cellpose/transforms.py

"""
Copyright © 2023 Howard Hughes Medical Institute, Authored by Carsen Stringer and Marius Pachitariu.
"""

import logging
import warnings

import cv2
import numpy as np
import torch
from scipy.ndimage import gaussian_filter1d
from torch.fft import fft2, fftshift, ifft2

transforms_logger = logging.getLogger(__name__)


def _taper_mask(ly=224, lx=224, sig=7.5):
    """
    Generate a taper mask.

    Args:
        ly (int): The height of the mask. Default is 224.
        lx (int): The width of the mask. Default is 224.
        sig (float): The sigma value for the tapering function. Default is 7.5.

    Returns:
        numpy.ndarray: The taper mask.

    """
    bsize = max(224, max(ly, lx))
    xm = np.arange(bsize)
    xm = np.abs(xm - xm.mean())
    mask = 1 / (1 + np.exp((xm - (bsize / 2 - 20)) / sig))
    mask = mask * mask[:, np.newaxis]
    mask = mask[bsize // 2 - ly // 2:bsize // 2 + ly // 2 + ly % 2,
                bsize // 2 - lx // 2:bsize // 2 + lx // 2 + lx % 2]
    return mask


def unaugment_tiles(y):
    """Reverse test-time augmentations for averaging (includes flipping of flowsY and flowsX).

    Args:
        y (float32): Array of shape (ntiles_y, ntiles_x, chan, Ly, Lx) where chan = (flowsY, flowsX, cell prob).

    Returns:
        float32: Array of shape (ntiles_y, ntiles_x, chan, Ly, Lx).

    """
    for j in range(y.shape[0]):
        for i in range(y.shape[1]):
            if j % 2 == 0 and i % 2 == 1:
                y[j, i] = y[j, i, :, ::-1, :]
                y[j, i, 0] *= -1
            elif j % 2 == 1 and i % 2 == 0:
                y[j, i] = y[j, i, :, :, ::-1]
                y[j, i, 1] *= -1
            elif j % 2 == 1 and i % 2 == 1:
                y[j, i] = y[j, i, :, ::-1, ::-1]
                y[j, i, 0] *= -1
                y[j, i, 1] *= -1
    return y


def average_tiles(y, ysub, xsub, Ly, Lx):
    """
    Average the results of the network over tiles.

    Args:
        y (float): Output of cellpose network for each tile. Shape: [ntiles x nclasses x bsize x bsize]
        ysub (list): List of arrays with start and end of tiles in Y of length ntiles
        xsub (list): List of arrays with start and end of tiles in X of length ntiles
        Ly (int): Size of pre-tiled image in Y (may be larger than original image if image size is less than bsize)
        Lx (int): Size of pre-tiled image in X (may be larger than original image if image size is less than bsize)

    Returns:
        yf (float32): Network output averaged over tiles. Shape: [nclasses x Ly x Lx]
    """
    Navg = np.zeros((Ly, Lx))
    yf = np.zeros((y.shape[1], Ly, Lx), np.float32)
    # taper edges of tiles
    mask = _taper_mask(ly=y.shape[-2], lx=y.shape[-1])
    for j in range(len(ysub)):
        yf[:, ysub[j][0]:ysub[j][1], xsub[j][0]:xsub[j][1]] += y[j] * mask
        Navg[ysub[j][0]:ysub[j][1], xsub[j][0]:xsub[j][1]] += mask
    yf /= Navg
    return yf


def make_tiles(imgi, bsize=224, augment=False, tile_overlap=0.1):
    """Make tiles of image to run at test-time.

    Args:
        imgi (np.ndarray): Array of shape (nchan, Ly, Lx) representing the input image.
        bsize (int, optional): Size of tiles. Defaults to 224.
        augment (bool, optional): Whether to flip tiles and set tile_overlap=2. Defaults to False.
        tile_overlap (float, optional): Fraction of overlap of tiles. Defaults to 0.1.

    Returns:
        A tuple containing (IMG, ysub, xsub, Ly, Lx):
        IMG (np.ndarray): Array of shape (ntiles, nchan, bsize, bsize) representing the tiles.
        ysub (list): List of arrays with start and end of tiles in Y of length ntiles.
        xsub (list): List of arrays with start and end of tiles in X of length ntiles.
        Ly (int): Height of the input image.
        Lx (int): Width of the input image.
    """
    nchan, Ly, Lx = imgi.shape
    if augment:
        bsize = np.int32(bsize)
        # pad if image smaller than bsize
        if Ly < bsize:
            imgi = np.concatenate((imgi, np.zeros((nchan, bsize - Ly, Lx))), axis=1)
            Ly = bsize
        if Lx < bsize:
            imgi = np.concatenate((imgi, np.zeros((nchan, Ly, bsize - Lx))), axis=2)
        Ly, Lx = imgi.shape[-2:]
        
        # tiles overlap by half of tile size
        ny = max(2, int(np.ceil(2. * Ly / bsize)))
        nx = max(2, int(np.ceil(2. * Lx / bsize)))
        ystart = np.linspace(0, Ly - bsize, ny).astype(int)
        xstart = np.linspace(0, Lx - bsize, nx).astype(int)

        ysub = []
        xsub = []

        # flip tiles so that overlapping segments are processed in rotation
        IMG = np.zeros((len(ystart), len(xstart), nchan, bsize, bsize), np.float32)
        for j in range(len(ystart)):
            for i in range(len(xstart)):
                ysub.append([ystart[j], ystart[j] + bsize])
                xsub.append([xstart[i], xstart[i] + bsize])
                IMG[j, i] = imgi[:, ysub[-1][0]:ysub[-1][1], xsub[-1][0]:xsub[-1][1]]
                # flip tiles to allow for augmentation of overlapping segments
                if j % 2 == 0 and i % 2 == 1:
                    IMG[j, i] = IMG[j, i, :, ::-1, :]
                elif j % 2 == 1 and i % 2 == 0:
                    IMG[j, i] = IMG[j, i, :, :, ::-1]
                elif j % 2 == 1 and i % 2 == 1:
                    IMG[j, i] = IMG[j, i, :, ::-1, ::-1]
    else:
        tile_overlap = min(0.5, max(0.05, tile_overlap))
        bsizeY, bsizeX = min(bsize, Ly), min(bsize, Lx)
        bsizeY = np.int32(bsizeY)
        bsizeX = np.int32(bsizeX)
        # tiles overlap by 10% tile size
        ny = 1 if Ly <= bsize else int(np.ceil((1. + 2 * tile_overlap) * Ly / bsize))
        nx = 1 if Lx <= bsize else int(np.ceil((1. + 2 * tile_overlap) * Lx / bsize))
        ystart = np.linspace(0, Ly - bsizeY, ny).astype(int)
        xstart = np.linspace(0, Lx - bsizeX, nx).astype(int)

        ysub = []
        xsub = []
        IMG = np.zeros((len(ystart), len(xstart), nchan, bsizeY, bsizeX), np.float32)
        for j in range(len(ystart)):
            for i in range(len(xstart)):
                ysub.append([ystart[j], ystart[j] + bsizeY])
                xsub.append([xstart[i], xstart[i] + bsizeX])
                IMG[j, i] = imgi[:, ysub[-1][0]:ysub[-1][1], xsub[-1][0]:xsub[-1][1]]

    return IMG, ysub, xsub, Ly, Lx


def normalize99(Y, lower=1, upper=99, copy=True, downsample=False):
    """
    Normalize the image so that 0.0 corresponds to the 1st percentile and 1.0 corresponds to the 99th percentile.

    Args:
        Y (ndarray): The input image (for downsample, use [Ly x Lx] or [Lz x Ly x Lx]).
        lower (int, optional): The lower percentile. Defaults to 1.
        upper (int, optional): The upper percentile. Defaults to 99.
        copy (bool, optional): Whether to create a copy of the input image. Defaults to True.
        downsample (bool, optional): Whether to downsample image to compute percentiles. Defaults to False.

    Returns:
        ndarray: The normalized image.
    """
    X = Y.copy() if copy else Y
    X = X.astype("float32") if X.dtype!="float64" and X.dtype!="float32" else X
    if downsample and X.size > 224**3:
        nskip = [max(1, X.shape[i] // 224) for i in range(X.ndim)]
        nskip[0] = max(1, X.shape[0] // 50) if X.ndim == 3 else nskip[0]
        slc = tuple([slice(0, X.shape[i], nskip[i]) for i in range(X.ndim)])
        x01 = np.percentile(X[slc], lower)
        x99 = np.percentile(X[slc], upper)
    else:
        x01 = np.percentile(X, lower)
        x99 = np.percentile(X, upper)
    if x99 - x01 > 1e-3:
        X -= x01 
        X /= (x99 - x01)
    else:
        X[:] = 0
    return X


def normalize99_tile(img, blocksize=100, lower=1., upper=99., tile_overlap=0.1,
                     norm3D=False, smooth3D=1, is3D=False):
    """Compute normalization like normalize99 function but in tiles.

    Args:
        img (numpy.ndarray): Array of shape (Lz x) Ly x Lx (x nchan) containing the image.
        blocksize (float, optional): Size of tiles. Defaults to 100.
        lower (float, optional): Lower percentile for normalization. Defaults to 1.0.
        upper (float, optional): Upper percentile for normalization. Defaults to 99.0.
        tile_overlap (float, optional): Fraction of overlap of tiles. Defaults to 0.1.
        norm3D (bool, optional): Use same tiled normalization for each z-plane. Defaults to False.
        smooth3D (int, optional): Smoothing factor for 3D normalization. Defaults to 1.
        is3D (bool, optional): Set to True if image is a 3D stack. Defaults to False.

    Returns:
        numpy.ndarray: Normalized image array of shape (Lz x) Ly x Lx (x nchan).
    """
    is1c = True if img.ndim == 2 or (is3D and img.ndim == 3) else False
    is3D = True if img.ndim > 3 or (is3D and img.ndim == 3) else False
    img = img[..., np.newaxis] if is1c else img
    img = img[np.newaxis, ...] if img.ndim == 3 else img
    Lz, Ly, Lx, nchan = img.shape

    tile_overlap = min(0.5, max(0.05, tile_overlap))
    blocksizeY, blocksizeX = min(blocksize, Ly), min(blocksize, Lx)
    blocksizeY = np.int32(blocksizeY)
    blocksizeX = np.int32(blocksizeX)
    # tiles overlap by 10% tile size
    ny = 1 if Ly <= blocksize else int(np.ceil(
        (1. + 2 * tile_overlap) * Ly / blocksize))
    nx = 1 if Lx <= blocksize else int(np.ceil(
        (1. + 2 * tile_overlap) * Lx / blocksize))
    ystart = np.linspace(0, Ly - blocksizeY, ny).astype(int)
    xstart = np.linspace(0, Lx - blocksizeX, nx).astype(int)
    ysub = []
    xsub = []
    for j in range(len(ystart)):
        for i in range(len(xstart)):
            ysub.append([ystart[j], ystart[j] + blocksizeY])
            xsub.append([xstart[i], xstart[i] + blocksizeX])

    x01_tiles_z = []
    x99_tiles_z = []
    for z in range(Lz):
        IMG = np.zeros((len(ystart), len(xstart), blocksizeY, blocksizeX, nchan),
                       "float32")
        k = 0
        for j in range(len(ystart)):
            for i in range(len(xstart)):
                IMG[j, i] = img[z, ysub[k][0]:ysub[k][1], xsub[k][0]:xsub[k][1], :]
                k += 1
        x01_tiles = np.percentile(IMG, lower, axis=(-3, -2))
        x99_tiles = np.percentile(IMG, upper, axis=(-3, -2))

        # fill areas with small differences with neighboring squares
        to_fill = np.zeros(x01_tiles.shape[:2], "bool")
        for c in range(nchan):
            to_fill = x99_tiles[:, :, c] - x01_tiles[:, :, c] < +1e-3
            if to_fill.sum() > 0 and to_fill.sum() < x99_tiles[:, :, c].size:
                fill_vals = np.nonzero(to_fill)
                fill_neigh = np.nonzero(~to_fill)
                nearest_neigh = (
                    (fill_vals[0] - fill_neigh[0][:, np.newaxis])**2 +
                    (fill_vals[1] - fill_neigh[1][:, np.newaxis])**2).argmin(axis=0)
                x01_tiles[fill_vals[0], fill_vals[1],
                          c] = x01_tiles[fill_neigh[0][nearest_neigh],
                                         fill_neigh[1][nearest_neigh], c]
                x99_tiles[fill_vals[0], fill_vals[1],
                          c] = x99_tiles[fill_neigh[0][nearest_neigh],
                                         fill_neigh[1][nearest_neigh], c]
            elif to_fill.sum() > 0 and to_fill.sum() == x99_tiles[:, :, c].size:
                x01_tiles[:, :, c] = 0
                x99_tiles[:, :, c] = 1
        x01_tiles_z.append(x01_tiles)
        x99_tiles_z.append(x99_tiles)

    x01_tiles_z = np.array(x01_tiles_z)
    x99_tiles_z = np.array(x99_tiles_z)
    # do not smooth over z-axis if not normalizing separately per plane
    for a in range(2):
        x01_tiles_z = gaussian_filter1d(x01_tiles_z, 1, axis=a)
        x99_tiles_z = gaussian_filter1d(x99_tiles_z, 1, axis=a)
    if norm3D:
        smooth3D = 1 if smooth3D == 0 else smooth3D
        x01_tiles_z = gaussian_filter1d(x01_tiles_z, smooth3D, axis=a)
        x99_tiles_z = gaussian_filter1d(x99_tiles_z, smooth3D, axis=a)

    if not norm3D and Lz > 1:
        x01 = np.zeros((len(x01_tiles_z), Ly, Lx, nchan), "float32")
        x99 = np.zeros((len(x01_tiles_z), Ly, Lx, nchan), "float32")
        for z in range(Lz):
            x01_rsz = cv2.resize(x01_tiles_z[z], (Lx, Ly),
                                 interpolation=cv2.INTER_LINEAR)
            x01[z] = x01_rsz[..., np.newaxis] if nchan == 1 else x01_rsz
            x99_rsz = cv2.resize(x99_tiles_z[z], (Lx, Ly),
                                 interpolation=cv2.INTER_LINEAR)
            x99[z] = x99_rsz[..., np.newaxis] if nchan == 1 else x01_rsz
        if (x99 - x01).min() < 1e-3:
            raise ZeroDivisionError(
                "cannot use norm3D=False with tile_norm, sample is too sparse; set norm3D=True or tile_norm=0"
            )
    else:
        x01 = cv2.resize(x01_tiles_z.mean(axis=0), (Lx, Ly),
                         interpolation=cv2.INTER_LINEAR)
        x99 = cv2.resize(x99_tiles_z.mean(axis=0), (Lx, Ly),
                         interpolation=cv2.INTER_LINEAR)
        if x01.ndim < 3:
            x01 = x01[..., np.newaxis]
            x99 = x99[..., np.newaxis]

    if is1c:
        img, x01, x99 = img.squeeze(), x01.squeeze(), x99.squeeze()
    elif not is3D:
        img, x01, x99 = img[0], x01[0], x99[0]

    # normalize
    img -= x01 
    img /= (x99 - x01)

    return img


def gaussian_kernel(sigma, Ly, Lx, device=torch.device("cpu")):
    """
    Generates a 2D Gaussian kernel.

    Args:
        sigma (float): Standard deviation of the Gaussian distribution.
        Ly (int): Number of pixels in the y-axis.
        Lx (int): Number of pixels in the x-axis.
        device (torch.device, optional): Device to store the kernel tensor. Defaults to torch.device("cpu").

    Returns:
        torch.Tensor: 2D Gaussian kernel tensor.

    """
    y = torch.linspace(-Ly / 2, Ly / 2 + 1, Ly, device=device)
    x = torch.linspace(-Ly / 2, Ly / 2 + 1, Lx, device=device)
    y, x = torch.meshgrid(y, x, indexing="ij")
    kernel = torch.exp(-(y**2 + x**2) / (2 * sigma**2))
    kernel /= kernel.sum()
    return kernel


def smooth_sharpen_img(img, smooth_radius=6, sharpen_radius=12,
                       device=torch.device("cpu"), is3D=False):
    """Sharpen blurry images with surround subtraction and/or smooth noisy images.

    Args:
        img (float32): Array that's (Lz x) Ly x Lx (x nchan).
        smooth_radius (float, optional): Size of gaussian smoothing filter, recommended to be 1/10-1/4 of cell diameter
            (if also sharpening, should be 2-3x smaller than sharpen_radius). Defaults to 6.
        sharpen_radius (float, optional): Size of gaussian surround filter, recommended to be 1/8-1/2 of cell diameter
            (if also smoothing, should be 2-3x larger than smooth_radius). Defaults to 12.
        device (torch.device, optional): Device on which to perform sharpening.
            Will be faster on GPU but need to ensure GPU has RAM for image. Defaults to torch.device("cpu").
        is3D (bool, optional): If image is 3D stack (only necessary to set if img.ndim==3). Defaults to False.

    Returns:
        img_sharpen (float32): Array that's (Lz x) Ly x Lx (x nchan).
    """
    img_sharpen = torch.from_numpy(img.astype("float32")).to(device)
    shape = img_sharpen.shape

    is1c = True if img_sharpen.ndim == 2 or (is3D and img_sharpen.ndim == 3) else False
    is3D = True if img_sharpen.ndim > 3 or (is3D and img_sharpen.ndim == 3) else False
    img_sharpen = img_sharpen.unsqueeze(-1) if is1c else img_sharpen
    img_sharpen = img_sharpen.unsqueeze(0) if img_sharpen.ndim == 3 else img_sharpen
    Lz, Ly, Lx, nchan = img_sharpen.shape

    if smooth_radius > 0:
        kernel = gaussian_kernel(smooth_radius, Ly, Lx, device=device)
        if sharpen_radius > 0:
            kernel += -1 * gaussian_kernel(sharpen_radius, Ly, Lx, device=device)
    elif sharpen_radius > 0:
        kernel = -1 * gaussian_kernel(sharpen_radius, Ly, Lx, device=device)
        kernel[Ly // 2, Lx // 2] = 1

    fhp = fft2(kernel)
    for z in range(Lz):
        for c in range(nchan):
            img_filt = torch.real(ifft2(
                fft2(img_sharpen[z, :, :, c]) * torch.conj(fhp)))
            img_filt = fftshift(img_filt)
            img_sharpen[z, :, :, c] = img_filt

    img_sharpen = img_sharpen.reshape(shape)
    return img_sharpen.cpu().numpy()


def move_axis(img, m_axis=-1, first=True):
    """ move axis m_axis to first or last position """
    if m_axis == -1:
        m_axis = img.ndim - 1
    m_axis = min(img.ndim - 1, m_axis)
    axes = np.arange(0, img.ndim)
    if first:
        axes[1:m_axis + 1] = axes[:m_axis]
        axes[0] = m_axis
    else:
        axes[m_axis:-1] = axes[m_axis + 1:]
        axes[-1] = m_axis
    img = img.transpose(tuple(axes))
    return img


def move_min_dim(img, force=False):
    """Move the minimum dimension last as channels if it is less than 10 or force is True.

    Args:
        img (ndarray): The input image.
        force (bool, optional): If True, the minimum dimension will always be moved.
            Defaults to False.

    Returns:
        ndarray: The image with the minimum dimension moved to the last axis as channels.
    """
    if len(img.shape) > 2:
        min_dim = min(img.shape)
        if min_dim < 10 or force:
            if img.shape[-1] == min_dim:
                channel_axis = -1
            else:
                channel_axis = (img.shape).index(min_dim)
            img = move_axis(img, m_axis=channel_axis, first=False)
    return img


def update_axis(m_axis, to_squeeze, ndim):
    """
    Squeeze the axis value based on the given parameters.

    Args:
        m_axis (int): The current axis value.
        to_squeeze (numpy.ndarray): An array of indices to squeeze.
        ndim (int): The number of dimensions.

    Returns:
        int or None: The updated axis value.
    """
    if m_axis == -1:
        m_axis = ndim - 1
    if (to_squeeze == m_axis).sum() == 1:
        m_axis = None
    else:
        inds = np.ones(ndim, bool)
        inds[to_squeeze] = False
        m_axis = np.nonzero(np.arange(0, ndim)[inds] == m_axis)[0]
        if len(m_axis) > 0:
            m_axis = m_axis[0]
        else:
            m_axis = None
    return m_axis


def convert_image(x, channels, channel_axis=None, z_axis=None, do_3D=False, nchan=2):
    """Converts the image to have the z-axis first, channels last.

    Args:
        x (numpy.ndarray or torch.Tensor): The input image.
        channels (list or None): The list of channels to use (ones-based, 0=gray). If None, all channels are kept.
        channel_axis (int or None): The axis of the channels in the input image. If None, the axis is determined automatically.
        z_axis (int or None): The axis of the z-dimension in the input image. If None, the axis is determined automatically.
        do_3D (bool): Whether to process the image in 3D mode. Defaults to False.
        nchan (int): The number of channels to keep if the input image has more than nchan channels.

    Returns:
        numpy.ndarray: The converted image.

    Raises:
        ValueError: If the input image has less than two channels and channels are not specified.
        ValueError: If the input image is 2D and do_3D is True.
        ValueError: If the input image is 4D and do_3D is False.
    """
    # check if image is a torch array instead of numpy array
    # converts torch to numpy
    ndim = x.ndim
    if torch.is_tensor(x):
        transforms_logger.warning("torch array used as input, converting to numpy")
        x = x.cpu().numpy()

    # squeeze image, and if channel_axis or z_axis given, transpose image
    if x.ndim > 3:
        to_squeeze = np.array([int(isq) for isq, s in enumerate(x.shape) if s == 1])
        # remove channel axis if number of channels is 1
        if len(to_squeeze) > 0:
            channel_axis = update_axis(
                channel_axis, to_squeeze,
                x.ndim) if channel_axis is not None else None
            z_axis = update_axis(z_axis, to_squeeze,
                                 x.ndim) if z_axis is not None else None
            x = x.squeeze()

    # put z axis first
    if z_axis is not None and x.ndim > 2 and z_axis != 0:
        x = move_axis(x, m_axis=z_axis, first=True)
        if channel_axis is not None:
            channel_axis += 1
        z_axis = 0
    elif z_axis is None and x.ndim > 2 and channels is not None and min(x.shape) > 5 :
        # if there are > 5 channels and channels!=None, assume first dimension is z
        min_dim = min(x.shape)
        if min_dim != channel_axis:
            z_axis = (x.shape).index(min_dim)
            if z_axis != 0:
                x = move_axis(x, m_axis=z_axis, first=True)
                if channel_axis is not None:
                    channel_axis += 1
            transforms_logger.warning(f"z_axis not specified, assuming it is dim {z_axis}")
            transforms_logger.warning(f"if this is actually the channel_axis, use 'model.eval(channel_axis={z_axis}, ...)'")
            z_axis = 0

    if z_axis is not None:
        if x.ndim == 3:
            x = x[..., np.newaxis]

    # put channel axis last
    if channel_axis is not None and x.ndim > 2:
        x = move_axis(x, m_axis=channel_axis, first=False)
    elif x.ndim == 2:
        x = x[:, :, np.newaxis]

    if do_3D:
        if ndim < 3:
            transforms_logger.critical("ERROR: cannot process 2D images in 3D mode")
            raise ValueError("ERROR: cannot process 2D images in 3D mode")
        elif x.ndim < 4:
            x = x[..., np.newaxis]

    if channel_axis is None:
        x = move_min_dim(x)

    if x.ndim > 3:
        transforms_logger.info(
            "multi-stack tiff read in as having %d planes %d channels" %
            (x.shape[0], x.shape[-1]))

    # convert to float32
    x = x.astype("float32")

    if channels is not None:
        channels = channels[0] if len(channels) == 1 else channels
        if len(channels) < 2:
            transforms_logger.critical("ERROR: two channels not specified")
            raise ValueError("ERROR: two channels not specified")
        x = reshape(x, channels=channels)

    else:
        # code above put channels last
        if nchan is not None and x.shape[-1] > nchan:
            transforms_logger.warning(
                "WARNING: more than %d channels given, use 'channels' input for specifying channels - just using first %d channels to run processing"
                % (nchan, nchan))
            x = x[..., :nchan]

        # if not do_3D and x.ndim > 3:
        #    transforms_logger.critical("ERROR: cannot process 4D images in 2D mode")
        #    raise ValueError("ERROR: cannot process 4D images in 2D mode")

        if nchan is not None and x.shape[-1] < nchan:
            x = np.concatenate((x, np.tile(np.zeros_like(x), (1, 1, nchan - 1))),
                               axis=-1)

    return x


def reshape(data, channels=[0, 0], chan_first=False):
    """Reshape data using channels.

    Args:
        data (numpy.ndarray): The input data. It should have shape (Z x ) Ly x Lx x nchan
            if data.ndim==3 and data.shape[0]<8, it is assumed to be nchan x Ly x Lx.
        channels (list of int, optional): The channels to use for reshaping. The first element
            of the list is the channel to segment (0=grayscale, 1=red, 2=green, 3=blue). The
            second element of the list is the optional nuclear channel (0=none, 1=red, 2=green, 3=blue).
            For instance, to train on grayscale images, input [0,0]. To train on images with cells
            in green and nuclei in blue, input [2,3]. Defaults to [0, 0].
        chan_first (bool, optional): Whether to return the reshaped data with channel as the first
            dimension. Defaults to False.

    Returns:
        numpy.ndarray: The reshaped data with shape (Z x ) Ly x Lx x nchan (if chan_first==False).
    """
    if data.ndim < 3:
        data = data[:, :, np.newaxis]
    elif data.shape[0] < 8 and data.ndim == 3:
        data = np.transpose(data, (1, 2, 0))

    # use grayscale image
    if data.shape[-1] == 1:
        data = np.concatenate((data, np.zeros(data.shape, "float32")), axis=-1)
    else:
        if channels[0] == 0:
            data = data.mean(axis=-1, keepdims=True)
            data = np.concatenate((data, np.zeros(data.shape, "float32")), axis=-1)
        else:
            chanid = [channels[0] - 1]
            if channels[1] > 0:
                chanid.append(channels[1] - 1)
            data = data[..., chanid]
            for i in range(data.shape[-1]):
                if np.ptp(data[..., i]) == 0.0:
                    if i == 0:
                        warnings.warn("'chan to seg' to seg has value range of ZERO")
                    else:
                        warnings.warn(
                            "'chan2 (opt)' has value range of ZERO, can instead set chan2 to 0"
                        )
            if data.shape[-1] == 1:
                data = np.concatenate((data, np.zeros(data.shape, "float32")), axis=-1)
    if chan_first:
        if data.ndim == 4:
            data = np.transpose(data, (3, 0, 1, 2))
        else:
            data = np.transpose(data, (2, 0, 1))
    return data


def normalize_img(img, normalize=True, norm3D=True, invert=False, lowhigh=None,
                  percentile=(1., 99.), sharpen_radius=0, smooth_radius=0,
                  tile_norm_blocksize=0, tile_norm_smooth3D=1, axis=-1):
    """Normalize each channel of the image with optional inversion, smoothing, and sharpening.

    Args:
        img (ndarray): The input image. It should have at least 3 dimensions.
            If it is 4-dimensional, it assumes the first non-channel axis is the Z dimension.
        normalize (bool, optional): Whether to perform normalization. Defaults to True.
        norm3D (bool, optional): Whether to normalize in 3D. If True, the entire 3D stack will
            be normalized per channel. If False, normalization is applied per Z-slice. Defaults to False.
        invert (bool, optional): Whether to invert the image. Useful if cells are dark instead of bright.
            Defaults to False.
        lowhigh (tuple or ndarray, optional): The lower and upper bounds for normalization.
            Can be a tuple of two values (applied to all channels) or an array of shape (nchan, 2)
            for per-channel normalization. Incompatible with smoothing and sharpening.
            Defaults to None.
        percentile (tuple, optional): The lower and upper percentiles for normalization. If provided, it should be
            a tuple of two values. Each value should be between 0 and 100. Defaults to (1.0, 99.0).
        sharpen_radius (int, optional): The radius for sharpening the image. Defaults to 0.
        smooth_radius (int, optional): The radius for smoothing the image. Defaults to 0.
        tile_norm_blocksize (int, optional): The block size for tile-based normalization. Defaults to 0.
        tile_norm_smooth3D (int, optional): The smoothness factor for tile-based normalization in 3D. Defaults to 1.
        axis (int, optional): The channel axis to loop over for normalization. Defaults to -1.

    Returns:
        ndarray: The normalized image of the same size.

    Raises:
        ValueError: If the image has less than 3 dimensions.
        ValueError: If the provided lowhigh or percentile values are invalid.
        ValueError: If the image is inverted without normalization.

    """
    if img.ndim < 3:
        error_message = "Image needs to have at least 3 dimensions"
        transforms_logger.critical(error_message)
        raise ValueError(error_message)

    img_norm = img if img.dtype=="float32" else img.astype(np.float32)
    if axis != -1 and axis != img_norm.ndim - 1:
        img_norm = np.moveaxis(img_norm, axis, -1)  # Move channel axis to last

    nchan = img_norm.shape[-1]

    # Validate and handle lowhigh bounds
    if lowhigh is not None:
        lowhigh = np.array(lowhigh)
        if lowhigh.shape == (2,):
            lowhigh = np.tile(lowhigh, (nchan, 1))  # Expand to per-channel bounds
        elif lowhigh.shape != (nchan, 2):
            error_message = "`lowhigh` must have shape (2,) or (nchan, 2)"
            transforms_logger.critical(error_message)
            raise ValueError(error_message)

    # Validate percentile
    if percentile is None:
        percentile = (1.0, 99.0)
    elif not (0 <= percentile[0] < percentile[1] <= 100):
        error_message = "Invalid percentile range, should be between 0 and 100"
        transforms_logger.critical(error_message)
        raise ValueError(error_message)

    # Apply normalization based on lowhigh or percentile
    cgood = np.zeros(nchan, "bool")
    if lowhigh is not None:
        for c in range(nchan):
            lower = lowhigh[c, 0]
            upper = lowhigh[c, 1]
            img_norm[..., c] -= lower 
            img_norm[..., c] /= (upper - lower)
            cgood[c] = True
    else:
        # Apply sharpening and smoothing if specified
        if sharpen_radius > 0 or smooth_radius > 0:
            img_norm = smooth_sharpen_img(
                img_norm, sharpen_radius=sharpen_radius, smooth_radius=smooth_radius
            )

        # Apply tile-based normalization or standard normalization
        if tile_norm_blocksize > 0:
            img_norm = normalize99_tile(
                img_norm,
                blocksize=tile_norm_blocksize,
                lower=percentile[0],
                upper=percentile[1],
                smooth3D=tile_norm_smooth3D,
                norm3D=norm3D,
            )
        elif normalize:
            if img_norm.ndim == 3 or norm3D:  # i.e. if YXC, or ZYXC with norm3D=True
                for c in range(nchan):
                    if np.ptp(img_norm[..., c]) > 0.:
                        img_norm[..., c] = normalize99(
                            img_norm[..., c],
                            lower=percentile[0],
                            upper=percentile[1],
                            copy=False, downsample=True,
                        )
                        cgood[c] = True
            else:  # i.e. if ZYXC with norm3D=False then per Z-slice
                for z in range(img_norm.shape[0]):
                    for c in range(nchan):
                        if np.ptp(img_norm[z, ..., c]) > 0.:
                            img_norm[z, ..., c] = normalize99(
                                img_norm[z, ..., c],
                                lower=percentile[0],
                                upper=percentile[1],
                                copy=False, downsample=True,
                            )
                            cgood[c] = True


    if invert:
        if lowhigh is not None or tile_norm_blocksize > 0 or normalize:
            for c in range(nchan):
                if cgood[c]:
                    img_norm[..., c] = 1 - img_norm[..., c]
        else:
            error_message = "Cannot invert image without normalization"
            transforms_logger.critical(error_message)
            raise ValueError(error_message)

    # Move channel axis back to the original position
    if axis != -1 and axis != img_norm.ndim - 1:
        img_norm = np.moveaxis(img_norm, -1, axis)

    return img_norm

def resize_safe(img, Ly, Lx, interpolation=cv2.INTER_LINEAR):
    """OpenCV resize function does not support uint32.

    This function converts the image to float32 before resizing and then converts it back to uint32. Not safe!
    References issue: https://github.com/MouseLand/cellpose/issues/937

    Implications:
    * Runtime: Runtime increases by 5x-50x due to type casting. However, with resizing being very efficient, this is not
    a big issue. A 10,000x10,000 image takes 0.47s instead of 0.016s to cast and resize on 32 cores on GPU.
    * Memory: However, memory usage increases. Not tested by how much.

    Args:
        img (ndarray): Image of size [Ly x Lx].
        Ly (int): Desired height of the resized image.
        Lx (int): Desired width of the resized image.
        interpolation (int, optional): OpenCV interpolation method. Defaults to cv2.INTER_LINEAR.

    Returns:
        ndarray: Resized image of size [Ly x Lx].

    """

    # cast image
    cast = img.dtype == np.uint32
    if cast:
        img = img.astype(np.float32)

    # resize
    img = cv2.resize(img, (Lx, Ly), interpolation=interpolation)

    # cast back
    if cast:
        img = img.round().astype(np.uint32)

    return img


def resize_image(img0, Ly=None, Lx=None, rsz=None, interpolation=cv2.INTER_LINEAR,
                 no_channels=False):
    """Resize image for computing flows / unresize for computing dynamics.

    Args:
        img0 (ndarray): Image of size [Y x X x nchan] or [Lz x Y x X x nchan] or [Lz x Y x X].
        Ly (int, optional): Desired height of the resized image. Defaults to None.
        Lx (int, optional): Desired width of the resized image. Defaults to None.
        rsz (float, optional): Resize coefficient(s) for the image. If Ly is None, rsz is used. Defaults to None.
        interpolation (int, optional): OpenCV interpolation method. Defaults to cv2.INTER_LINEAR.
        no_channels (bool, optional): Flag indicating whether to treat the third dimension as a channel.
            Defaults to False.

    Returns:
        ndarray: Resized image of size [Ly x Lx x nchan] or [Lz x Ly x Lx x nchan].

    Raises:
        ValueError: If Ly is None and rsz is None.

    """
    if Ly is None and rsz is None:
        error_message = "must give size to resize to or factor to use for resizing"
        transforms_logger.critical(error_message)
        raise ValueError(error_message)

    if Ly is None:
        # determine Ly and Lx using rsz
        if not isinstance(rsz, list) and not isinstance(rsz, np.ndarray):
            rsz = [rsz, rsz]
        if no_channels:
            Ly = int(img0.shape[-2] * rsz[-2])
            Lx = int(img0.shape[-1] * rsz[-1])
        else:
            Ly = int(img0.shape[-3] * rsz[-2])
            Lx = int(img0.shape[-2] * rsz[-1])

    # no_channels useful for z-stacks, so the third dimension is not treated as a channel
    # but if this is called for grayscale images, they first become [Ly,Lx,2] so ndim=3 but
    if (img0.ndim > 2 and no_channels) or (img0.ndim == 4 and not no_channels):
        if Ly == 0 or Lx == 0:
            raise ValueError(
                "anisotropy too high / low -- not enough pixels to resize to ratio")
        for i, img in enumerate(img0):
            imgi = resize_safe(img, Ly, Lx, interpolation=interpolation)
            if i==0:
                if no_channels:
                    imgs = np.zeros((img0.shape[0], Ly, Lx), imgi.dtype)
                else:
                    imgs = np.zeros((img0.shape[0], Ly, Lx, img0.shape[-1]), imgi.dtype)
            imgs[i] = imgi if imgi.ndim > 2 or no_channels else imgi[..., np.newaxis]
    else:
        imgs = resize_safe(img0, Ly, Lx, interpolation=interpolation)
    return imgs

def get_pad_yx(Ly, Lx, div=16, extra=1, min_size=None):
    if min_size is None or Ly >= min_size[-2]:
        Lpad = int(div * np.ceil(Ly / div) - Ly)
    else:
        Lpad = min_size[-2] - Ly
    ypad1 = extra * div // 2 + Lpad // 2
    ypad2 = extra * div // 2 + Lpad - Lpad // 2
    if min_size is None or Lx >= min_size[-1]:
        Lpad = int(div * np.ceil(Lx / div) - Lx)
    else:
        Lpad = min_size[-1] - Lx
    xpad1 = extra * div // 2 + Lpad // 2
    xpad2 = extra * div // 2 + Lpad - Lpad // 2

    return ypad1, ypad2, xpad1, xpad2


def pad_image_ND(img0, div=16, extra=1, min_size=None, zpad=False):
    """Pad image for test-time so that its dimensions are a multiple of 16 (2D or 3D).

    Args:
        img0 (ndarray): Image of size [nchan (x Lz) x Ly x Lx].
        div (int, optional): Divisor for padding. Defaults to 16.
        extra (int, optional): Extra padding. Defaults to 1.
        min_size (tuple, optional): Minimum size of the image. Defaults to None.

    Returns:
        A tuple containing (I, ysub, xsub) or (I, ysub, xsub, zsub), I is padded image, -sub are ranges of pixels in the padded image corresponding to img0.
            
    """
    Ly, Lx = img0.shape[-2:]
    ypad1, ypad2, xpad1, xpad2 = get_pad_yx(Ly, Lx, div=div, extra=extra, min_size=min_size)

    if img0.ndim > 3:
        if zpad:
            Lpad = int(div * np.ceil(img0.shape[-3] / div) - img0.shape[-3])
            zpad1 = extra * div // 2 + Lpad // 2
            zpad2 = extra * div // 2 + Lpad - Lpad // 2
        else:
            zpad1, zpad2 = 0, 0
        pads = np.array([[0, 0], [zpad1, zpad2], [ypad1, ypad2], [xpad1, xpad2]])
    else:
        pads = np.array([[0, 0], [ypad1, ypad2], [xpad1, xpad2]])

    I = np.pad(img0, pads, mode="constant")

    ysub = np.arange(ypad1, ypad1 + Ly)
    xsub = np.arange(xpad1, xpad1 + Lx)
    if zpad:
        zsub = np.arange(zpad1, zpad1 + img0.shape[-3])
        return I, ysub, xsub, zsub
    else:
        return I, ysub, xsub


def random_rotate_and_resize(X, Y=None, scale_range=1., xy=(224, 224), do_3D=False,
                             zcrop=48, do_flip=True, rotate=True, rescale=None, unet=False,
                             random_per_image=True):
    """Augmentation by random rotation and resizing.

    Args:
        X (list of ND-arrays, float): List of image arrays of size [nchan x Ly x Lx] or [Ly x Lx].
        Y (list of ND-arrays, float, optional): List of image labels of size [nlabels x Ly x Lx] or [Ly x Lx].
            The 1st channel of Y is always nearest-neighbor interpolated (assumed to be masks or 0-1 representation).
            If Y.shape[0]==3 and not unet, then the labels are assumed to be [cell probability, Y flow, X flow].
            If unet, second channel is dist_to_bound. Defaults to None.
        scale_range (float, optional): Range of resizing of images for augmentation.
            Images are resized by (1-scale_range/2) + scale_range * np.random.rand(). Defaults to 1.0.
        xy (tuple, int, optional): Size of transformed images to return. Defaults to (224,224).
        do_flip (bool, optional): Whether or not to flip images horizontally. Defaults to True.
        rotate (bool, optional): Whether or not to rotate images. Defaults to True.
        rescale (array, float, optional): How much to resize images by before performing augmentations. Defaults to None.
        unet (bool, optional): Whether or not to use unet. Defaults to False.
        random_per_image (bool, optional): Different random rotate and resize per image. Defaults to True.

    Returns:
        A tuple containing (imgi, lbl, scale): imgi (ND-array, float): Transformed images in array [nimg x nchan x xy[0] x xy[1]]; 
        lbl (ND-array, float): Transformed labels in array [nimg x nchan x xy[0] x xy[1]]; 
        scale (array, float): Amount each image was resized by.
    """
    scale_range = max(0, min(2, float(scale_range)))
    nimg = len(X)
    if X[0].ndim > 2:
        nchan = X[0].shape[0]
    else:
        nchan = 1
    if do_3D and X[0].ndim > 3:
        shape = (zcrop, xy[0], xy[1])
    else:
        shape = (xy[0], xy[1])
    imgi = np.zeros((nimg, nchan, *shape), "float32")

    lbl = []
    if Y is not None:
        if Y[0].ndim > 2:
            nt = Y[0].shape[0]
        else:
            nt = 1
        lbl = np.zeros((nimg, nt, *shape), np.float32)

    scale = np.ones(nimg, np.float32)

    for n in range(nimg):

        if random_per_image or n == 0:
            Ly, Lx = X[n].shape[-2:]
            # generate random augmentation parameters
            flip = np.random.rand() > .5
            theta = np.random.rand() * np.pi * 2 if rotate else 0.
            scale[n] =  (1 - scale_range / 2) + scale_range * np.random.rand()
            if rescale is not None:
                scale[n] *= 1. / rescale[n]
            dxy = np.maximum(0, np.array([Lx * scale[n] - xy[1],
                                          Ly * scale[n] - xy[0]]))
            dxy = (np.random.rand(2,) - .5) * dxy

            # create affine transform
            cc = np.array([Lx / 2, Ly / 2])
            cc1 = cc - np.array([Lx - xy[1], Ly - xy[0]]) / 2 + dxy
            pts1 = np.float32([cc, cc + np.array([1, 0]), cc + np.array([0, 1])])
            pts2 = np.float32([
                cc1,
                cc1 + scale[n] * np.array([np.cos(theta), np.sin(theta)]),
                cc1 + scale[n] *
                np.array([np.cos(np.pi / 2 + theta),
                          np.sin(np.pi / 2 + theta)])
            ])
            M = cv2.getAffineTransform(pts1, pts2)

        img = X[n].copy()
        if Y is not None:
            labels = Y[n].copy()
            if labels.ndim < 3:
                labels = labels[np.newaxis, :, :]

        if do_3D:
            Lz = X[n].shape[-3]
            flip_z = np.random.rand() > .5
            lz = int(np.round(zcrop / scale[n]))
            iz = np.random.randint(0, Lz - lz)
            img = img[:,iz:iz + lz,:,:]
            if Y is not None:
                labels = labels[:,iz:iz + lz,:,:]
        
        if do_flip:
            if flip:
                img = img[..., ::-1]
                if Y is not None:
                    labels = labels[..., ::-1]
                    if nt > 1 and not unet:
                        labels[-1] = -labels[-1]
            if do_3D and flip_z:
                img = img[:, ::-1]
                if Y is not None:
                    labels = labels[:,::-1]
                    if nt > 1 and not unet:
                        labels[-3] = -labels[-3]

        for k in range(nchan):
            if do_3D:
                img0 = np.zeros((lz, xy[0], xy[1]), "float32")
                for z in range(lz):
                    I = cv2.warpAffine(img[k, z], M, (xy[1], xy[0]),
                                       flags=cv2.INTER_LINEAR)
                    img0[z] = I
                if scale[n] != 1.0:
                    for y in range(imgi.shape[-2]):
                        imgi[n, k, :, y] = cv2.resize(img0[:, y], (xy[1], zcrop),
                                                      interpolation=cv2.INTER_LINEAR)
                else:
                    imgi[n, k] = img0
            else:
                I = cv2.warpAffine(img[k], M, (xy[1], xy[0]), flags=cv2.INTER_LINEAR)
                imgi[n, k] = I

        if Y is not None:
            for k in range(nt):
                flag = cv2.INTER_NEAREST if k == 0 else cv2.INTER_LINEAR
                if do_3D:
                    lbl0 = np.zeros((lz, xy[0], xy[1]), "float32")
                    for z in range(lz):
                        I = cv2.warpAffine(labels[k, z], M, (xy[1], xy[0]),
                                                      flags=flag)
                        lbl0[z] = I
                    if scale[n] != 1.0:
                        for y in range(lbl.shape[-2]):
                            lbl[n, k, :, y] = cv2.resize(lbl0[:, y], (xy[1], zcrop),
                                                          interpolation=flag)
                    else:
                        lbl[n, k] = lbl0
                else:
                    lbl[n, k] = cv2.warpAffine(labels[k], M, (xy[1], xy[0]), flags=flag)

            if nt > 1 and not unet:
                v1 = lbl[n, -1].copy()
                v2 = lbl[n, -2].copy()
                lbl[n, -2] = (-v1 * np.sin(-theta) + v2 * np.cos(-theta))
                lbl[n, -1] = (v1 * np.cos(-theta) + v2 * np.sin(-theta))

    return imgi, lbl, scale