ultralytics/ultralytics/utils/metrics.py

# Ultralytics 🚀 AGPL-3.0 License - https://ultralytics.com/license
"""Model validation metrics."""

import math
import warnings
from pathlib import Path

import matplotlib.pyplot as plt
import numpy as np
import torch

from ultralytics.utils import LOGGER, SimpleClass, TryExcept, checks, plt_settings

OKS_SIGMA = (
    np.array([0.26, 0.25, 0.25, 0.35, 0.35, 0.79, 0.79, 0.72, 0.72, 0.62, 0.62, 1.07, 1.07, 0.87, 0.87, 0.89, 0.89])
    / 10.0
)


def bbox_ioa(box1, box2, iou=False, eps=1e-7):
    """
    Calculate the intersection over box2 area given box1 and box2. Boxes are in x1y1x2y2 format.

    Args:
        box1 (np.ndarray): A numpy array of shape (n, 4) representing n bounding boxes.
        box2 (np.ndarray): A numpy array of shape (m, 4) representing m bounding boxes.
        iou (bool): Calculate the standard IoU if True else return inter_area/box2_area.
        eps (float, optional): A small value to avoid division by zero.

    Returns:
        (np.ndarray): A numpy array of shape (n, m) representing the intersection over box2 area.
    """
    # Get the coordinates of bounding boxes
    b1_x1, b1_y1, b1_x2, b1_y2 = box1.T
    b2_x1, b2_y1, b2_x2, b2_y2 = box2.T

    # Intersection area
    inter_area = (np.minimum(b1_x2[:, None], b2_x2) - np.maximum(b1_x1[:, None], b2_x1)).clip(0) * (
        np.minimum(b1_y2[:, None], b2_y2) - np.maximum(b1_y1[:, None], b2_y1)
    ).clip(0)

    # Box2 area
    area = (b2_x2 - b2_x1) * (b2_y2 - b2_y1)
    if iou:
        box1_area = (b1_x2 - b1_x1) * (b1_y2 - b1_y1)
        area = area + box1_area[:, None] - inter_area

    # Intersection over box2 area
    return inter_area / (area + eps)


def box_iou(box1, box2, eps=1e-7):
    """
    Calculate intersection-over-union (IoU) of boxes. Both sets of boxes are expected to be in (x1, y1, x2, y2) format.
    Based on https://github.com/pytorch/vision/blob/main/torchvision/ops/boxes.py.

    Args:
        box1 (torch.Tensor): A tensor of shape (N, 4) representing N bounding boxes.
        box2 (torch.Tensor): A tensor of shape (M, 4) representing M bounding boxes.
        eps (float, optional): A small value to avoid division by zero.

    Returns:
        (torch.Tensor): An NxM tensor containing the pairwise IoU values for every element in box1 and box2.
    """
    # NOTE: Need .float() to get accurate iou values
    # inter(N,M) = (rb(N,M,2) - lt(N,M,2)).clamp(0).prod(2)
    (a1, a2), (b1, b2) = box1.float().unsqueeze(1).chunk(2, 2), box2.float().unsqueeze(0).chunk(2, 2)
    inter = (torch.min(a2, b2) - torch.max(a1, b1)).clamp_(0).prod(2)

    # IoU = inter / (area1 + area2 - inter)
    return inter / ((a2 - a1).prod(2) + (b2 - b1).prod(2) - inter + eps)


def bbox_iou(box1, box2, xywh=True, GIoU=False, DIoU=False, CIoU=False, eps=1e-7):
    """
    Calculate the Intersection over Union (IoU) between bounding boxes.

    This function supports various shapes for `box1` and `box2` as long as the last dimension is 4.
    For instance, you may pass tensors shaped like (4,), (N, 4), (B, N, 4), or (B, N, 1, 4).
    Internally, the code will split the last dimension into (x, y, w, h) if `xywh=True`,
    or (x1, y1, x2, y2) if `xywh=False`.

    Args:
        box1 (torch.Tensor): A tensor representing one or more bounding boxes, with the last dimension being 4.
        box2 (torch.Tensor): A tensor representing one or more bounding boxes, with the last dimension being 4.
        xywh (bool, optional): If True, input boxes are in (x, y, w, h) format. If False, input boxes are in
                               (x1, y1, x2, y2) format.
        GIoU (bool, optional): If True, calculate Generalized IoU.
        DIoU (bool, optional): If True, calculate Distance IoU.
        CIoU (bool, optional): If True, calculate Complete IoU.
        eps (float, optional): A small value to avoid division by zero.

    Returns:
        (torch.Tensor): IoU, GIoU, DIoU, or CIoU values depending on the specified flags.
    """
    # Get the coordinates of bounding boxes
    if xywh:  # transform from xywh to xyxy
        (x1, y1, w1, h1), (x2, y2, w2, h2) = box1.chunk(4, -1), box2.chunk(4, -1)
        w1_, h1_, w2_, h2_ = w1 / 2, h1 / 2, w2 / 2, h2 / 2
        b1_x1, b1_x2, b1_y1, b1_y2 = x1 - w1_, x1 + w1_, y1 - h1_, y1 + h1_
        b2_x1, b2_x2, b2_y1, b2_y2 = x2 - w2_, x2 + w2_, y2 - h2_, y2 + h2_
    else:  # x1, y1, x2, y2 = box1
        b1_x1, b1_y1, b1_x2, b1_y2 = box1.chunk(4, -1)
        b2_x1, b2_y1, b2_x2, b2_y2 = box2.chunk(4, -1)
        w1, h1 = b1_x2 - b1_x1, b1_y2 - b1_y1 + eps
        w2, h2 = b2_x2 - b2_x1, b2_y2 - b2_y1 + eps

    # Intersection area
    inter = (b1_x2.minimum(b2_x2) - b1_x1.maximum(b2_x1)).clamp_(0) * (
        b1_y2.minimum(b2_y2) - b1_y1.maximum(b2_y1)
    ).clamp_(0)

    # Union Area
    union = w1 * h1 + w2 * h2 - inter + eps

    # IoU
    iou = inter / union
    if CIoU or DIoU or GIoU:
        cw = b1_x2.maximum(b2_x2) - b1_x1.minimum(b2_x1)  # convex (smallest enclosing box) width
        ch = b1_y2.maximum(b2_y2) - b1_y1.minimum(b2_y1)  # convex height
        if CIoU or DIoU:  # Distance or Complete IoU https://arxiv.org/abs/1911.08287v1
            c2 = cw.pow(2) + ch.pow(2) + eps  # convex diagonal squared
            rho2 = (
                (b2_x1 + b2_x2 - b1_x1 - b1_x2).pow(2) + (b2_y1 + b2_y2 - b1_y1 - b1_y2).pow(2)
            ) / 4  # center dist**2
            if CIoU:  # https://github.com/Zzh-tju/DIoU-SSD-pytorch/blob/master/utils/box/box_utils.py#L47
                v = (4 / math.pi**2) * ((w2 / h2).atan() - (w1 / h1).atan()).pow(2)
                with torch.no_grad():
                    alpha = v / (v - iou + (1 + eps))
                return iou - (rho2 / c2 + v * alpha)  # CIoU
            return iou - rho2 / c2  # DIoU
        c_area = cw * ch + eps  # convex area
        return iou - (c_area - union) / c_area  # GIoU https://arxiv.org/pdf/1902.09630.pdf
    return iou  # IoU


def mask_iou(mask1, mask2, eps=1e-7):
    """
    Calculate masks IoU.

    Args:
        mask1 (torch.Tensor): A tensor of shape (N, n) where N is the number of ground truth objects and n is the
                        product of image width and height.
        mask2 (torch.Tensor): A tensor of shape (M, n) where M is the number of predicted objects and n is the
                        product of image width and height.
        eps (float, optional): A small value to avoid division by zero.

    Returns:
        (torch.Tensor): A tensor of shape (N, M) representing masks IoU.
    """
    intersection = torch.matmul(mask1, mask2.T).clamp_(0)
    union = (mask1.sum(1)[:, None] + mask2.sum(1)[None]) - intersection  # (area1 + area2) - intersection
    return intersection / (union + eps)


def kpt_iou(kpt1, kpt2, area, sigma, eps=1e-7):
    """
    Calculate Object Keypoint Similarity (OKS).

    Args:
        kpt1 (torch.Tensor): A tensor of shape (N, 17, 3) representing ground truth keypoints.
        kpt2 (torch.Tensor): A tensor of shape (M, 17, 3) representing predicted keypoints.
        area (torch.Tensor): A tensor of shape (N,) representing areas from ground truth.
        sigma (list): A list containing 17 values representing keypoint scales.
        eps (float, optional): A small value to avoid division by zero.

    Returns:
        (torch.Tensor): A tensor of shape (N, M) representing keypoint similarities.
    """
    d = (kpt1[:, None, :, 0] - kpt2[..., 0]).pow(2) + (kpt1[:, None, :, 1] - kpt2[..., 1]).pow(2)  # (N, M, 17)
    sigma = torch.tensor(sigma, device=kpt1.device, dtype=kpt1.dtype)  # (17, )
    kpt_mask = kpt1[..., 2] != 0  # (N, 17)
    e = d / ((2 * sigma).pow(2) * (area[:, None, None] + eps) * 2)  # from cocoeval
    # e = d / ((area[None, :, None] + eps) * sigma) ** 2 / 2  # from formula
    return ((-e).exp() * kpt_mask[:, None]).sum(-1) / (kpt_mask.sum(-1)[:, None] + eps)


def _get_covariance_matrix(boxes):
    """
    Generate covariance matrix from oriented bounding boxes.

    Args:
        boxes (torch.Tensor): A tensor of shape (N, 5) representing rotated bounding boxes, with xywhr format.

    Returns:
        (torch.Tensor): Covariance matrices corresponding to original rotated bounding boxes.
    """
    # Gaussian bounding boxes, ignore the center points (the first two columns) because they are not needed here.
    gbbs = torch.cat((boxes[:, 2:4].pow(2) / 12, boxes[:, 4:]), dim=-1)
    a, b, c = gbbs.split(1, dim=-1)
    cos = c.cos()
    sin = c.sin()
    cos2 = cos.pow(2)
    sin2 = sin.pow(2)
    return a * cos2 + b * sin2, a * sin2 + b * cos2, (a - b) * cos * sin


def probiou(obb1, obb2, CIoU=False, eps=1e-7):
    """
    Calculate probabilistic IoU between oriented bounding boxes.

    Args:
        obb1 (torch.Tensor): Ground truth OBBs, shape (N, 5), format xywhr.
        obb2 (torch.Tensor): Predicted OBBs, shape (N, 5), format xywhr.
        CIoU (bool, optional): If True, calculate CIoU.
        eps (float, optional): Small value to avoid division by zero.

    Returns:
        (torch.Tensor): OBB similarities, shape (N,).

    Notes:
        - OBB format: [center_x, center_y, width, height, rotation_angle].
        - Implements the algorithm from https://arxiv.org/pdf/2106.06072v1.pdf.
    """
    x1, y1 = obb1[..., :2].split(1, dim=-1)
    x2, y2 = obb2[..., :2].split(1, dim=-1)
    a1, b1, c1 = _get_covariance_matrix(obb1)
    a2, b2, c2 = _get_covariance_matrix(obb2)

    t1 = (
        ((a1 + a2) * (y1 - y2).pow(2) + (b1 + b2) * (x1 - x2).pow(2)) / ((a1 + a2) * (b1 + b2) - (c1 + c2).pow(2) + eps)
    ) * 0.25
    t2 = (((c1 + c2) * (x2 - x1) * (y1 - y2)) / ((a1 + a2) * (b1 + b2) - (c1 + c2).pow(2) + eps)) * 0.5
    t3 = (
        ((a1 + a2) * (b1 + b2) - (c1 + c2).pow(2))
        / (4 * ((a1 * b1 - c1.pow(2)).clamp_(0) * (a2 * b2 - c2.pow(2)).clamp_(0)).sqrt() + eps)
        + eps
    ).log() * 0.5
    bd = (t1 + t2 + t3).clamp(eps, 100.0)
    hd = (1.0 - (-bd).exp() + eps).sqrt()
    iou = 1 - hd
    if CIoU:  # only include the wh aspect ratio part
        w1, h1 = obb1[..., 2:4].split(1, dim=-1)
        w2, h2 = obb2[..., 2:4].split(1, dim=-1)
        v = (4 / math.pi**2) * ((w2 / h2).atan() - (w1 / h1).atan()).pow(2)
        with torch.no_grad():
            alpha = v / (v - iou + (1 + eps))
        return iou - v * alpha  # CIoU
    return iou


def batch_probiou(obb1, obb2, eps=1e-7):
    """
    Calculate the probabilistic IoU between oriented bounding boxes.

    Args:
        obb1 (torch.Tensor | np.ndarray): A tensor of shape (N, 5) representing ground truth obbs, with xywhr format.
        obb2 (torch.Tensor | np.ndarray): A tensor of shape (M, 5) representing predicted obbs, with xywhr format.
        eps (float, optional): A small value to avoid division by zero.

    Returns:
        (torch.Tensor): A tensor of shape (N, M) representing obb similarities.

    References:
        https://arxiv.org/pdf/2106.06072v1.pdf
    """
    obb1 = torch.from_numpy(obb1) if isinstance(obb1, np.ndarray) else obb1
    obb2 = torch.from_numpy(obb2) if isinstance(obb2, np.ndarray) else obb2

    x1, y1 = obb1[..., :2].split(1, dim=-1)
    x2, y2 = (x.squeeze(-1)[None] for x in obb2[..., :2].split(1, dim=-1))
    a1, b1, c1 = _get_covariance_matrix(obb1)
    a2, b2, c2 = (x.squeeze(-1)[None] for x in _get_covariance_matrix(obb2))

    t1 = (
        ((a1 + a2) * (y1 - y2).pow(2) + (b1 + b2) * (x1 - x2).pow(2)) / ((a1 + a2) * (b1 + b2) - (c1 + c2).pow(2) + eps)
    ) * 0.25
    t2 = (((c1 + c2) * (x2 - x1) * (y1 - y2)) / ((a1 + a2) * (b1 + b2) - (c1 + c2).pow(2) + eps)) * 0.5
    t3 = (
        ((a1 + a2) * (b1 + b2) - (c1 + c2).pow(2))
        / (4 * ((a1 * b1 - c1.pow(2)).clamp_(0) * (a2 * b2 - c2.pow(2)).clamp_(0)).sqrt() + eps)
        + eps
    ).log() * 0.5
    bd = (t1 + t2 + t3).clamp(eps, 100.0)
    hd = (1.0 - (-bd).exp() + eps).sqrt()
    return 1 - hd


def smooth_bce(eps=0.1):
    """
    Compute smoothed positive and negative Binary Cross-Entropy targets.

    Args:
        eps (float, optional): The epsilon value for label smoothing.

    Returns:
        (tuple): A tuple containing the positive and negative label smoothing BCE targets.

    References:
        https://github.com/ultralytics/yolov3/issues/238#issuecomment-598028441
    """
    return 1.0 - 0.5 * eps, 0.5 * eps


class ConfusionMatrix:
    """
    A class for calculating and updating a confusion matrix for object detection and classification tasks.

    Attributes:
        task (str): The type of task, either 'detect' or 'classify'.
        matrix (np.ndarray): The confusion matrix, with dimensions depending on the task.
        nc (int): The number of classes.
        conf (float): The confidence threshold for detections.
        iou_thres (float): The Intersection over Union threshold.
    """

    def __init__(self, nc, conf=0.25, iou_thres=0.45, task="detect"):
        """
        Initialize a ConfusionMatrix instance.

        Args:
            nc (int): Number of classes.
            conf (float, optional): Confidence threshold for detections.
            iou_thres (float, optional): IoU threshold for matching detections to ground truth.
            task (str, optional): Type of task, either 'detect' or 'classify'.
        """
        self.task = task
        self.matrix = np.zeros((nc + 1, nc + 1)) if self.task == "detect" else np.zeros((nc, nc))
        self.nc = nc  # number of classes
        self.conf = 0.25 if conf in {None, 0.001} else conf  # apply 0.25 if default val conf is passed
        self.iou_thres = iou_thres

    def process_cls_preds(self, preds, targets):
        """
        Update confusion matrix for classification task.

        Args:
            preds (Array[N, min(nc,5)]): Predicted class labels.
            targets (Array[N, 1]): Ground truth class labels.
        """
        preds, targets = torch.cat(preds)[:, 0], torch.cat(targets)
        for p, t in zip(preds.cpu().numpy(), targets.cpu().numpy()):
            self.matrix[p][t] += 1

    def process_batch(self, detections, gt_bboxes, gt_cls):
        """
        Update confusion matrix for object detection task.

        Args:
            detections (Array[N, 6] | Array[N, 7]): Detected bounding boxes and their associated information.
                                      Each row should contain (x1, y1, x2, y2, conf, class)
                                      or with an additional element `angle` when it's obb.
            gt_bboxes (Array[M, 4]| Array[N, 5]): Ground truth bounding boxes with xyxy/xyxyr format.
            gt_cls (Array[M]): The class labels.
        """
        if gt_cls.shape[0] == 0:  # Check if labels is empty
            if detections is not None:
                detections = detections[detections[:, 4] > self.conf]
                detection_classes = detections[:, 5].int()
                for dc in detection_classes:
                    self.matrix[dc, self.nc] += 1  # false positives
            return
        if detections is None:
            gt_classes = gt_cls.int()
            for gc in gt_classes:
                self.matrix[self.nc, gc] += 1  # background FN
            return

        detections = detections[detections[:, 4] > self.conf]
        gt_classes = gt_cls.int()
        detection_classes = detections[:, 5].int()
        is_obb = detections.shape[1] == 7 and gt_bboxes.shape[1] == 5  # with additional `angle` dimension
        iou = (
            batch_probiou(gt_bboxes, torch.cat([detections[:, :4], detections[:, -1:]], dim=-1))
            if is_obb
            else box_iou(gt_bboxes, detections[:, :4])
        )

        x = torch.where(iou > self.iou_thres)
        if x[0].shape[0]:
            matches = torch.cat((torch.stack(x, 1), iou[x[0], x[1]][:, None]), 1).cpu().numpy()
            if x[0].shape[0] > 1:
                matches = matches[matches[:, 2].argsort()[::-1]]
                matches = matches[np.unique(matches[:, 1], return_index=True)[1]]
                matches = matches[matches[:, 2].argsort()[::-1]]
                matches = matches[np.unique(matches[:, 0], return_index=True)[1]]
        else:
            matches = np.zeros((0, 3))

        n = matches.shape[0] > 0
        m0, m1, _ = matches.transpose().astype(int)
        for i, gc in enumerate(gt_classes):
            j = m0 == i
            if n and sum(j) == 1:
                self.matrix[detection_classes[m1[j]], gc] += 1  # correct
            else:
                self.matrix[self.nc, gc] += 1  # true background

        for i, dc in enumerate(detection_classes):
            if not any(m1 == i):
                self.matrix[dc, self.nc] += 1  # predicted background

    def matrix(self):
        """Return the confusion matrix."""
        return self.matrix

    def tp_fp(self):
        """
        Return true positives and false positives.

        Returns:
            (tuple): True positives and false positives.
        """
        tp = self.matrix.diagonal()  # true positives
        fp = self.matrix.sum(1) - tp  # false positives
        # fn = self.matrix.sum(0) - tp  # false negatives (missed detections)
        return (tp[:-1], fp[:-1]) if self.task == "detect" else (tp, fp)  # remove background class if task=detect

    @TryExcept(msg="ConfusionMatrix plot failure")
    @plt_settings()
    def plot(self, normalize=True, save_dir="", names=(), on_plot=None):
        """
        Plot the confusion matrix using seaborn and save it to a file.

        Args:
            normalize (bool): Whether to normalize the confusion matrix.
            save_dir (str): Directory where the plot will be saved.
            names (tuple): Names of classes, used as labels on the plot.
            on_plot (func): An optional callback to pass plots path and data when they are rendered.
        """
        import seaborn  # scope for faster 'import ultralytics'

        array = self.matrix / ((self.matrix.sum(0).reshape(1, -1) + 1e-9) if normalize else 1)  # normalize columns
        array[array < 0.005] = np.nan  # don't annotate (would appear as 0.00)

        fig, ax = plt.subplots(1, 1, figsize=(12, 9), tight_layout=True)
        nc, nn = self.nc, len(names)  # number of classes, names
        seaborn.set_theme(font_scale=1.0 if nc < 50 else 0.8)  # for label size
        labels = (0 < nn < 99) and (nn == nc)  # apply names to ticklabels
        ticklabels = (list(names) + ["background"]) if labels else "auto"
        with warnings.catch_warnings():
            warnings.simplefilter("ignore")  # suppress empty matrix RuntimeWarning: All-NaN slice encountered
            seaborn.heatmap(
                array,
                ax=ax,
                annot=nc < 30,
                annot_kws={"size": 8},
                cmap="Blues",
                fmt=".2f" if normalize else ".0f",
                square=True,
                vmin=0.0,
                xticklabels=ticklabels,
                yticklabels=ticklabels,
            ).set_facecolor((1, 1, 1))
        title = "Confusion Matrix" + " Normalized" * normalize
        ax.set_xlabel("True")
        ax.set_ylabel("Predicted")
        ax.set_title(title)
        plot_fname = Path(save_dir) / f"{title.lower().replace(' ', '_')}.png"
        fig.savefig(plot_fname, dpi=250)
        plt.close(fig)
        if on_plot:
            on_plot(plot_fname)

    def print(self):
        """Print the confusion matrix to the console."""
        for i in range(self.matrix.shape[0]):
            LOGGER.info(" ".join(map(str, self.matrix[i])))


def smooth(y, f=0.05):
    """Box filter of fraction f."""
    nf = round(len(y) * f * 2) // 2 + 1  # number of filter elements (must be odd)
    p = np.ones(nf // 2)  # ones padding
    yp = np.concatenate((p * y[0], y, p * y[-1]), 0)  # y padded
    return np.convolve(yp, np.ones(nf) / nf, mode="valid")  # y-smoothed


@plt_settings()
def plot_pr_curve(px, py, ap, save_dir=Path("pr_curve.png"), names={}, on_plot=None):
    """
    Plot precision-recall curve.

    Args:
        px (np.ndarray): X values for the PR curve.
        py (np.ndarray): Y values for the PR curve.
        ap (np.ndarray): Average precision values.
        save_dir (Path, optional): Path to save the plot.
        names (dict, optional): Dictionary mapping class indices to class names.
        on_plot (callable, optional): Function to call after plot is saved.
    """
    fig, ax = plt.subplots(1, 1, figsize=(9, 6), tight_layout=True)
    py = np.stack(py, axis=1)

    if 0 < len(names) < 21:  # display per-class legend if < 21 classes
        for i, y in enumerate(py.T):
            ax.plot(px, y, linewidth=1, label=f"{names[i]} {ap[i, 0]:.3f}")  # plot(recall, precision)
    else:
        ax.plot(px, py, linewidth=1, color="grey")  # plot(recall, precision)

    ax.plot(px, py.mean(1), linewidth=3, color="blue", label=f"all classes {ap[:, 0].mean():.3f} mAP@0.5")
    ax.set_xlabel("Recall")
    ax.set_ylabel("Precision")
    ax.set_xlim(0, 1)
    ax.set_ylim(0, 1)
    ax.legend(bbox_to_anchor=(1.04, 1), loc="upper left")
    ax.set_title("Precision-Recall Curve")
    fig.savefig(save_dir, dpi=250)
    plt.close(fig)
    if on_plot:
        on_plot(save_dir)


@plt_settings()
def plot_mc_curve(px, py, save_dir=Path("mc_curve.png"), names={}, xlabel="Confidence", ylabel="Metric", on_plot=None):
    """
    Plot metric-confidence curve.

    Args:
        px (np.ndarray): X values for the metric-confidence curve.
        py (np.ndarray): Y values for the metric-confidence curve.
        save_dir (Path, optional): Path to save the plot.
        names (dict, optional): Dictionary mapping class indices to class names.
        xlabel (str, optional): X-axis label.
        ylabel (str, optional): Y-axis label.
        on_plot (callable, optional): Function to call after plot is saved.
    """
    fig, ax = plt.subplots(1, 1, figsize=(9, 6), tight_layout=True)

    if 0 < len(names) < 21:  # display per-class legend if < 21 classes
        for i, y in enumerate(py):
            ax.plot(px, y, linewidth=1, label=f"{names[i]}")  # plot(confidence, metric)
    else:
        ax.plot(px, py.T, linewidth=1, color="grey")  # plot(confidence, metric)

    y = smooth(py.mean(0), 0.1)
    ax.plot(px, y, linewidth=3, color="blue", label=f"all classes {y.max():.2f} at {px[y.argmax()]:.3f}")
    ax.set_xlabel(xlabel)
    ax.set_ylabel(ylabel)
    ax.set_xlim(0, 1)
    ax.set_ylim(0, 1)
    ax.legend(bbox_to_anchor=(1.04, 1), loc="upper left")
    ax.set_title(f"{ylabel}-Confidence Curve")
    fig.savefig(save_dir, dpi=250)
    plt.close(fig)
    if on_plot:
        on_plot(save_dir)


def compute_ap(recall, precision):
    """
    Compute the average precision (AP) given the recall and precision curves.

    Args:
        recall (list): The recall curve.
        precision (list): The precision curve.

    Returns:
        (float): Average precision.
        (np.ndarray): Precision envelope curve.
        (np.ndarray): Modified recall curve with sentinel values added at the beginning and end.
    """
    # Append sentinel values to beginning and end
    mrec = np.concatenate(([0.0], recall, [1.0]))
    mpre = np.concatenate(([1.0], precision, [0.0]))

    # Compute the precision envelope
    mpre = np.flip(np.maximum.accumulate(np.flip(mpre)))

    # Integrate area under curve
    method = "interp"  # methods: 'continuous', 'interp'
    if method == "interp":
        x = np.linspace(0, 1, 101)  # 101-point interp (COCO)
        func = np.trapezoid if checks.check_version(np.__version__, ">=2.0") else np.trapz  # np.trapz deprecated
        ap = func(np.interp(x, mrec, mpre), x)  # integrate
    else:  # 'continuous'
        i = np.where(mrec[1:] != mrec[:-1])[0]  # points where x-axis (recall) changes
        ap = np.sum((mrec[i + 1] - mrec[i]) * mpre[i + 1])  # area under curve

    return ap, mpre, mrec


def ap_per_class(
    tp, conf, pred_cls, target_cls, plot=False, on_plot=None, save_dir=Path(), names={}, eps=1e-16, prefix=""
):
    """
    Compute the average precision per class for object detection evaluation.

    Args:
        tp (np.ndarray): Binary array indicating whether the detection is correct (True) or not (False).
        conf (np.ndarray): Array of confidence scores of the detections.
        pred_cls (np.ndarray): Array of predicted classes of the detections.
        target_cls (np.ndarray): Array of true classes of the detections.
        plot (bool, optional): Whether to plot PR curves or not.
        on_plot (func, optional): A callback to pass plots path and data when they are rendered.
        save_dir (Path, optional): Directory to save the PR curves.
        names (dict, optional): Dict of class names to plot PR curves.
        eps (float, optional): A small value to avoid division by zero.
        prefix (str, optional): A prefix string for saving the plot files.

    Returns:
        tp (np.ndarray): True positive counts at threshold given by max F1 metric for each class.
        fp (np.ndarray): False positive counts at threshold given by max F1 metric for each class.
        p (np.ndarray): Precision values at threshold given by max F1 metric for each class.
        r (np.ndarray): Recall values at threshold given by max F1 metric for each class.
        f1 (np.ndarray): F1-score values at threshold given by max F1 metric for each class.
        ap (np.ndarray): Average precision for each class at different IoU thresholds.
        unique_classes (np.ndarray): An array of unique classes that have data.
        p_curve (np.ndarray): Precision curves for each class.
        r_curve (np.ndarray): Recall curves for each class.
        f1_curve (np.ndarray): F1-score curves for each class.
        x (np.ndarray): X-axis values for the curves.
        prec_values (np.ndarray): Precision values at mAP@0.5 for each class.
    """
    # Sort by objectness
    i = np.argsort(-conf)
    tp, conf, pred_cls = tp[i], conf[i], pred_cls[i]

    # Find unique classes
    unique_classes, nt = np.unique(target_cls, return_counts=True)
    nc = unique_classes.shape[0]  # number of classes, number of detections

    # Create Precision-Recall curve and compute AP for each class
    x, prec_values = np.linspace(0, 1, 1000), []

    # Average precision, precision and recall curves
    ap, p_curve, r_curve = np.zeros((nc, tp.shape[1])), np.zeros((nc, 1000)), np.zeros((nc, 1000))
    for ci, c in enumerate(unique_classes):
        i = pred_cls == c
        n_l = nt[ci]  # number of labels
        n_p = i.sum()  # number of predictions
        if n_p == 0 or n_l == 0:
            continue

        # Accumulate FPs and TPs
        fpc = (1 - tp[i]).cumsum(0)
        tpc = tp[i].cumsum(0)

        # Recall
        recall = tpc / (n_l + eps)  # recall curve
        r_curve[ci] = np.interp(-x, -conf[i], recall[:, 0], left=0)  # negative x, xp because xp decreases

        # Precision
        precision = tpc / (tpc + fpc)  # precision curve
        p_curve[ci] = np.interp(-x, -conf[i], precision[:, 0], left=1)  # p at pr_score

        # AP from recall-precision curve
        for j in range(tp.shape[1]):
            ap[ci, j], mpre, mrec = compute_ap(recall[:, j], precision[:, j])
            if j == 0:
                prec_values.append(np.interp(x, mrec, mpre))  # precision at mAP@0.5

    prec_values = np.array(prec_values) if prec_values else np.zeros((1, 1000))  # (nc, 1000)

    # Compute F1 (harmonic mean of precision and recall)
    f1_curve = 2 * p_curve * r_curve / (p_curve + r_curve + eps)
    names = [v for k, v in names.items() if k in unique_classes]  # list: only classes that have data
    names = dict(enumerate(names))  # to dict
    if plot:
        plot_pr_curve(x, prec_values, ap, save_dir / f"{prefix}PR_curve.png", names, on_plot=on_plot)
        plot_mc_curve(x, f1_curve, save_dir / f"{prefix}F1_curve.png", names, ylabel="F1", on_plot=on_plot)
        plot_mc_curve(x, p_curve, save_dir / f"{prefix}P_curve.png", names, ylabel="Precision", on_plot=on_plot)
        plot_mc_curve(x, r_curve, save_dir / f"{prefix}R_curve.png", names, ylabel="Recall", on_plot=on_plot)

    i = smooth(f1_curve.mean(0), 0.1).argmax()  # max F1 index
    p, r, f1 = p_curve[:, i], r_curve[:, i], f1_curve[:, i]  # max-F1 precision, recall, F1 values
    tp = (r * nt).round()  # true positives
    fp = (tp / (p + eps) - tp).round()  # false positives
    return tp, fp, p, r, f1, ap, unique_classes.astype(int), p_curve, r_curve, f1_curve, x, prec_values


class Metric(SimpleClass):
    """
    Class for computing evaluation metrics for YOLOv8 model.

    Attributes:
        p (list): Precision for each class. Shape: (nc,).
        r (list): Recall for each class. Shape: (nc,).
        f1 (list): F1 score for each class. Shape: (nc,).
        all_ap (list): AP scores for all classes and all IoU thresholds. Shape: (nc, 10).
        ap_class_index (list): Index of class for each AP score. Shape: (nc,).
        nc (int): Number of classes.

    Methods:
        ap50(): AP at IoU threshold of 0.5 for all classes. Returns: List of AP scores. Shape: (nc,) or [].
        ap(): AP at IoU thresholds from 0.5 to 0.95 for all classes. Returns: List of AP scores. Shape: (nc,) or [].
        mp(): Mean precision of all classes. Returns: Float.
        mr(): Mean recall of all classes. Returns: Float.
        map50(): Mean AP at IoU threshold of 0.5 for all classes. Returns: Float.
        map75(): Mean AP at IoU threshold of 0.75 for all classes. Returns: Float.
        map(): Mean AP at IoU thresholds from 0.5 to 0.95 for all classes. Returns: Float.
        mean_results(): Mean of results, returns mp, mr, map50, map.
        class_result(i): Class-aware result, returns p[i], r[i], ap50[i], ap[i].
        maps(): mAP of each class. Returns: Array of mAP scores, shape: (nc,).
        fitness(): Model fitness as a weighted combination of metrics. Returns: Float.
        update(results): Update metric attributes with new evaluation results.
    """

    def __init__(self) -> None:
        """Initialize a Metric instance for computing evaluation metrics for the YOLOv8 model."""
        self.p = []  # (nc, )
        self.r = []  # (nc, )
        self.f1 = []  # (nc, )
        self.all_ap = []  # (nc, 10)
        self.ap_class_index = []  # (nc, )
        self.nc = 0

    @property
    def ap50(self):
        """
        Return the Average Precision (AP) at an IoU threshold of 0.5 for all classes.

        Returns:
            (np.ndarray, list): Array of shape (nc,) with AP50 values per class, or an empty list if not available.
        """
        return self.all_ap[:, 0] if len(self.all_ap) else []

    @property
    def ap(self):
        """
        Return the Average Precision (AP) at an IoU threshold of 0.5-0.95 for all classes.

        Returns:
            (np.ndarray, list): Array of shape (nc,) with AP50-95 values per class, or an empty list if not available.
        """
        return self.all_ap.mean(1) if len(self.all_ap) else []

    @property
    def mp(self):
        """
        Return the Mean Precision of all classes.

        Returns:
            (float): The mean precision of all classes.
        """
        return self.p.mean() if len(self.p) else 0.0

    @property
    def mr(self):
        """
        Return the Mean Recall of all classes.

        Returns:
            (float): The mean recall of all classes.
        """
        return self.r.mean() if len(self.r) else 0.0

    @property
    def map50(self):
        """
        Return the mean Average Precision (mAP) at an IoU threshold of 0.5.

        Returns:
            (float): The mAP at an IoU threshold of 0.5.
        """
        return self.all_ap[:, 0].mean() if len(self.all_ap) else 0.0

    @property
    def map75(self):
        """
        Return the mean Average Precision (mAP) at an IoU threshold of 0.75.

        Returns:
            (float): The mAP at an IoU threshold of 0.75.
        """
        return self.all_ap[:, 5].mean() if len(self.all_ap) else 0.0

    @property
    def map(self):
        """
        Return the mean Average Precision (mAP) over IoU thresholds of 0.5 - 0.95 in steps of 0.05.

        Returns:
            (float): The mAP over IoU thresholds of 0.5 - 0.95 in steps of 0.05.
        """
        return self.all_ap.mean() if len(self.all_ap) else 0.0

    def mean_results(self):
        """Return mean of results, mp, mr, map50, map."""
        return [self.mp, self.mr, self.map50, self.map]

    def class_result(self, i):
        """Return class-aware result, p[i], r[i], ap50[i], ap[i]."""
        return self.p[i], self.r[i], self.ap50[i], self.ap[i]

    @property
    def maps(self):
        """Return mAP of each class."""
        maps = np.zeros(self.nc) + self.map
        for i, c in enumerate(self.ap_class_index):
            maps[c] = self.ap[i]
        return maps

    def fitness(self):
        """Return model fitness as a weighted combination of metrics."""
        w = [0.0, 0.0, 0.1, 0.9]  # weights for [P, R, mAP@0.5, mAP@0.5:0.95]
        return (np.array(self.mean_results()) * w).sum()

    def update(self, results):
        """
        Update the evaluation metrics with a new set of results.

        Args:
            results (tuple): A tuple containing evaluation metrics:
                - p (list): Precision for each class.
                - r (list): Recall for each class.
                - f1 (list): F1 score for each class.
                - all_ap (list): AP scores for all classes and all IoU thresholds.
                - ap_class_index (list): Index of class for each AP score.
                - p_curve (list): Precision curve for each class.
                - r_curve (list): Recall curve for each class.
                - f1_curve (list): F1 curve for each class.
                - px (list): X values for the curves.
                - prec_values (list): Precision values for each class.
        """
        (
            self.p,
            self.r,
            self.f1,
            self.all_ap,
            self.ap_class_index,
            self.p_curve,
            self.r_curve,
            self.f1_curve,
            self.px,
            self.prec_values,
        ) = results

    @property
    def curves(self):
        """Return a list of curves for accessing specific metrics curves."""
        return []

    @property
    def curves_results(self):
        """Return a list of curves for accessing specific metrics curves."""
        return [
            [self.px, self.prec_values, "Recall", "Precision"],
            [self.px, self.f1_curve, "Confidence", "F1"],
            [self.px, self.p_curve, "Confidence", "Precision"],
            [self.px, self.r_curve, "Confidence", "Recall"],
        ]


class DetMetrics(SimpleClass):
    """
    Utility class for computing detection metrics such as precision, recall, and mean average precision (mAP).

    Attributes:
        save_dir (Path): A path to the directory where the output plots will be saved.
        plot (bool): A flag that indicates whether to plot precision-recall curves for each class.
        names (dict): A dictionary of class names.
        box (Metric): An instance of the Metric class for storing detection results.
        speed (dict): A dictionary for storing execution times of different parts of the detection process.
        task (str): The task type, set to 'detect'.
    """

    def __init__(self, save_dir=Path("."), plot=False, names={}) -> None:
        """
        Initialize a DetMetrics instance with a save directory, plot flag, and class names.

        Args:
            save_dir (Path, optional): Directory to save plots.
            plot (bool, optional): Whether to plot precision-recall curves.
            names (dict, optional): Dictionary mapping class indices to names.
        """
        self.save_dir = save_dir
        self.plot = plot
        self.names = names
        self.box = Metric()
        self.speed = {"preprocess": 0.0, "inference": 0.0, "loss": 0.0, "postprocess": 0.0}
        self.task = "detect"

    def process(self, tp, conf, pred_cls, target_cls, on_plot=None):
        """
        Process predicted results for object detection and update metrics.

        Args:
            tp (np.ndarray): True positive array.
            conf (np.ndarray): Confidence array.
            pred_cls (np.ndarray): Predicted class indices array.
            target_cls (np.ndarray): Target class indices array.
            on_plot (callable, optional): Function to call after plots are generated.
        """
        results = ap_per_class(
            tp,
            conf,
            pred_cls,
            target_cls,
            plot=self.plot,
            save_dir=self.save_dir,
            names=self.names,
            on_plot=on_plot,
        )[2:]
        self.box.nc = len(self.names)
        self.box.update(results)

    @property
    def keys(self):
        """Return a list of keys for accessing specific metrics."""
        return ["metrics/precision(B)", "metrics/recall(B)", "metrics/mAP50(B)", "metrics/mAP50-95(B)"]

    def mean_results(self):
        """Calculate mean of detected objects & return precision, recall, mAP50, and mAP50-95."""
        return self.box.mean_results()

    def class_result(self, i):
        """Return the result of evaluating the performance of an object detection model on a specific class."""
        return self.box.class_result(i)

    @property
    def maps(self):
        """Return mean Average Precision (mAP) scores per class."""
        return self.box.maps

    @property
    def fitness(self):
        """Return the fitness of box object."""
        return self.box.fitness()

    @property
    def ap_class_index(self):
        """Return the average precision index per class."""
        return self.box.ap_class_index

    @property
    def results_dict(self):
        """Return dictionary of computed performance metrics and statistics."""
        return dict(zip(self.keys + ["fitness"], self.mean_results() + [self.fitness]))

    @property
    def curves(self):
        """Return a list of curves for accessing specific metrics curves."""
        return ["Precision-Recall(B)", "F1-Confidence(B)", "Precision-Confidence(B)", "Recall-Confidence(B)"]

    @property
    def curves_results(self):
        """Return dictionary of computed performance metrics and statistics."""
        return self.box.curves_results


class SegmentMetrics(SimpleClass):
    """
    Calculates and aggregates detection and segmentation metrics over a given set of classes.

    Attributes:
        save_dir (Path): Path to the directory where the output plots should be saved.
        plot (bool): Whether to save the detection and segmentation plots.
        names (dict): Dictionary of class names.
        box (Metric): An instance of the Metric class to calculate box detection metrics.
        seg (Metric): An instance of the Metric class to calculate mask segmentation metrics.
        speed (dict): Dictionary to store the time taken in different phases of inference.
        task (str): The task type, set to 'segment'.
    """

    def __init__(self, save_dir=Path("."), plot=False, names=()) -> None:
        """
        Initialize a SegmentMetrics instance with a save directory, plot flag, and class names.

        Args:
            save_dir (Path, optional): Directory to save plots.
            plot (bool, optional): Whether to plot precision-recall curves.
            names (dict, optional): Dictionary mapping class indices to names.
        """
        self.save_dir = save_dir
        self.plot = plot
        self.names = names
        self.box = Metric()
        self.seg = Metric()
        self.speed = {"preprocess": 0.0, "inference": 0.0, "loss": 0.0, "postprocess": 0.0}
        self.task = "segment"

    def process(self, tp, tp_m, conf, pred_cls, target_cls, on_plot=None):
        """
        Process the detection and segmentation metrics over the given set of predictions.

        Args:
            tp (np.ndarray): True positive array for boxes.
            tp_m (np.ndarray): True positive array for masks.
            conf (np.ndarray): Confidence array.
            pred_cls (np.ndarray): Predicted class indices array.
            target_cls (np.ndarray): Target class indices array.
            on_plot (callable, optional): Function to call after plots are generated.
        """
        results_mask = ap_per_class(
            tp_m,
            conf,
            pred_cls,
            target_cls,
            plot=self.plot,
            on_plot=on_plot,
            save_dir=self.save_dir,
            names=self.names,
            prefix="Mask",
        )[2:]
        self.seg.nc = len(self.names)
        self.seg.update(results_mask)
        results_box = ap_per_class(
            tp,
            conf,
            pred_cls,
            target_cls,
            plot=self.plot,
            on_plot=on_plot,
            save_dir=self.save_dir,
            names=self.names,
            prefix="Box",
        )[2:]
        self.box.nc = len(self.names)
        self.box.update(results_box)

    @property
    def keys(self):
        """Return a list of keys for accessing metrics."""
        return [
            "metrics/precision(B)",
            "metrics/recall(B)",
            "metrics/mAP50(B)",
            "metrics/mAP50-95(B)",
            "metrics/precision(M)",
            "metrics/recall(M)",
            "metrics/mAP50(M)",
            "metrics/mAP50-95(M)",
        ]

    def mean_results(self):
        """Return the mean metrics for bounding box and segmentation results."""
        return self.box.mean_results() + self.seg.mean_results()

    def class_result(self, i):
        """Return classification results for a specified class index."""
        return self.box.class_result(i) + self.seg.class_result(i)

    @property
    def maps(self):
        """Return mAP scores for object detection and semantic segmentation models."""
        return self.box.maps + self.seg.maps

    @property
    def fitness(self):
        """Return the fitness score for both segmentation and bounding box models."""
        return self.seg.fitness() + self.box.fitness()

    @property
    def ap_class_index(self):
        """
        Return the class indices.

        Boxes and masks have the same ap_class_index.
        """
        return self.box.ap_class_index

    @property
    def results_dict(self):
        """Return results of object detection model for evaluation."""
        return dict(zip(self.keys + ["fitness"], self.mean_results() + [self.fitness]))

    @property
    def curves(self):
        """Return a list of curves for accessing specific metrics curves."""
        return [
            "Precision-Recall(B)",
            "F1-Confidence(B)",
            "Precision-Confidence(B)",
            "Recall-Confidence(B)",
            "Precision-Recall(M)",
            "F1-Confidence(M)",
            "Precision-Confidence(M)",
            "Recall-Confidence(M)",
        ]

    @property
    def curves_results(self):
        """Return dictionary of computed performance metrics and statistics."""
        return self.box.curves_results + self.seg.curves_results


class PoseMetrics(SegmentMetrics):
    """
    Calculates and aggregates detection and pose metrics over a given set of classes.

    Attributes:
        save_dir (Path): Path to the directory where the output plots should be saved.
        plot (bool): Whether to save the detection and pose plots.
        names (dict): Dictionary of class names.
        box (Metric): An instance of the Metric class to calculate box detection metrics.
        pose (Metric): An instance of the Metric class to calculate pose metrics.
        speed (dict): Dictionary to store the time taken in different phases of inference.
        task (str): The task type, set to 'pose'.

    Methods:
        process(tp_m, tp_b, conf, pred_cls, target_cls): Processes metrics over the given set of predictions.
        mean_results(): Returns the mean of the detection and segmentation metrics over all the classes.
        class_result(i): Returns the detection and segmentation metrics of class `i`.
        maps: Returns the mean Average Precision (mAP) scores for IoU thresholds ranging from 0.50 to 0.95.
        fitness: Returns the fitness scores, which are a single weighted combination of metrics.
        ap_class_index: Returns the list of indices of classes used to compute Average Precision (AP).
        results_dict: Returns the dictionary containing all the detection and segmentation metrics and fitness score.
    """

    def __init__(self, save_dir=Path("."), plot=False, names=()) -> None:
        """
        Initialize the PoseMetrics class with directory path, class names, and plotting options.

        Args:
            save_dir (Path, optional): Directory to save plots.
            plot (bool, optional): Whether to plot precision-recall curves.
            names (dict, optional): Dictionary mapping class indices to names.
        """
        super().__init__(save_dir, plot, names)
        self.save_dir = save_dir
        self.plot = plot
        self.names = names
        self.box = Metric()
        self.pose = Metric()
        self.speed = {"preprocess": 0.0, "inference": 0.0, "loss": 0.0, "postprocess": 0.0}
        self.task = "pose"

    def process(self, tp, tp_p, conf, pred_cls, target_cls, on_plot=None):
        """
        Process the detection and pose metrics over the given set of predictions.

        Args:
            tp (np.ndarray): True positive array for boxes.
            tp_p (np.ndarray): True positive array for keypoints.
            conf (np.ndarray): Confidence array.
            pred_cls (np.ndarray): Predicted class indices array.
            target_cls (np.ndarray): Target class indices array.
            on_plot (callable, optional): Function to call after plots are generated.
        """
        results_pose = ap_per_class(
            tp_p,
            conf,
            pred_cls,
            target_cls,
            plot=self.plot,
            on_plot=on_plot,
            save_dir=self.save_dir,
            names=self.names,
            prefix="Pose",
        )[2:]
        self.pose.nc = len(self.names)
        self.pose.update(results_pose)
        results_box = ap_per_class(
            tp,
            conf,
            pred_cls,
            target_cls,
            plot=self.plot,
            on_plot=on_plot,
            save_dir=self.save_dir,
            names=self.names,
            prefix="Box",
        )[2:]
        self.box.nc = len(self.names)
        self.box.update(results_box)

    @property
    def keys(self):
        """Return list of evaluation metric keys."""
        return [
            "metrics/precision(B)",
            "metrics/recall(B)",
            "metrics/mAP50(B)",
            "metrics/mAP50-95(B)",
            "metrics/precision(P)",
            "metrics/recall(P)",
            "metrics/mAP50(P)",
            "metrics/mAP50-95(P)",
        ]

    def mean_results(self):
        """Return the mean results of box and pose."""
        return self.box.mean_results() + self.pose.mean_results()

    def class_result(self, i):
        """Return the class-wise detection results for a specific class i."""
        return self.box.class_result(i) + self.pose.class_result(i)

    @property
    def maps(self):
        """Return the mean average precision (mAP) per class for both box and pose detections."""
        return self.box.maps + self.pose.maps

    @property
    def fitness(self):
        """Return combined fitness score for pose and box detection."""
        return self.pose.fitness() + self.box.fitness()

    @property
    def curves(self):
        """Return a list of curves for accessing specific metrics curves."""
        return [
            "Precision-Recall(B)",
            "F1-Confidence(B)",
            "Precision-Confidence(B)",
            "Recall-Confidence(B)",
            "Precision-Recall(P)",
            "F1-Confidence(P)",
            "Precision-Confidence(P)",
            "Recall-Confidence(P)",
        ]

    @property
    def curves_results(self):
        """Return dictionary of computed performance metrics and statistics."""
        return self.box.curves_results + self.pose.curves_results


class ClassifyMetrics(SimpleClass):
    """
    Class for computing classification metrics including top-1 and top-5 accuracy.

    Attributes:
        top1 (float): The top-1 accuracy.
        top5 (float): The top-5 accuracy.
        speed (dict): A dictionary containing the time taken for each step in the pipeline.
        task (str): The task type, set to 'classify'.
    """

    def __init__(self) -> None:
        """Initialize a ClassifyMetrics instance."""
        self.top1 = 0
        self.top5 = 0
        self.speed = {"preprocess": 0.0, "inference": 0.0, "loss": 0.0, "postprocess": 0.0}
        self.task = "classify"

    def process(self, targets, pred):
        """
        Process target classes and predicted classes to compute metrics.

        Args:
            targets (torch.Tensor): Target classes.
            pred (torch.Tensor): Predicted classes.
        """
        pred, targets = torch.cat(pred), torch.cat(targets)
        correct = (targets[:, None] == pred).float()
        acc = torch.stack((correct[:, 0], correct.max(1).values), dim=1)  # (top1, top5) accuracy
        self.top1, self.top5 = acc.mean(0).tolist()

    @property
    def fitness(self):
        """Return mean of top-1 and top-5 accuracies as fitness score."""
        return (self.top1 + self.top5) / 2

    @property
    def results_dict(self):
        """Return a dictionary with model's performance metrics and fitness score."""
        return dict(zip(self.keys + ["fitness"], [self.top1, self.top5, self.fitness]))

    @property
    def keys(self):
        """Return a list of keys for the results_dict property."""
        return ["metrics/accuracy_top1", "metrics/accuracy_top5"]

    @property
    def curves(self):
        """Return a list of curves for accessing specific metrics curves."""
        return []

    @property
    def curves_results(self):
        """Return a list of curves for accessing specific metrics curves."""
        return []


class OBBMetrics(SimpleClass):
    """
    Metrics for evaluating oriented bounding box (OBB) detection.

    Attributes:
        save_dir (Path): Path to the directory where the output plots should be saved.
        plot (bool): Whether to save the detection plots.
        names (dict): Dictionary of class names.
        box (Metric): An instance of the Metric class for storing detection results.
        speed (dict): A dictionary for storing execution times of different parts of the detection process.

    References:
        https://arxiv.org/pdf/2106.06072.pdf
    """

    def __init__(self, save_dir=Path("."), plot=False, names=()) -> None:
        """
        Initialize an OBBMetrics instance with directory, plotting, and class names.

        Args:
            save_dir (Path, optional): Directory to save plots.
            plot (bool, optional): Whether to plot precision-recall curves.
            names (dict, optional): Dictionary mapping class indices to names.
        """
        self.save_dir = save_dir
        self.plot = plot
        self.names = names
        self.box = Metric()
        self.speed = {"preprocess": 0.0, "inference": 0.0, "loss": 0.0, "postprocess": 0.0}

    def process(self, tp, conf, pred_cls, target_cls, on_plot=None):
        """
        Process predicted results for object detection and update metrics.

        Args:
            tp (np.ndarray): True positive array.
            conf (np.ndarray): Confidence array.
            pred_cls (np.ndarray): Predicted class indices array.
            target_cls (np.ndarray): Target class indices array.
            on_plot (callable, optional): Function to call after plots are generated.
        """
        results = ap_per_class(
            tp,
            conf,
            pred_cls,
            target_cls,
            plot=self.plot,
            save_dir=self.save_dir,
            names=self.names,
            on_plot=on_plot,
        )[2:]
        self.box.nc = len(self.names)
        self.box.update(results)

    @property
    def keys(self):
        """Return a list of keys for accessing specific metrics."""
        return ["metrics/precision(B)", "metrics/recall(B)", "metrics/mAP50(B)", "metrics/mAP50-95(B)"]

    def mean_results(self):
        """Calculate mean of detected objects & return precision, recall, mAP50, and mAP50-95."""
        return self.box.mean_results()

    def class_result(self, i):
        """Return the result of evaluating the performance of an object detection model on a specific class."""
        return self.box.class_result(i)

    @property
    def maps(self):
        """Return mean Average Precision (mAP) scores per class."""
        return self.box.maps

    @property
    def fitness(self):
        """Return the fitness of box object."""
        return self.box.fitness()

    @property
    def ap_class_index(self):
        """Return the average precision index per class."""
        return self.box.ap_class_index

    @property
    def results_dict(self):
        """Return dictionary of computed performance metrics and statistics."""
        return dict(zip(self.keys + ["fitness"], self.mean_results() + [self.fitness]))

    @property
    def curves(self):
        """Return a list of curves for accessing specific metrics curves."""
        return []

    @property
    def curves_results(self):
        """Return a list of curves for accessing specific metrics curves."""
        return []