Link to this sectionReference for ultralytics/utils/ops.py#

class Profile(contextlib.ContextDecorator):
    """Ultralytics Profile class for timing code execution.

    Use as a decorator with @Profile() or as a context manager with 'with Profile():'. Provides accurate timing
    measurements with CUDA synchronization support for GPU operations.

    Attributes:
        t (float): Accumulated time in seconds.
        device (torch.device): Device used for model inference.
        cuda (bool): Whether CUDA is being used for timing synchronization.

    Examples:
        Use as a context manager to time code execution
        >>> with Profile() as dt:
        ...     pass  # slow operation here
        >>> str(dt).startswith("Elapsed time is ")
        True

        Use as a decorator to time function execution
        >>> @Profile()
        ... def slow_function():
        ...     time.sleep(0.1)
    """

    def __init__(self, t: float = 0.0, device: torch.device | None = None):
        """Initialize the Profile class.

        Args:
            t (float): Initial accumulated time in seconds.
            device (torch.device, optional): Device used for model inference to enable CUDA synchronization.
        """
        self.t = t
        self.device = device
        self.cuda = bool(device and str(device).startswith("cuda"))

def __enter__(self):
    """Start timing."""
    self.start = self.time()
    return self

def __exit__(self, type, value, traceback):
    """Stop timing."""
    self.dt = self.time() - self.start  # delta-time
    self.t += self.dt  # accumulate dt

def __str__(self):
    """Return a human-readable string representing the accumulated elapsed time."""
    return f"Elapsed time is {self.t} s"

def time(self):
    """Get current time with CUDA synchronization if applicable."""
    if self.cuda:
        torch.cuda.synchronize(self.device)
    return time.perf_counter()

def segment2box(segment: np.ndarray, width: int = 640, height: int = 640) -> np.ndarray:
    """Convert segment coordinates to bounding box coordinates.

    Converts a single segment label to a box label by finding the minimum and maximum x and y coordinates. Applies
    inside-image constraint and clips coordinates when necessary.

    Args:
        segment (np.ndarray): Segment coordinates in format (N, 2) where N is number of points.
        width (int): Width of the image in pixels.
        height (int): Height of the image in pixels.

    Returns:
        (np.ndarray): Bounding box coordinates in xyxy format [x1, y1, x2, y2].
    """
    x, y = segment.T  # segment xy
    # Clip coordinates if 3 out of 4 sides are outside the image
    if np.array([x.min() < 0, y.min() < 0, x.max() > width, y.max() > height]).sum() >= 3:
        x = x.clip(0, width)
        y = y.clip(0, height)
    inside = (x >= 0) & (y >= 0) & (x <= width) & (y <= height)
    x = x[inside]
    y = y[inside]
    return (
        np.array([x.min(), y.min(), x.max(), y.max()], dtype=segment.dtype)
        if any(x)
        else np.zeros(4, dtype=segment.dtype)
    )  # xyxy

def scale_boxes(
    img1_shape: tuple[int, int],
    boxes: torch.Tensor | np.ndarray,
    img0_shape: tuple[int, int],
    ratio_pad: tuple | None = None,
    padding: bool = True,
    xywh: bool = False,
) -> torch.Tensor | np.ndarray:
    """Rescale bounding boxes from one image shape to another.

    Rescales bounding boxes from img1_shape to img0_shape, accounting for padding and aspect ratio changes. Supports
    both xyxy and xywh box formats.

    Args:
        img1_shape (tuple[int, int]): Shape of the source image (height, width).
        boxes (torch.Tensor | np.ndarray): Bounding boxes to rescale in format (N, 4).
        img0_shape (tuple[int, int]): Shape of the target image (height, width).
        ratio_pad (tuple, optional): Tuple of (ratio, pad) for scaling. If None, calculated from image shapes.
        padding (bool): Whether boxes are based on YOLO-style augmented images with padding.
        xywh (bool): Whether box format is xywh (True) or xyxy (False).

    Returns:
        (torch.Tensor | np.ndarray): Rescaled bounding boxes in the same format as input.
    """
    if ratio_pad is None:  # calculate from img0_shape
        gain = min(img1_shape[0] / img0_shape[0], img1_shape[1] / img0_shape[1])  # gain  = old / new
        pad_x = round((img1_shape[1] - round(img0_shape[1] * gain)) / 2 - 0.1)
        pad_y = round((img1_shape[0] - round(img0_shape[0] * gain)) / 2 - 0.1)
    else:
        gain = ratio_pad[0][0]
        pad_x, pad_y = ratio_pad[1]

    if padding:
        boxes[..., 0] -= pad_x  # x padding
        boxes[..., 1] -= pad_y  # y padding
        if not xywh:
            boxes[..., 2] -= pad_x  # x padding
            boxes[..., 3] -= pad_y  # y padding
    boxes[..., :4] /= gain
    return boxes if xywh else clip_boxes(boxes, img0_shape)

def make_divisible(x: int, divisor):
    """Return the smallest number >= x that is divisible by the given divisor.

    Args:
        x (int): The number to make divisible.
        divisor (int | torch.Tensor): The divisor.

    Returns:
        (int): The smallest number >= x divisible by the divisor.
    """
    if isinstance(divisor, torch.Tensor):
        divisor = int(divisor.max())  # to int
    return math.ceil(x / divisor) * divisor

def clip_boxes(boxes, shape):
    """Clip bounding boxes to image boundaries.

    Args:
        boxes (torch.Tensor | np.ndarray): Bounding boxes to clip.
        shape (tuple): Image shape as HWC or HW (supports both).

    Returns:
        (torch.Tensor | np.ndarray): Clipped bounding boxes.
    """
    h, w = shape[:2]  # supports both HWC or HW shapes
    if isinstance(boxes, torch.Tensor):  # faster individually
        if NOT_MACOS14:
            boxes[..., 0].clamp_(0, w)  # x1
            boxes[..., 1].clamp_(0, h)  # y1
            boxes[..., 2].clamp_(0, w)  # x2
            boxes[..., 3].clamp_(0, h)  # y2
        else:  # Apple macOS14 MPS bug https://github.com/ultralytics/ultralytics/pull/21878
            boxes[..., 0] = boxes[..., 0].clamp(0, w)
            boxes[..., 1] = boxes[..., 1].clamp(0, h)
            boxes[..., 2] = boxes[..., 2].clamp(0, w)
            boxes[..., 3] = boxes[..., 3].clamp(0, h)
    else:  # np.array (faster grouped)
        boxes[..., [0, 2]] = boxes[..., [0, 2]].clip(0, w)  # x1, x2
        boxes[..., [1, 3]] = boxes[..., [1, 3]].clip(0, h)  # y1, y2
    return boxes

def clip_coords(coords, shape):
    """Clip line coordinates to image boundaries.

    Args:
        coords (torch.Tensor | np.ndarray): Line coordinates to clip.
        shape (tuple): Image shape as HWC or HW (supports both).

    Returns:
        (torch.Tensor | np.ndarray): Clipped coordinates.
    """
    h, w = shape[:2]  # supports both HWC or HW shapes
    if isinstance(coords, torch.Tensor):
        if NOT_MACOS14:
            coords[..., 0].clamp_(0, w)  # x
            coords[..., 1].clamp_(0, h)  # y
        else:  # Apple macOS14 MPS bug https://github.com/ultralytics/ultralytics/pull/21878
            coords[..., 0] = coords[..., 0].clamp(0, w)
            coords[..., 1] = coords[..., 1].clamp(0, h)
    else:  # np.array
        coords[..., 0] = coords[..., 0].clip(0, w)  # x
        coords[..., 1] = coords[..., 1].clip(0, h)  # y
    return coords

def xyxy2xywh(x):
    """Convert bounding box coordinates from (x1, y1, x2, y2) format to (x, y, width, height) format where (x1, y1) is
    the top-left corner and (x2, y2) is the bottom-right corner.

    Args:
        x (np.ndarray | torch.Tensor): Input bounding box coordinates in (x1, y1, x2, y2) format.

    Returns:
        (np.ndarray | torch.Tensor): Bounding box coordinates in (x, y, width, height) format.
    """
    assert x.shape[-1] == 4, f"input shape last dimension expected 4 but input shape is {x.shape}"
    y = empty_like(x)  # faster than clone/copy
    x1, y1, x2, y2 = x[..., 0], x[..., 1], x[..., 2], x[..., 3]
    y[..., 0] = (x1 + x2) / 2  # x center
    y[..., 1] = (y1 + y2) / 2  # y center
    y[..., 2] = x2 - x1  # width
    y[..., 3] = y2 - y1  # height
    return y

def xywh2xyxy(x):
    """Convert bounding box coordinates from (x, y, width, height) format to (x1, y1, x2, y2) format where (x1, y1) is
    the top-left corner and (x2, y2) is the bottom-right corner. Note: ops per 2 channels faster than per channel.

    Args:
        x (np.ndarray | torch.Tensor): Input bounding box coordinates in (x, y, width, height) format.

    Returns:
        (np.ndarray | torch.Tensor): Bounding box coordinates in (x1, y1, x2, y2) format.
    """
    assert x.shape[-1] == 4, f"input shape last dimension expected 4 but input shape is {x.shape}"
    y = empty_like(x)  # faster than clone/copy
    xy = x[..., :2]  # centers
    wh = x[..., 2:] / 2  # half width-height
    y[..., :2] = xy - wh  # top left xy
    y[..., 2:] = xy + wh  # bottom right xy
    return y

def xywhn2xyxy(x, w: int = 640, h: int = 640, padw: int = 0, padh: int = 0):
    """Convert normalized bounding box coordinates to pixel coordinates.

    Args:
        x (np.ndarray | torch.Tensor): Normalized bounding box coordinates in (x, y, w, h) format.
        w (int): Image width in pixels.
        h (int): Image height in pixels.
        padw (int): Padding width in pixels.
        padh (int): Padding height in pixels.

    Returns:
        (np.ndarray | torch.Tensor): Bounding box coordinates in (x1, y1, x2, y2) format.
    """
    assert x.shape[-1] == 4, f"input shape last dimension expected 4 but input shape is {x.shape}"
    y = empty_like(x)  # faster than clone/copy
    xc, yc, xw, xh = x[..., 0], x[..., 1], x[..., 2], x[..., 3]
    half_w, half_h = xw / 2, xh / 2
    y[..., 0] = w * (xc - half_w) + padw  # top left x
    y[..., 1] = h * (yc - half_h) + padh  # top left y
    y[..., 2] = w * (xc + half_w) + padw  # bottom right x
    y[..., 3] = h * (yc + half_h) + padh  # bottom right y
    return y

def xyxy2xywhn(x, w: int = 640, h: int = 640, clip: bool = False, eps: float = 0.0):
    """Convert bounding box coordinates from (x1, y1, x2, y2) format to normalized (x, y, width, height) format. x, y,
    width and height are normalized to image dimensions.

    Args:
        x (np.ndarray | torch.Tensor): Input bounding box coordinates in (x1, y1, x2, y2) format.
        w (int): Image width in pixels.
        h (int): Image height in pixels.
        clip (bool): Whether to clip boxes to image boundaries.
        eps (float): Minimum value for box width and height.

    Returns:
        (np.ndarray | torch.Tensor): Normalized bounding box coordinates in (x, y, width, height) format.
    """
    if clip:
        x = clip_boxes(x, (h - eps, w - eps))
    assert x.shape[-1] == 4, f"input shape last dimension expected 4 but input shape is {x.shape}"
    y = empty_like(x)  # faster than clone/copy
    x1, y1, x2, y2 = x[..., 0], x[..., 1], x[..., 2], x[..., 3]
    y[..., 0] = ((x1 + x2) / 2) / w  # x center
    y[..., 1] = ((y1 + y2) / 2) / h  # y center
    y[..., 2] = (x2 - x1) / w  # width
    y[..., 3] = (y2 - y1) / h  # height
    return y

def xywh2ltwh(x):
    """Convert bounding box format from [x, y, w, h] to [x1, y1, w, h] where x1, y1 are top-left coordinates.

    Args:
        x (np.ndarray | torch.Tensor): Input bounding box coordinates in xywh format.

    Returns:
        (np.ndarray | torch.Tensor): Bounding box coordinates in ltwh format.
    """
    y = x.clone() if isinstance(x, torch.Tensor) else np.copy(x)
    y[..., 0] = x[..., 0] - x[..., 2] / 2  # top left x
    y[..., 1] = x[..., 1] - x[..., 3] / 2  # top left y
    return y

def xyxy2ltwh(x):
    """Convert bounding boxes from [x1, y1, x2, y2] to [x1, y1, w, h] format.

    Args:
        x (np.ndarray | torch.Tensor): Input bounding box coordinates in xyxy format.

    Returns:
        (np.ndarray | torch.Tensor): Bounding box coordinates in ltwh format.
    """
    y = x.clone() if isinstance(x, torch.Tensor) else np.copy(x)
    y[..., 2] = x[..., 2] - x[..., 0]  # width
    y[..., 3] = x[..., 3] - x[..., 1]  # height
    return y

def ltwh2xywh(x):
    """Convert bounding boxes from [x1, y1, w, h] to [x, y, w, h] where xy1=top-left, xy=center.

    Args:
        x (np.ndarray | torch.Tensor): Input bounding box coordinates.

    Returns:
        (np.ndarray | torch.Tensor): Bounding box coordinates in xywh format.
    """
    y = x.clone() if isinstance(x, torch.Tensor) else np.copy(x)
    y[..., 0] = x[..., 0] + x[..., 2] / 2  # center x
    y[..., 1] = x[..., 1] + x[..., 3] / 2  # center y
    return y

def xyxyxyxy2xywhr(x):
    """Convert batched Oriented Bounding Boxes (OBB) from [xy1, xy2, xy3, xy4] to [xywh, rotation] format.

    Args:
        x (np.ndarray | torch.Tensor): Input box corners with shape (N, 8) in [xy1, xy2, xy3, xy4] format.

    Returns:
        (np.ndarray | torch.Tensor): Converted data in [cx, cy, w, h, rotation] format with shape (N, 5). Rotation
            values are in radians from [-pi/4, 3pi/4).
    """
    is_torch = isinstance(x, torch.Tensor)
    points = x.cpu().numpy() if is_torch else x
    points = points.reshape(len(x), -1, 2)
    rboxes = []
    for pts in points:
        # NOTE: Use cv2.minAreaRect to get accurate xywhr,
        # especially some objects are cut off by augmentations in dataloader.
        (cx, cy), (w, h), angle = cv2.minAreaRect(pts)
        # convert angle to radian and normalize to [-pi/4, 3pi/4)
        theta = angle / 180 * np.pi
        if w < h:
            w, h = h, w
            theta += np.pi / 2
        while theta >= 3 * np.pi / 4:
            theta -= np.pi
        while theta < -np.pi / 4:
            theta += np.pi
        rboxes.append([cx, cy, w, h, theta])
    return torch.tensor(rboxes, device=x.device, dtype=x.dtype) if is_torch else np.asarray(rboxes)

def xywhr2xyxyxyxy(x):
    """Convert batched Oriented Bounding Boxes (OBB) from [xywh, rotation] to [xy1, xy2, xy3, xy4] format.

    Args:
        x (np.ndarray | torch.Tensor): Boxes in [cx, cy, w, h, rotation] format with shape (N, 5) or (B, N, 5). Rotation
            values should be in radians from [-pi/4, 3pi/4).

    Returns:
        (np.ndarray | torch.Tensor): Converted corner points with shape (N, 4, 2) or (B, N, 4, 2).
    """
    cos, sin, cat, stack = (
        (torch.cos, torch.sin, torch.cat, torch.stack)
        if isinstance(x, torch.Tensor)
        else (np.cos, np.sin, np.concatenate, np.stack)
    )

    ctr = x[..., :2]
    w, h, angle = (x[..., i : i + 1] for i in range(2, 5))
    cos_value, sin_value = cos(angle), sin(angle)
    vec1 = [w / 2 * cos_value, w / 2 * sin_value]
    vec2 = [-h / 2 * sin_value, h / 2 * cos_value]
    vec1 = cat(vec1, -1)
    vec2 = cat(vec2, -1)
    pt1 = ctr + vec1 + vec2
    pt2 = ctr + vec1 - vec2
    pt3 = ctr - vec1 - vec2
    pt4 = ctr - vec1 + vec2
    return stack([pt1, pt2, pt3, pt4], -2)

def ltwh2xyxy(x):
    """Convert bounding box from [x1, y1, w, h] to [x1, y1, x2, y2] where xy1=top-left, xy2=bottom-right.

    Args:
        x (np.ndarray | torch.Tensor): Input bounding box coordinates.

    Returns:
        (np.ndarray | torch.Tensor): Bounding box coordinates in xyxy format.
    """
    y = x.clone() if isinstance(x, torch.Tensor) else np.copy(x)
    y[..., 2] = x[..., 2] + x[..., 0]  # x2
    y[..., 3] = x[..., 3] + x[..., 1]  # y2
    return y

def segments2boxes(segments):
    """Convert segment coordinates to bounding box labels in xywh format.

    Args:
        segments (list): List of segments where each segment is a list of points, each point is [x, y] coordinates.

    Returns:
        (np.ndarray): Bounding box coordinates in xywh format.
    """
    boxes = []
    for s in segments:
        x, y = s.T  # segment xy
        boxes.append([x.min(), y.min(), x.max(), y.max()])  # cls, xyxy
    return xyxy2xywh(np.array(boxes))  # cls, xywh

def resample_segments(segments, n: int = 1000):
    """Resample segments to n points each using linear interpolation.

    Args:
        segments (list): List of (N, 2) arrays where N is the number of points in each segment.
        n (int): Number of points to resample each segment to.

    Returns:
        (list): Resampled segments with n points each.
    """
    for i, s in enumerate(segments):
        if len(s) == n:
            continue
        s = np.concatenate((s, s[0:1, :]), axis=0)
        x = np.linspace(0, len(s) - 1, n - len(s) if len(s) < n else n)
        xp = np.arange(len(s))
        x = np.insert(x, np.searchsorted(x, xp), xp) if len(s) < n else x
        segments[i] = (
            np.concatenate([np.interp(x, xp, s[:, i]) for i in range(2)], dtype=np.float32).reshape(2, -1).T
        )  # segment xy
    return segments

def crop_mask(masks: torch.Tensor, boxes: torch.Tensor) -> torch.Tensor:
    """Crop masks to bounding box regions.

    Args:
        masks (torch.Tensor): Masks with shape (N, H, W).
        boxes (torch.Tensor): Bounding box coordinates with shape (N, 4) in xyxy pixel format.

    Returns:
        (torch.Tensor): Cropped masks.
    """
    if boxes.device != masks.device:
        boxes = boxes.to(masks.device)
    _, h, w = masks.shape
    x1, y1, x2, y2 = torch.chunk(boxes[:, :, None], 4, 1)  # each shape (n,1,1)
    r = torch.arange(w, device=masks.device, dtype=x1.dtype)[None, None, :]  # columns (1,1,w)
    c = torch.arange(h, device=masks.device, dtype=x1.dtype)[None, :, None]  # rows (1,h,1)
    # Apply the column and row masks separately and in place: the box region is separable, so this avoids ever
    # materializing the full (n, h, w) boolean grid the combined product would build, and has no per-mask Python loop.
    masks *= (r >= x1) * (r < x2)  # zero columns outside the box
    masks *= (c >= y1) * (c < y2)  # zero rows outside the box
    return masks

def process_mask(protos, masks_in, bboxes, shape, upsample: bool = False):
    """Apply masks to bounding boxes using mask head output.

    Args:
        protos (torch.Tensor): Mask prototypes with shape (mask_dim, mask_h, mask_w).
        masks_in (torch.Tensor): Mask coefficients with shape (N, mask_dim) where N is number of masks after NMS.
        bboxes (torch.Tensor): Bounding boxes with shape (N, 4) where N is number of masks after NMS.
        shape (tuple): Input image size as (height, width).
        upsample (bool): Whether to upsample masks to original image size.

    Returns:
        (torch.Tensor): A binary mask tensor of shape [n, h, w], where n is the number of masks after NMS. When
            upsample=True h and w match the input image size; otherwise they are the prototype mask resolution.
    """
    c, mh, mw = protos.shape  # CHW
    masks = (masks_in @ protos.float().view(c, -1)).view(-1, mh, mw)  # NHW

    width_ratio = mw / shape[1]
    height_ratio = mh / shape[0]
    ratios = torch.tensor([[width_ratio, height_ratio, width_ratio, height_ratio]], device=bboxes.device)

    masks = crop_mask(masks, boxes=bboxes * ratios)  # NHW
    if upsample:
        masks = F.interpolate(masks[None], shape, mode="bilinear")[0]  # NHW
    return masks.gt_(0.0).byte()

def process_mask_native(protos, masks_in, bboxes, shape):
    """Apply masks to bounding boxes using mask head output with native upsampling.

    Args:
        protos (torch.Tensor): Mask prototypes with shape (mask_dim, mask_h, mask_w).
        masks_in (torch.Tensor): Mask coefficients with shape (N, mask_dim) where N is number of masks after NMS.
        bboxes (torch.Tensor): Bounding boxes with shape (N, 4) where N is number of masks after NMS.
        shape (tuple): Input image size as (height, width).

    Returns:
        (torch.Tensor): Binary mask tensor with shape (N, H, W).
    """
    c, mh, mw = protos.shape  # CHW
    coeffs = masks_in @ protos.float().view(c, -1)  # (N, mh*mw) prototype-resolution mask logits
    h, w = shape
    # Upsampling all N masks at once allocates an N*H*W float intermediate (~9 GB on a large image with many
    # detections), which OOMs the worker. Upsample in chunks bounded by a pixel budget, thresholding each chunk to
    # uint8 immediately so the float intermediate stays small, then crop the assembled uint8 stack.
    step = max(1, 32_000_000 // (h * w))
    masks = [
        scale_masks(coeffs[i : i + step].view(-1, mh, mw)[None], shape)[0].gt_(0.0).byte()
        for i in range(0, coeffs.shape[0], step)
    ]
    return crop_mask(torch.cat(masks), bboxes)

def scale_masks(
    masks: torch.Tensor,
    shape: tuple[int, int],
    ratio_pad: tuple[tuple[int, int], tuple[int, int]] | None = None,
    padding: bool = True,
    mode: str = "bilinear",
) -> torch.Tensor:
    """Rescale segment masks to target shape.

    Args:
        masks (torch.Tensor): Masks with shape (N, C, H, W).
        shape (tuple[int, int]): Target height and width as (height, width).
        ratio_pad (tuple, optional): Ratio and padding values as ((ratio_h, ratio_w), (pad_w, pad_h)).
        padding (bool): Whether masks are based on YOLO-style augmented images with padding.
        mode (str): Interpolation mode, e.g. 'bilinear' for logits or 'nearest' for integer class maps.

    Returns:
        (torch.Tensor): Rescaled masks.
    """
    im1_h, im1_w = masks.shape[2:]
    im0_h, im0_w = shape[:2]
    if im1_h == im0_h and im1_w == im0_w:
        return masks

    if ratio_pad is None:  # calculate from im0_shape
        gain = min(im1_h / im0_h, im1_w / im0_w)  # gain  = old / new
        pad_w, pad_h = (im1_w - round(im0_w * gain)), (im1_h - round(im0_h * gain))  # wh padding
        if padding:
            pad_w /= 2
            pad_h /= 2
    else:
        pad_w, pad_h = ratio_pad[1]
    top, left = (round(pad_h - 0.1), round(pad_w - 0.1)) if padding else (0, 0)
    bottom = im1_h - round(pad_h + 0.1)
    right = im1_w - round(pad_w + 0.1)
    return F.interpolate(masks[..., top:bottom, left:right].float(), shape, mode=mode)  # NCHW masks

def scale_coords(img1_shape, coords, img0_shape, ratio_pad=None, normalize: bool = False, padding: bool = True):
    """Rescale segment coordinates from img1_shape to img0_shape.

    Args:
        img1_shape (tuple): Source image shape as HWC or HW (supports both).
        coords (torch.Tensor): Coordinates to scale with shape (N, 2).
        img0_shape (tuple): Image 0 shape as HWC or HW (supports both).
        ratio_pad (tuple, optional): Ratio and padding values as ((ratio_h, ratio_w), (pad_w, pad_h)).
        normalize (bool): Whether to normalize coordinates to range [0, 1].
        padding (bool): Whether coordinates are based on YOLO-style augmented images with padding.

    Returns:
        (torch.Tensor): Scaled coordinates.
    """
    img0_h, img0_w = img0_shape[:2]  # supports both HWC or HW shapes
    if ratio_pad is None:  # calculate from img0_shape
        img1_h, img1_w = img1_shape[:2]  # supports both HWC or HW shapes
        gain = min(img1_h / img0_h, img1_w / img0_w)  # gain  = old / new
        pad = (img1_w - round(img0_w * gain)) / 2, (img1_h - round(img0_h * gain)) / 2  # wh padding
    else:
        gain = ratio_pad[0][0]
        pad = ratio_pad[1]

    if padding:
        coords[..., 0] -= pad[0]  # x padding
        coords[..., 1] -= pad[1]  # y padding
    coords[..., 0] /= gain
    coords[..., 1] /= gain
    coords = clip_coords(coords, img0_shape)
    if normalize:
        coords[..., 0] /= img0_w  # width
        coords[..., 1] /= img0_h  # height
    return coords

def regularize_rboxes(rboxes):
    """Regularize rotated bounding boxes to range [0, pi/2).

    Args:
        rboxes (torch.Tensor): Input rotated boxes with shape (N, 5) in xywhr format.

    Returns:
        (torch.Tensor): Regularized rotated boxes.
    """
    x, y, w, h, t = rboxes.unbind(dim=-1)
    # Swap edge if t >= pi/2 while not being symmetrically opposite
    swap = t % math.pi >= math.pi / 2
    w_ = torch.where(swap, h, w)
    h_ = torch.where(swap, w, h)
    t = t % (math.pi / 2)
    return torch.stack([x, y, w_, h_, t], dim=-1)  # regularized boxes

def masks2segments(masks: np.ndarray | torch.Tensor, strategy: str = "all") -> list[np.ndarray]:
    """Convert masks to segments using contour detection.

    Args:
        masks (np.ndarray | torch.Tensor): Binary masks with shape (N, H, W).
        strategy (str): Segmentation strategy, either 'all' or 'largest'.

    Returns:
        (list): List of segment masks as float32 arrays.
    """
    from ultralytics.data.converter import merge_multi_segment

    masks = masks.astype("uint8") if isinstance(masks, np.ndarray) else masks.byte().cpu().numpy()
    segments = []
    for x in np.ascontiguousarray(masks):
        c = cv2.findContours(x, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)[0]
        if c:
            if strategy == "all":  # merge and concatenate all segments
                c = (
                    np.concatenate(merge_multi_segment([x.reshape(-1, 2) for x in c]))
                    if len(c) > 1
                    else c[0].reshape(-1, 2)
                )
            elif strategy == "largest":  # select largest segment
                c = np.array(c[np.array([len(x) for x in c]).argmax()]).reshape(-1, 2)
        else:
            c = np.zeros((0, 2))  # no segments found
        segments.append(c.astype("float32"))
    return segments

def convert_torch2numpy_batch(batch: torch.Tensor) -> np.ndarray:
    """Convert a batch of FP32 torch tensors to NumPy uint8 arrays, changing from BCHW to BHWC layout.

    Args:
        batch (torch.Tensor): Input tensor batch with shape (Batch, Channels, Height, Width) and dtype torch.float32.

    Returns:
        (np.ndarray): Output NumPy array batch with shape (Batch, Height, Width, Channels) and dtype uint8.
    """
    return (batch.permute(0, 2, 3, 1).contiguous() * 255).clamp(0, 255).byte().cpu().numpy()

def clean_str(s):
    """Clean a string by replacing special characters with '_' character.

    Args:
        s (str): A string needing special characters replaced.

    Returns:
        (str): A string with special characters replaced by an underscore _.
    """
    return re.sub(pattern="[|@#!¡·$€%&()=?¿^*;:,¨`><+]", repl="_", string=s)

def empty_like(x):
    """Create empty torch.Tensor or np.ndarray with same shape and dtype as input."""
    return torch.empty_like(x, dtype=x.dtype) if isinstance(x, torch.Tensor) else np.empty_like(x, dtype=x.dtype)

def linear_sum_assignment(cost_matrix):
    """Solve the rectangular linear sum assignment problem (minimum-cost one-to-one matching).

    Uses `scipy.optimize.linear_sum_assignment` when SciPy is installed (faster compiled C++ solver), and otherwise
    falls back to an equivalent pure-NumPy implementation of the same modified Jonker-Volgenant shortest augmenting path
    algorithm (Crouse 2016). This keeps SciPy out of Ultralytics' required dependencies while preserving its speed when
    present. SciPy is imported lazily so it never slows `import ultralytics`. For a rectangular matrix only min(rows,
    columns) entries are matched.

    The NumPy fallback expects finite costs: an `inf` entry marks a forbidden assignment (matching SciPy), while `NaN`
    is not rejected (SciPy raises), so callers must sanitize NaN upstream (e.g. the RT-DETR matcher zeros NaN/inf
    beforehand). The two backends may return a different equal-cost assignment under exact ties, but the total cost is
    identical.

    The NumPy fallback is validated against SciPy with exact optimal-cost parity across ~6.9k randomized cases (every
    shape including empty/tall/wide, ties, negatives, IoU- and RT-DETR-style matrices, `maximize` via negation,
    torch-tensor input) plus ~2k independent brute-force global-optimum checks. SciPy's compiled inner loop is faster,
    but at the call-site sizes (smaller dimension = object count) the fallback runs in well under a millisecond:

        cost matrix   NumPy   SciPy
        300 x 20      0.2ms   0.02ms
        300 x 80      0.6ms   0.1ms
        300 x 300     28ms    1.5ms

    Args:
        cost_matrix (np.ndarray | torch.Tensor): Cost matrix with shape (N, M) and finite values.

    Returns:
        row_ind (np.ndarray): Row indices of the optimal assignment, sorted ascending, with length min(N, M).
        col_ind (np.ndarray): Column indices matched to each row in row_ind.

    Examples:
        >>> cost = np.array([[4, 1, 3], [2, 0, 5], [3, 2, 2]], dtype=float)
        >>> row_ind, col_ind = linear_sum_assignment(cost)
        >>> float(cost[row_ind, col_ind].sum())
        5.0
    """
    global _assignment_solver
    if _assignment_solver is None:  # resolve the backend once, then reuse it on every later call
        try:
            from scipy.optimize import linear_sum_assignment as solver  # faster compiled C++ solver when installed

            _assignment_solver = solver
        except ImportError:
            _assignment_solver = _linear_sum_assignment_numpy
    return _assignment_solver(np.asarray(cost_matrix, dtype=np.float64))

def _linear_sum_assignment_numpy(a):
    """Solve the rectangular linear sum assignment problem with NumPy (Jonker-Volgenant SciPy-free fallback).

    Args:
        a (np.ndarray): Cost matrix of shape (N, M) with dtype float64 and finite values.

    Returns:
        row_ind (np.ndarray): Row indices of the optimal assignment, sorted ascending, with length min(N, M).
        col_ind (np.ndarray): Column indices matched to each row in row_ind.
    """
    n, m = a.shape
    if n == 0 or m == 0:
        return np.empty(0, dtype=np.intp), np.empty(0, dtype=np.intp)
    transposed = n > m
    if transposed:
        a, n, m = a.T, m, n  # ensure rows <= columns
    u, v = np.zeros(n + 1), np.zeros(m + 1)  # row and column dual potentials
    p, way = np.zeros(m + 1, np.intp), np.zeros(m + 1, np.intp)  # column->row matches and path pointers
    for i in range(1, n + 1):
        p[0], j0 = i, 0
        minv, used = np.full(m + 1, np.inf), np.zeros(m + 1, bool)
        while True:  # grow a shortest augmenting path from row i
            used[j0] = True
            i0 = p[j0]
            cur = a[i0 - 1] - u[i0] - v[1:]
            improve = (~used[1:]) & (cur < minv[1:])
            minv[1:][improve], way[1:][improve] = cur[improve], j0
            j1 = int(np.argmin(np.where(used[1:], np.inf, minv[1:]))) + 1
            delta = minv[j1]
            u[p[used]] += delta
            v[used] -= delta
            minv[~used] -= delta
            j0 = j1
            if p[j0] == 0:
                break
        while j0:  # augment along the path
            p[j0] = p[way[j0]]
            j0 = way[j0]
    cols = np.nonzero(p[1:])[0]
    rows = p[1:][cols] - 1
    row_ind, col_ind = (cols, rows) if transposed else (rows, cols)
    order = np.argsort(row_ind, kind="stable")  # match scipy's row-sorted output
    return row_ind[order].astype(np.intp), col_ind[order].astype(np.intp)