e-2 * np.ones_like(mean[:, 3]),
            self._std_weight_position * mean[:, 3],
        ]
        std_vel = [
            self._std_weight_velocity * mean[:, 3],
            self._std_weight_velocity * mean[:, 3],
            1e-5 * np.ones_like(mean[:, 3]),
            self._std_weight_velocity * mean[:, 3],
        ]
        sqr = np.square(np.r_[std_pos, std_vel]).T

        motion_cov = [np.diag(sqr[i]) for i in range(len(mean))]
        motion_cov = np.asarray(motion_cov)

        mean = np.dot(mean, self._motion_mat.T)
        left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
        covariance = np.dot(left, self._motion_mat.T) + motion_cov

        return mean, covariance

    def update(self, mean: np.ndarray, covariance: np.ndarray, measurement: np.ndarray) -> tuple:
        """
        Run Kalman filter correction step.

        Args:
            mean (ndarray): The predicted state's mean vector (8 dimensional).
            covariance (ndarray): The state's covariance matrix (8x8 dimensional).
            measurement (ndarray): The 4 dimensional measurement vector (x, y, a, h), where (x, y) is the center
                position, a the aspect ratio, and h the height of the bounding box.

        Returns:
            (tuple[ndarray, ndarray]): Returns the measurement-corrected state distribution.
        """
        projected_mean, projected_cov = self.project(mean, covariance)

        chol_factor, lower = scipy.linalg.cho_factor(projected_cov, lower=True, check_finite=False)
        kalman_gain = scipy.linalg.cho_solve(
            (chol_factor, lower), np.dot(covariance, self._update_mat.T).T, check_finite=False
        ).T
        innovation = measurement - projected_mean

        new_mean = mean + np.dot(innovation, kalman_gain.T)
        new_covariance = covariance - np.linalg.multi_dot((kalman_gain, projected_cov, kalman_gain.T))
        return new_mean, new_covariance

    def gating_distance(
        self,
        mean: np.ndarray,
        covariance: np.ndarray,
        measurements: np.ndarray,
        only_position: bool = False,
        metric: str = "maha",
    ) -> np.ndarray:
        """
        Compute gating distance between state distribution and measurements. A suitable distance threshold can be
        obtained from `chi2inv95`. If `only_position` is False, the chi-square distribution has 4 degrees of freedom,
        otherwise 2.

        Args:
            mean (ndarray): Mean vector over the state distribution (8 dimensional).
            covariance (ndarray): Covariance of the state distribution (8x8 dimensional).
            measurements (ndarray): An Nx4 matrix of N measurements, each in format (x, y, a, h) where (x, y)
                is the bounding box center position, a the aspect ratio, and h the height.
            only_position (bool, optional): If True, distance computation is done with respect to the bounding box
                center position only. Defaults to False.
            metric (str, optional): The metric to use for calculating the distance. Options are 'gaussian' for the
                squared Euclidean distance and 'maha' for the squared Mahalanobis distance. Defaults to 'maha'.

        Returns:
            (np.ndarray): Returns an array of length N, where the i-th element contains the squared distance between
                (mean, covariance) and `measurements[i]`.
        """
        mean, covariance = self.project(mean, covariance)
        if only_position:
            mean, covariance = mean[:2], covariance[:2, :2]
            measurements = measurements[:, :2]

        d = measurements - mean
        if metric == "gaussian":
            return np.sum(d * d, axis=1)
        elif metric == "maha":
            cholesky_factor = np.linalg.cholesky(covariance)
            z = scipy.linalg.solve_triangular(cholesky_factor, d.T, lower=True, check_finite=False, overwrite_b=True)
            return np.sum(z * z, axis=0)  # square maha
        else:
            raise ValueError("Invalid distance metric")

__init__()

Kalman filtresi model matrislerini hareket ve g├Âzlem belirsizli─či a─č─▒rl─▒klar─▒ ile ba┼člat─▒n.

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def __init__(self):
    """Initialize Kalman filter model matrices with motion and observation uncertainty weights."""
    ndim, dt = 4, 1.0

    # Create Kalman filter model matrices
    self._motion_mat = np.eye(2 * ndim, 2 * ndim)
    for i in range(ndim):
        self._motion_mat[i, ndim + i] = dt
    self._update_mat = np.eye(ndim, 2 * ndim)

    # Motion and observation uncertainty are chosen relative to the current state estimate. These weights control
    # the amount of uncertainty in the model.
    self._std_weight_position = 1.0 / 20
    self._std_weight_velocity = 1.0 / 160

gating_distance(mean, covariance, measurements, only_position=False, metric='maha')

Durum da─č─▒l─▒m─▒ ve ├Âl├ž├╝mler aras─▒ndaki ge├žitleme mesafesini hesaplay─▒n. Uygun bir mesafe e┼či─či ┼čunlar olabilir 'den elde edilmi┼čtir. chi2inv95. E─čer only_position Yanl─▒┼č ise, ki-kare da─č─▒l─▒m─▒ 4 serbestlik derecesine sahiptir, Aksi takdirde 2.

Parametreler:

─░sim Tip A├ž─▒klama Varsay─▒lan
mean ndarray

Durum da─č─▒l─▒m─▒ ├╝zerinde ortalama vekt├Âr (8 boyutlu).

gerekli
covariance ndarray

Durum da─č─▒l─▒m─▒n─▒n kovaryans─▒ (8x8 boyutlu).

gerekli
measurements ndarray

Her biri (x, y, a, h) bi├žiminde N ├Âl├ž├╝mden olu┼čan bir Nx4 matrisi, burada (x, y) s─▒n─▒rlay─▒c─▒ kutu merkez konumu, a en boy oran─▒ ve h y├╝ksekliktir.

gerekli
only_position bool

True ise, mesafe hesaplamas─▒ s─▒n─▒rlay─▒c─▒ kutuya g├Âre yap─▒l─▒r yaln─▒zca merkez konum. Varsay─▒lan de─čer False'dir.

False
metric str

Mesafeyi hesaplamak i├žin kullan─▒lacak metrik. Se├ženekler 'gaussian' i├žin kareli ├ľklid mesafesi ve kareli Mahalanobis mesafesi i├žin 'maha'. Varsay─▒lan de─čer 'maha'd─▒r.

'maha'

─░ade:

Tip A├ž─▒klama
ndarray

N uzunlu─čunda bir dizi d├Ând├╝r├╝r; burada i'inci eleman, i ile i aras─▒ndaki karesel uzakl─▒─č─▒ i├žerir. (ortalama, kovaryans) ve measurements[i].

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def gating_distance(
    self,
    mean: np.ndarray,
    covariance: np.ndarray,
    measurements: np.ndarray,
    only_position: bool = False,
    metric: str = "maha",
) -> np.ndarray:
    """
    Compute gating distance between state distribution and measurements. A suitable distance threshold can be
    obtained from `chi2inv95`. If `only_position` is False, the chi-square distribution has 4 degrees of freedom,
    otherwise 2.

    Args:
        mean (ndarray): Mean vector over the state distribution (8 dimensional).
        covariance (ndarray): Covariance of the state distribution (8x8 dimensional).
        measurements (ndarray): An Nx4 matrix of N measurements, each in format (x, y, a, h) where (x, y)
            is the bounding box center position, a the aspect ratio, and h the height.
        only_position (bool, optional): If True, distance computation is done with respect to the bounding box
            center position only. Defaults to False.
        metric (str, optional): The metric to use for calculating the distance. Options are 'gaussian' for the
            squared Euclidean distance and 'maha' for the squared Mahalanobis distance. Defaults to 'maha'.

    Returns:
        (np.ndarray): Returns an array of length N, where the i-th element contains the squared distance between
            (mean, covariance) and `measurements[i]`.
    """
    mean, covariance = self.project(mean, covariance)
    if only_position:
        mean, covariance = mean[:2], covariance[:2, :2]
        measurements = measurements[:, :2]

    d = measurements - mean
    if metric == "gaussian":
        return np.sum(d * d, axis=1)
    elif metric == "maha":
        cholesky_factor = np.linalg.cholesky(covariance)
        z = scipy.linalg.solve_triangular(cholesky_factor, d.T, lower=True, check_finite=False, overwrite_b=True)
        return np.sum(z * z, axis=0)  # square maha
    else:
        raise ValueError("Invalid distance metric")

initiate(measurement)

─░li┼čkilendirilmemi┼č ├Âl├ž├╝mden iz olu┼čturun.

Parametreler:

─░sim Tip A├ž─▒klama Varsay─▒lan
measurement ndarray

Merkez konumu (x, y), en boy oran─▒ a ile s─▒n─▒rlay─▒c─▒ kutu koordinatlar─▒ (x, y, a, h), ve h y├╝ksekli─či.

gerekli

─░ade:

Tip A├ž─▒klama
tuple[ndarray, ndarray]

Ortalama vekt├Âr├╝ (8 boyutlu) ve kovaryans matrisini (8x8 boyutlu) d├Ând├╝r├╝r yeni par├žan─▒n. G├Âzlemlenmemi┼č h─▒zlar 0 ortalama ile ba┼člat─▒l─▒r.

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def initiate(self, measurement: np.ndarray) -> tuple:
    """
    Create track from unassociated measurement.

    Args:
        measurement (ndarray): Bounding box coordinates (x, y, a, h) with center position (x, y), aspect ratio a,
            and height h.

    Returns:
        (tuple[ndarray, ndarray]): Returns the mean vector (8 dimensional) and covariance matrix (8x8 dimensional)
            of the new track. Unobserved velocities are initialized to 0 mean.
    """
    mean_pos = measurement
    mean_vel = np.zeros_like(mean_pos)
    mean = np.r_[mean_pos, mean_vel]

    std = [
        2 * self._std_weight_position * measurement[3],
        2 * self._std_weight_position * measurement[3],
        1e-2,
        2 * self._std_weight_position * measurement[3],
        10 * self._std_weight_velocity * measurement[3],
        10 * self._std_weight_velocity * measurement[3],
        1e-5,
        10 * self._std_weight_velocity * measurement[3],
    ]
    covariance = np.diag(np.square(std))
    return mean, covariance

multi_predict(mean, covariance)

Kalman filtresi tahmin ad─▒m─▒n─▒ ├žal─▒┼čt─▒r─▒n (Vekt├Ârle┼čtirilmi┼č versiyon).

Parametreler:

─░sim Tip A├ž─▒klama Varsay─▒lan
mean ndarray

Bir ├Ânceki zaman ad─▒m─▒ndaki nesne durumlar─▒n─▒n Nx8 boyutlu ortalama matrisi.

gerekli
covariance ndarray

Bir ├Ânceki zaman ad─▒m─▒ndaki nesne durumlar─▒n─▒n Nx8x8 kovaryans matrisi.

gerekli

─░ade:

Tip A├ž─▒klama
tuple[ndarray, ndarray]

Tahmin edilen durumun ortalama vekt├Âr├╝n├╝ ve kovaryans matrisini d├Ând├╝r├╝r. G├Âzlemlenmemi┼č h─▒zlar ortalama 0 olarak ba┼člat─▒l─▒r.

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def multi_predict(self, mean: np.ndarray, covariance: np.ndarray) -> tuple:
    """
    Run Kalman filter prediction step (Vectorized version).

    Args:
        mean (ndarray): The Nx8 dimensional mean matrix of the object states at the previous time step.
        covariance (ndarray): The Nx8x8 covariance matrix of the object states at the previous time step.

    Returns:
        (tuple[ndarray, ndarray]): Returns the mean vector and covariance matrix of the predicted state. Unobserved
            velocities are initialized to 0 mean.
    """
    std_pos = [
        self._std_weight_position * mean[:, 3],
        self._std_weight_position * mean[:, 3],
        1e-2 * np.ones_like(mean[:, 3]),
        self._std_weight_position * mean[:, 3],
    ]
    std_vel = [
        self._std_weight_velocity * mean[:, 3],
        self._std_weight_velocity * mean[:, 3],
        1e-5 * np.ones_like(mean[:, 3]),
        self._std_weight_velocity * mean[:, 3],
    ]
    sqr = np.square(np.r_[std_pos, std_vel]).T

    motion_cov = [np.diag(sqr[i]) for i in range(len(mean))]
    motion_cov = np.asarray(motion_cov)

    mean = np.dot(mean, self._motion_mat.T)
    left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
    covariance = np.dot(left, self._motion_mat.T) + motion_cov

    return mean, covariance

predict(mean, covariance)

Kalman filtresi tahmin ad─▒m─▒n─▒ ├žal─▒┼čt─▒r─▒n.

Parametreler:

─░sim Tip A├ž─▒klama Varsay─▒lan
mean ndarray

Bir ├Ânceki zaman ad─▒m─▒ndaki nesne durumunun 8 boyutlu ortalama vekt├Âr├╝.

gerekli
covariance ndarray

Bir ├Ânceki zaman ad─▒m─▒ndaki nesne durumunun 8x8 boyutlu kovaryans matrisi.

gerekli

─░ade:

Tip A├ž─▒klama
tuple[ndarray, ndarray]

Tahmin edilen durumun ortalama vekt├Âr├╝n├╝ ve kovaryans matrisini d├Ând├╝r├╝r. G├Âzlemlenmemi┼č h─▒zlar ortalama 0 olarak ba┼člat─▒l─▒r.

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def predict(self, mean: np.ndarray, covariance: np.ndarray) -> tuple:
    """
    Run Kalman filter prediction step.

    Args:
        mean (ndarray): The 8 dimensional mean vector of the object state at the previous time step.
        covariance (ndarray): The 8x8 dimensional covariance matrix of the object state at the previous time step.

    Returns:
        (tuple[ndarray, ndarray]): Returns the mean vector and covariance matrix of the predicted state. Unobserved
            velocities are initialized to 0 mean.
    """
    std_pos = [
        self._std_weight_position * mean[3],
        self._std_weight_position * mean[3],
        1e-2,
        self._std_weight_position * mean[3],
    ]
    std_vel = [
        self._std_weight_velocity * mean[3],
        self._std_weight_velocity * mean[3],
        1e-5,
        self._std_weight_velocity * mean[3],
    ]
    motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))

    mean = np.dot(mean, self._motion_mat.T)
    covariance = np.linalg.multi_dot((self._motion_mat, covariance, self._motion_mat.T)) + motion_cov

    return mean, covariance

project(mean, covariance)

Durum da─č─▒l─▒m─▒n─▒ ├Âl├ž├╝m uzay─▒na yans─▒t─▒n.

Parametreler:

─░sim Tip A├ž─▒klama Varsay─▒lan
mean ndarray

Durumun ortalama vekt├Âr├╝ (8 boyutlu dizi).

gerekli
covariance ndarray

Durumun kovaryans matrisi (8x8 boyutlu).

gerekli

─░ade:

Tip A├ž─▒klama
tuple[ndarray, ndarray]

Verilen durum tahmininin ├Âng├Âr├╝len ortalamas─▒n─▒ ve kovaryans matrisini d├Ând├╝r├╝r.

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def project(self, mean: np.ndarray, covariance: np.ndarray) -> tuple:
    """
    Project state distribution to measurement space.

    Args:
        mean (ndarray): The state's mean vector (8 dimensional array).
        covariance (ndarray): The state's covariance matrix (8x8 dimensional).

    Returns:
        (tuple[ndarray, ndarray]): Returns the projected mean and covariance matrix of the given state estimate.
    """
    std = [
        self._std_weight_position * mean[3],
        self._std_weight_position * mean[3],
        1e-1,
        self._std_weight_position * mean[3],
    ]
    innovation_cov = np.diag(np.square(std))

    mean = np.dot(self._update_mat, mean)
    covariance = np.linalg.multi_dot((self._update_mat, covariance, self._update_mat.T))
    return mean, covariance + innovation_cov

update(mean, covariance, measurement)

Kalman filtresi d├╝zeltme ad─▒m─▒n─▒ ├žal─▒┼čt─▒r─▒n.

Parametreler:

─░sim Tip A├ž─▒klama Varsay─▒lan
mean ndarray

Tahmin edilen durumun ortalama vekt├Âr├╝ (8 boyutlu).

gerekli
covariance ndarray

Durumun kovaryans matrisi (8x8 boyutlu).

gerekli
measurement ndarray

4 boyutlu ├Âl├ž├╝m vekt├Âr├╝ (x, y, a, h), burada (x, y) merkezdir konumu, a en boy oran─▒ ve h s─▒n─▒rlay─▒c─▒ kutunun y├╝ksekli─čidir.

gerekli

─░ade:

Tip A├ž─▒klama
tuple[ndarray, ndarray]

├ľl├ž├╝mle d├╝zeltilmi┼č durum da─č─▒l─▒m─▒n─▒ d├Ând├╝r├╝r.

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def update(self, mean: np.ndarray, covariance: np.ndarray, measurement: np.ndarray) -> tuple:
    """
    Run Kalman filter correction step.

    Args:
        mean (ndarray): The predicted state's mean vector (8 dimensional).
        covariance (ndarray): The state's covariance matrix (8x8 dimensional).
        measurement (ndarray): The 4 dimensional measurement vector (x, y, a, h), where (x, y) is the center
            position, a the aspect ratio, and h the height of the bounding box.

    Returns:
        (tuple[ndarray, ndarray]): Returns the measurement-corrected state distribution.
    """
    projected_mean, projected_cov = self.project(mean, covariance)

    chol_factor, lower = scipy.linalg.cho_factor(projected_cov, lower=True, check_finite=False)
    kalman_gain = scipy.linalg.cho_solve(
        (chol_factor, lower), np.dot(covariance, self._update_mat.T).T, check_finite=False
    ).T
    innovation = measurement - projected_mean

    new_mean = mean + np.dot(innovation, kalman_gain.T)
    new_covariance = covariance - np.linalg.multi_dot((kalman_gain, projected_cov, kalman_gain.T))
    return new_mean, new_covariance



ultralytics.trackers.utils.kalman_filter.KalmanFilterXYWH

├ťsler: KalmanFilterXYAH

BoT-SORT i├žin. G├Âr├╝nt├╝ uzay─▒nda s─▒n─▒rlay─▒c─▒ kutular─▒ izlemek i├žin basit bir Kalman filtresi.

8 boyutlu durum uzay─▒ (x, y, w, h, vx, vy, vw, vh) s─▒n─▒rlay─▒c─▒ kutu merkez konumunu (x, y), geni┼čli─čini w, y├╝kseklik h ve bunlar─▒n ilgili h─▒zlar─▒.

Nesne hareketi sabit h─▒z modelini takip eder. S─▒n─▒rlay─▒c─▒ kutu konumu (x, y, w, h) do─črudan olarak al─▒n─▒r durum uzay─▒n─▒n g├Âzlemlenmesi (do─črusal g├Âzlem modeli).

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
class KalmanFilterXYWH(KalmanFilterXYAH):
    """
    For BoT-SORT. A simple Kalman filter for tracking bounding boxes in image space.

    The 8-dimensional state space (x, y, w, h, vx, vy, vw, vh) contains the bounding box center position (x, y), width
    w, height h, and their respective velocities.

    Object motion follows a constant velocity model. The bounding box location (x, y, w, h) is taken as direct
    observation of the state space (linear observation model).
    """

    def initiate(self, measurement: np.ndarray) -> tuple:
        """
        Create track from unassociated measurement.

        Args:
            measurement (ndarray): Bounding box coordinates (x, y, w, h) with center position (x, y), width, and height.

        Returns:
            (tuple[ndarray, ndarray]): Returns the mean vector (8 dimensional) and covariance matrix (8x8 dimensional)
                of the new track. Unobserved velocities are initialized to 0 mean.
        """
        mean_pos = measurement
        mean_vel = np.zeros_like(mean_pos)
        mean = np.r_[mean_pos, mean_vel]

        std = [
            2 * self._std_weight_position * measurement[2],
            2 * self._std_weight_position * measurement[3],
            2 * self._std_weight_position * measurement[2],
            2 * self._std_weight_position * measurement[3],
            10 * self._std_weight_velocity * measurement[2],
            10 * self._std_weight_velocity * measurement[3],
            10 * self._std_weight_velocity * measurement[2],
            10 * self._std_weight_velocity * measurement[3],
        ]
        covariance = np.diag(np.square(std))
        return mean, covariance

    def predict(self, mean, covariance) -> tuple:
        """
        Run Kalman filter prediction step.

        Args:
            mean (ndarray): The 8 dimensional mean vector of the object state at the previous time step.
            covariance (ndarray): The 8x8 dimensional covariance matrix of the object state at the previous time step.

        Returns:
            (tuple[ndarray, ndarray]): Returns the mean vector and covariance matrix of the predicted state. Unobserved
                velocities are initialized to 0 mean.
        """
        std_pos = [
            self._std_weight_position * mean[2],
            self._std_weight_position * mean[3],
            self._std_weight_position * mean[2],
            self._std_weight_position * mean[3],
        ]
        std_vel = [
            self._std_weight_velocity * mean[2],
            self._std_weight_velocity * mean[3],
            self._std_weight_velocity * mean[2],
            self._std_weight_velocity * mean[3],
        ]
        motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))

        mean = np.dot(mean, self._motion_mat.T)
        covariance = np.linalg.multi_dot((self._motion_mat, covariance, self._motion_mat.T)) + motion_cov

        return mean, covariance

    def project(self, mean, covariance) -> tuple:
        """
        Project state distribution to measurement space.

        Args:
            mean (ndarray): The state's mean vector (8 dimensional array).
            covariance (ndarray): The state's covariance matrix (8x8 dimensional).

        Returns:
            (tuple[ndarray, ndarray]): Returns the projected mean and covariance matrix of the given state estimate.
        """
        std = [
            self._std_weight_position * mean[2],
            self._std_weight_position * mean[3],
            self._std_weight_position * mean[2],
            self._std_weight_position * mean[3],
        ]
        innovation_cov = np.diag(np.square(std))

        mean = np.dot(self._update_mat, mean)
        covariance = np.linalg.multi_dot((self._update_mat, covariance, self._update_mat.T))
        return mean, covariance + innovation_cov

    def multi_predict(self, mean, covariance) -> tuple:
        """
        Run Kalman filter prediction step (Vectorized version).

        Args:
            mean (ndarray): The Nx8 dimensional mean matrix of the object states at the previous time step.
            covariance (ndarray): The Nx8x8 covariance matrix of the object states at the previous time step.

        Returns:
            (tuple[ndarray, ndarray]): Returns the mean vector and covariance matrix of the predicted state. Unobserved
                velocities are initialized to 0 mean.
        """
        std_pos = [
            self._std_weight_position * mean[:, 2],
            self._std_weight_position * mean[:, 3],
            self._std_weight_position * mean[:, 2],
            self._std_weight_position * mean[:, 3],
        ]
        std_vel = [
            self._std_weight_velocity * mean[:, 2],
            self._std_weight_velocity * mean[:, 3],
            self._std_weight_velocity * mean[:, 2],
            self._std_weight_velocity * mean[:, 3],
        ]
        sqr = np.square(np.r_[std_pos, std_vel]).T

        motion_cov = [np.diag(sqr[i]) for i in range(len(mean))]
        motion_cov = np.asarray(motion_cov)

        mean = np.dot(mean, self._motion_mat.T)
        left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
        covariance = np.dot(left, self._motion_mat.T) + motion_cov

        return mean, covariance

    def update(self, mean, covariance, measurement) -> tuple:
        """
        Run Kalman filter correction step.

        Args:
            mean (ndarray): The predicted state's mean vector (8 dimensional).
            covariance (ndarray): The state's covariance matrix (8x8 dimensional).
            measurement (ndarray): The 4 dimensional measurement vector (x, y, w, h), where (x, y) is the center
                position, w the width, and h the height of the bounding box.

        Returns:
            (tuple[ndarray, ndarray]): Returns the measurement-corrected state distribution.
        """
        return super().update(mean, covariance, measurement)

initiate(measurement)

─░li┼čkilendirilmemi┼č ├Âl├ž├╝mden iz olu┼čturun.

Parametreler:

─░sim Tip A├ž─▒klama Varsay─▒lan
measurement ndarray

Merkez konumu (x, y), geni┼člik ve y├╝kseklik ile s─▒n─▒rlay─▒c─▒ kutu koordinatlar─▒ (x, y, w, h).

gerekli

─░ade:

Tip A├ž─▒klama
tuple[ndarray, ndarray]

Ortalama vekt├Âr├╝ (8 boyutlu) ve kovaryans matrisini (8x8 boyutlu) d├Ând├╝r├╝r yeni par├žan─▒n. G├Âzlemlenmemi┼č h─▒zlar 0 ortalama ile ba┼člat─▒l─▒r.

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def initiate(self, measurement: np.ndarray) -> tuple:
    """
    Create track from unassociated measurement.

    Args:
        measurement (ndarray): Bounding box coordinates (x, y, w, h) with center position (x, y), width, and height.

    Returns:
        (tuple[ndarray, ndarray]): Returns the mean vector (8 dimensional) and covariance matrix (8x8 dimensional)
            of the new track. Unobserved velocities are initialized to 0 mean.
    """
    mean_pos = measurement
    mean_vel = np.zeros_like(mean_pos)
    mean = np.r_[mean_pos, mean_vel]

    std = [
        2 * self._std_weight_position * measurement[2],
        2 * self._std_weight_position * measurement[3],
        2 * self._std_weight_position * measurement[2],
        2 * self._std_weight_position * measurement[3],
        10 * self._std_weight_velocity * measurement[2],
        10 * self._std_weight_velocity * measurement[3],
        10 * self._std_weight_velocity * measurement[2],
        10 * self._std_weight_velocity * measurement[3],
    ]
    covariance = np.diag(np.square(std))
    return mean, covariance

multi_predict(mean, covariance)

Kalman filtresi tahmin ad─▒m─▒n─▒ ├žal─▒┼čt─▒r─▒n (Vekt├Ârle┼čtirilmi┼č versiyon).

Parametreler:

─░sim Tip A├ž─▒klama Varsay─▒lan
mean ndarray

Bir ├Ânceki zaman ad─▒m─▒ndaki nesne durumlar─▒n─▒n Nx8 boyutlu ortalama matrisi.

gerekli
covariance ndarray

Bir ├Ânceki zaman ad─▒m─▒ndaki nesne durumlar─▒n─▒n Nx8x8 kovaryans matrisi.

gerekli

─░ade:

Tip A├ž─▒klama
tuple[ndarray, ndarray]

Tahmin edilen durumun ortalama vekt├Âr├╝n├╝ ve kovaryans matrisini d├Ând├╝r├╝r. G├Âzlemlenmemi┼č h─▒zlar ortalama 0 olarak ba┼člat─▒l─▒r.

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def multi_predict(self, mean, covariance) -> tuple:
    """
    Run Kalman filter prediction step (Vectorized version).

    Args:
        mean (ndarray): The Nx8 dimensional mean matrix of the object states at the previous time step.
        covariance (ndarray): The Nx8x8 covariance matrix of the object states at the previous time step.

    Returns:
        (tuple[ndarray, ndarray]): Returns the mean vector and covariance matrix of the predicted state. Unobserved
            velocities are initialized to 0 mean.
    """
    std_pos = [
        self._std_weight_position * mean[:, 2],
        self._std_weight_position * mean[:, 3],
        self._std_weight_position * mean[:, 2],
        self._std_weight_position * mean[:, 3],
    ]
    std_vel = [
        self._std_weight_velocity * mean[:, 2],
        self._std_weight_velocity * mean[:, 3],
        self._std_weight_velocity * mean[:, 2],
        self._std_weight_velocity * mean[:, 3],
    ]
    sqr = np.square(np.r_[std_pos, std_vel]).T

    motion_cov = [np.diag(sqr[i]) for i in range(len(mean))]
    motion_cov = np.asarray(motion_cov)

    mean = np.dot(mean, self._motion_mat.T)
    left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
    covariance = np.dot(left, self._motion_mat.T) + motion_cov

    return mean, covariance

predict(mean, covariance)

Kalman filtresi tahmin ad─▒m─▒n─▒ ├žal─▒┼čt─▒r─▒n.

Parametreler:

─░sim Tip A├ž─▒klama Varsay─▒lan
mean ndarray

Bir ├Ânceki zaman ad─▒m─▒ndaki nesne durumunun 8 boyutlu ortalama vekt├Âr├╝.

gerekli
covariance ndarray

Bir ├Ânceki zaman ad─▒m─▒ndaki nesne durumunun 8x8 boyutlu kovaryans matrisi.

gerekli

─░ade:

Tip A├ž─▒klama
tuple[ndarray, ndarray]

Tahmin edilen durumun ortalama vekt├Âr├╝n├╝ ve kovaryans matrisini d├Ând├╝r├╝r. G├Âzlemlenmemi┼č h─▒zlar ortalama 0 olarak ba┼člat─▒l─▒r.

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def predict(self, mean, covariance) -> tuple:
    """
    Run Kalman filter prediction step.

    Args:
        mean (ndarray): The 8 dimensional mean vector of the object state at the previous time step.
        covariance (ndarray): The 8x8 dimensional covariance matrix of the object state at the previous time step.

    Returns:
        (tuple[ndarray, ndarray]): Returns the mean vector and covariance matrix of the predicted state. Unobserved
            velocities are initialized to 0 mean.
    """
    std_pos = [
        self._std_weight_position * mean[2],
        self._std_weight_position * mean[3],
        self._std_weight_position * mean[2],
        self._std_weight_position * mean[3],
    ]
    std_vel = [
        self._std_weight_velocity * mean[2],
        self._std_weight_velocity * mean[3],
        self._std_weight_velocity * mean[2],
        self._std_weight_velocity * mean[3],
    ]
    motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))

    mean = np.dot(mean, self._motion_mat.T)
    covariance = np.linalg.multi_dot((self._motion_mat, covariance, self._motion_mat.T)) + motion_cov

    return mean, covariance

project(mean, covariance)

Durum da─č─▒l─▒m─▒n─▒ ├Âl├ž├╝m uzay─▒na yans─▒t─▒n.

Parametreler:

─░sim Tip A├ž─▒klama Varsay─▒lan
mean ndarray

Durumun ortalama vekt├Âr├╝ (8 boyutlu dizi).

gerekli
covariance ndarray

Durumun kovaryans matrisi (8x8 boyutlu).

gerekli

─░ade:

Tip A├ž─▒klama
tuple[ndarray, ndarray]

Verilen durum tahmininin ├Âng├Âr├╝len ortalamas─▒n─▒ ve kovaryans matrisini d├Ând├╝r├╝r.

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def project(self, mean, covariance) -> tuple:
    """
    Project state distribution to measurement space.

    Args:
        mean (ndarray): The state's mean vector (8 dimensional array).
        covariance (ndarray): The state's covariance matrix (8x8 dimensional).

    Returns:
        (tuple[ndarray, ndarray]): Returns the projected mean and covariance matrix of the given state estimate.
    """
    std = [
        self._std_weight_position * mean[2],
        self._std_weight_position * mean[3],
        self._std_weight_position * mean[2],
        self._std_weight_position * mean[3],
    ]
    innovation_cov = np.diag(np.square(std))

    mean = np.dot(self._update_mat, mean)
    covariance = np.linalg.multi_dot((self._update_mat, covariance, self._update_mat.T))
    return mean, covariance + innovation_cov

update(mean, covariance, measurement)

Kalman filtresi d├╝zeltme ad─▒m─▒n─▒ ├žal─▒┼čt─▒r─▒n.

Parametreler:

─░sim Tip A├ž─▒klama Varsay─▒lan
mean ndarray

Tahmin edilen durumun ortalama vekt├Âr├╝ (8 boyutlu).

gerekli
covariance ndarray

Durumun kovaryans matrisi (8x8 boyutlu).

gerekli
measurement ndarray

4 boyutlu ├Âl├ž├╝m vekt├Âr├╝ (x, y, w, h), burada (x, y) merkezdir konumunu, w s─▒n─▒rlay─▒c─▒ kutunun geni┼čli─čini ve h y├╝ksekli─čini belirtir.

gerekli

─░ade:

Tip A├ž─▒klama
tuple[ndarray, ndarray]

├ľl├ž├╝mle d├╝zeltilmi┼č durum da─č─▒l─▒m─▒n─▒ d├Ând├╝r├╝r.

Kaynak kodu ultralytics/trackers/utils/kalman_filter.py
def update(self, mean, covariance, measurement) -> tuple:
    """
    Run Kalman filter correction step.

    Args:
        mean (ndarray): The predicted state's mean vector (8 dimensional).
        covariance (ndarray): The state's covariance matrix (8x8 dimensional).
        measurement (ndarray): The 4 dimensional measurement vector (x, y, w, h), where (x, y) is the center
            position, w the width, and h the height of the bounding box.

    Returns:
        (tuple[ndarray, ndarray]): Returns the measurement-corrected state distribution.
    """
    return super().update(mean, covariance, measurement)





Created 2023-11-12, Updated 2024-06-02
Authors: glenn-jocher (5), Burhan-Q (1)