cellpose/dynamics.py

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

import time, os
from scipy.ndimage import maximum_filter1d, find_objects, center_of_mass
import torch
import numpy as np
import tifffile
from tqdm import trange
from numba import njit, prange, float32, int32, vectorize
import cv2
import fastremap

import logging

dynamics_logger = logging.getLogger(__name__)

from . import utils, metrics, transforms

import torch
from torch import optim, nn
import torch.nn.functional as F
from . import resnet_torch

@njit("(float64[:], int32[:], int32[:], int32, int32, int32, int32)", nogil=True)
def _extend_centers(T, y, x, ymed, xmed, Lx, niter):
    """Run diffusion from the center of the mask on the mask pixels.

    Args:
        T (numpy.ndarray): Array of shape (Ly * Lx) where diffusion is run.
        y (numpy.ndarray): Array of y-coordinates of pixels inside the mask.
        x (numpy.ndarray): Array of x-coordinates of pixels inside the mask.
        ymed (int): Center of the mask in the y-coordinate.
        xmed (int): Center of the mask in the x-coordinate.
        Lx (int): Size of the x-dimension of the masks.
        niter (int): Number of iterations to run diffusion.

    Returns:
        numpy.ndarray: Array of shape (Ly * Lx) representing the amount of diffused particles at each pixel.
    """
    for t in range(niter):
        T[ymed * Lx + xmed] += 1
        T[y * Lx +
          x] = 1 / 9. * (T[y * Lx + x] + T[(y - 1) * Lx + x] + T[(y + 1) * Lx + x] +
                         T[y * Lx + x - 1] + T[y * Lx + x + 1] +
                         T[(y - 1) * Lx + x - 1] + T[(y - 1) * Lx + x + 1] +
                         T[(y + 1) * Lx + x - 1] + T[(y + 1) * Lx + x + 1])
    return T


def _extend_centers_gpu(neighbors, meds, isneighbor, shape, n_iter=200, 
                        device=torch.device("cpu")):
    """Runs diffusion on GPU to generate flows for training images or quality control.

    Args:
        neighbors (torch.Tensor): 9 x pixels in masks.
        meds (torch.Tensor): Mask centers.
        isneighbor (torch.Tensor): Valid neighbor boolean 9 x pixels.
        shape (tuple): Shape of the tensor.
        n_iter (int, optional): Number of iterations. Defaults to 200.
        device (torch.device, optional): Device to run the computation on. Defaults to torch.device("cpu").

    Returns:
        torch.Tensor: Generated flows.

    """
    if torch.prod(torch.tensor(shape)) > 4e7 or device.type == "mps":
        T = torch.zeros(shape, dtype=torch.float, device=device)
    else:
        T = torch.zeros(shape, dtype=torch.double, device=device)

    for i in range(n_iter):
        T[tuple(meds.T)] += 1
        Tneigh = T[tuple(neighbors)]
        Tneigh *= isneighbor
        T[tuple(neighbors[:, 0])] = Tneigh.mean(axis=0)
    del meds, isneighbor, Tneigh

    if T.ndim == 2:
        grads = T[neighbors[0, [2, 1, 4, 3]], neighbors[1, [2, 1, 4, 3]]]
        del neighbors
        dy = grads[0] - grads[1]
        dx = grads[2] - grads[3]
        del grads
        mu_torch = np.stack((dy.cpu().squeeze(0), dx.cpu().squeeze(0)), axis=-2)
    else:
        grads = T[tuple(neighbors[:, 1:])]
        del neighbors
        dz = grads[0] - grads[1]
        dy = grads[2] - grads[3]
        dx = grads[4] - grads[5]
        del grads
        mu_torch = np.stack(
            (dz.cpu().squeeze(0), dy.cpu().squeeze(0), dx.cpu().squeeze(0)), axis=-2)
    return mu_torch

@njit(nogil=True)
def get_centers(masks, slices):
    """
    Get the centers of the masks and their extents.

    Args:
        masks (ndarray): The labeled masks.
        slices (ndarray): The slices of the masks.

    Returns:
        A tuple containing the centers of the masks and the extents of the masks.
    """
    centers = np.zeros((len(slices), 2), "int32")
    ext = np.zeros((len(slices),), "int32")
    for p in prange(len(slices)):
        si = slices[p]
        i = si[0]
        sr, sc = si[1:3], si[3:5]
        # find center in slice around mask
        yi, xi = np.nonzero(masks[sr[0]:sr[-1], sc[0]:sc[-1]] == (i + 1))
        ymed = yi.mean()
        xmed = xi.mean()
        # center is closest point to (ymed, xmed) within mask
        imin = ((xi - xmed)**2 + (yi - ymed)**2).argmin()
        ymed = yi[imin] + sr[0]
        xmed = xi[imin] + sc[0]
        centers[p] = np.array([ymed, xmed])
        ext[p] = (sr[-1] - sr[0]) + (sc[-1] - sc[0]) + 2
    return centers, ext


def masks_to_flows_gpu(masks, device=torch.device("cpu"), niter=None):
    """Convert masks to flows using diffusion from center pixel.

    Center of masks where diffusion starts is defined by pixel closest to median within the mask.

    Args:
        masks (int, 2D or 3D array): Labelled masks. 0=NO masks; 1,2,...=mask labels.
        device (torch.device, optional): The device to run the computation on. Defaults to torch.device("cpu").
        niter (int, optional): Number of iterations for the diffusion process. Defaults to None.

    Returns:
        np.ndarray: A 4D array representing the flows for each pixel in Z, X, and Y.
       

    Returns:
        A tuple containing (mu, meds_p). mu is float 3D or 4D array of flows in (Z)XY. 
        meds_p are cell centers.
    """
    if device is None:
        device = torch.device('cuda') if torch.cuda.is_available() else torch.device('mps') if torch.backends.mps.is_available() else None

    Ly0, Lx0 = masks.shape
    Ly, Lx = Ly0 + 2, Lx0 + 2
    
    masks_padded = torch.from_numpy(masks.astype("int64")).to(device)
    masks_padded = F.pad(masks_padded, (1, 1, 1, 1))
    shape = masks_padded.shape
    
    ### get mask pixel neighbors
    y, x = torch.nonzero(masks_padded, as_tuple=True)
    y = y.int()
    x = x.int()
    neighbors = torch.zeros((2, 9, y.shape[0]), dtype=torch.long, device=device)
    yxi = [[0, -1, 1, 0, 0, -1, -1, 1, 1], [0, 0, 0, -1, 1, -1, 1, -1, 1]]
    for i in range(9):
        neighbors[0, i] = y + yxi[0][i]
        neighbors[1, i] = x + yxi[1][i]
    isneighbor = torch.ones((9, y.shape[0]), dtype=torch.bool, device=device)
    m0 = masks_padded[neighbors[0, 0], neighbors[1, 0]]
    for i in range(1, 9):
        isneighbor[i] = masks_padded[neighbors[0, i], neighbors[1, i]] == m0
    del m0, masks_padded
    
    ### get center-of-mass within cell
    slices = find_objects(masks)
    # turn slices into array
    slices = np.array([
        np.array([i, si[0].start, si[0].stop, si[1].start, si[1].stop])
        for i, si in enumerate(slices)
        if si is not None
    ])
    centers, ext = get_centers(masks, slices)
    meds_p = torch.from_numpy(centers).to(device).long()
    meds_p += 1  # for padding

    ### run diffusion
    n_iter = 2 * ext.max() if niter is None else niter
    mu = _extend_centers_gpu(neighbors, meds_p, isneighbor, shape, n_iter=n_iter,
                             device=device)
    mu = mu.astype("float64")

    # new normalization
    mu /= (1e-60 + (mu**2).sum(axis=0)**0.5)

    # put into original image
    mu0 = np.zeros((2, Ly0, Lx0))
    mu0[:, y.cpu().numpy() - 1, x.cpu().numpy() - 1] = mu

    return mu0, meds_p.cpu().numpy() - 1


def masks_to_flows_gpu_3d(masks, device=None, niter=None):
    """Convert masks to flows using diffusion from center pixel.

    Args:
        masks (int, 2D or 3D array): Labelled masks. 0=NO masks; 1,2,...=mask labels.
        device (torch.device, optional): The device to run the computation on. Defaults to None.
        niter (int, optional): Number of iterations for the diffusion process. Defaults to None.

    Returns:
        np.ndarray: A 4D array representing the flows for each pixel in Z, X, and Y.
        
    """
    if device is None:
        device = torch.device('cuda') if torch.cuda.is_available() else torch.device('mps') if torch.backends.mps.is_available() else None

    Lz0, Ly0, Lx0 = masks.shape
    Lz, Ly, Lx = Lz0 + 2, Ly0 + 2, Lx0 + 2

    masks_padded = torch.from_numpy(masks.astype("int64")).to(device)
    masks_padded = F.pad(masks_padded, (1, 1, 1, 1, 1, 1))

    # get mask pixel neighbors
    z, y, x = torch.nonzero(masks_padded).T
    neighborsZ = torch.stack((z, z + 1, z - 1, z, z, z, z))
    neighborsY = torch.stack((y, y, y, y + 1, y - 1, y, y), axis=0)
    neighborsX = torch.stack((x, x, x, x, x, x + 1, x - 1), axis=0)

    neighbors = torch.stack((neighborsZ, neighborsY, neighborsX), axis=0)

    # get mask centers
    slices = find_objects(masks)

    centers = np.zeros((masks.max(), 3), "int")
    for i, si in enumerate(slices):
        if si is not None:
            sz, sy, sx = si
            #lz, ly, lx = sr.stop - sr.start + 1, sc.stop - sc.start + 1
            zi, yi, xi = np.nonzero(masks[sz, sy, sx] == (i + 1))
            zi = zi.astype(np.int32) + 1  # add padding
            yi = yi.astype(np.int32) + 1  # add padding
            xi = xi.astype(np.int32) + 1  # add padding
            zmed = np.mean(zi)
            ymed = np.mean(yi)
            xmed = np.mean(xi)
            imin = np.argmin((zi - zmed)**2 + (xi - xmed)**2 + (yi - ymed)**2)
            zmed = zi[imin]
            ymed = yi[imin]
            xmed = xi[imin]
            centers[i, 0] = zmed + sz.start
            centers[i, 1] = ymed + sy.start
            centers[i, 2] = xmed + sx.start

    # get neighbor validator (not all neighbors are in same mask)
    neighbor_masks = masks_padded[tuple(neighbors)]
    isneighbor = neighbor_masks == neighbor_masks[0]
    ext = np.array(
        [[sz.stop - sz.start + 1, sy.stop - sy.start + 1, sx.stop - sx.start + 1]
         for sz, sy, sx in slices])
    n_iter = 6 * (ext.sum(axis=1)).max() if niter is None else niter

    # run diffusion
    shape = masks_padded.shape
    mu = _extend_centers_gpu(neighbors, centers, isneighbor, shape, n_iter=n_iter,
                             device=device)
    # normalize
    mu /= (1e-60 + (mu**2).sum(axis=0)**0.5)

    # put into original image
    mu0 = np.zeros((3, Lz0, Ly0, Lx0))
    mu0[:, z.cpu().numpy() - 1, y.cpu().numpy() - 1, x.cpu().numpy() - 1] = mu
    return mu0


def masks_to_flows_cpu(masks, niter=None, device=None):
    """Convert masks to flows using diffusion from center pixel.

    Center of masks where diffusion starts is defined to be the closest pixel to the mean of all pixels that is inside the mask.
    Result of diffusion is converted into flows by computing the gradients of the diffusion density map.

    Args:
        masks (int, 2D or 3D array): Labelled masks 0=NO masks; 1,2,...=mask labels
        niter (int, optional): Number of iterations for computing flows. Defaults to None.
    
    Returns:
        A tuple containing (mu, meds_p). mu is float 3D or 4D array of flows in (Z)XY. 
        meds_p are cell centers.
    """
    Ly, Lx = masks.shape
    mu = np.zeros((2, Ly, Lx), np.float64)

    slices = find_objects(masks)
    meds = []
    for i in prange(len(slices)):
        si = slices[i]
        if si is not None:
            sr, sc = si
            ly, lx = sr.stop - sr.start + 2, sc.stop - sc.start + 2
            ### get center-of-mass within cell
            y, x = np.nonzero(masks[sr, sc] == (i + 1))
            y = y.astype(np.int32) + 1
            x = x.astype(np.int32) + 1
            ymed = y.mean()
            xmed = x.mean()
            imin = ((x - xmed)**2 + (y - ymed)**2).argmin()
            xmed = x[imin]
            ymed = y[imin]

            n_iter = 2 * np.int32(ly + lx) if niter is None else niter
            T = np.zeros((ly) * (lx), np.float64)
            T = _extend_centers(T, y, x, ymed, xmed, np.int32(lx), np.int32(n_iter))
            dy = T[(y + 1) * lx + x] - T[(y - 1) * lx + x]
            dx = T[y * lx + x + 1] - T[y * lx + x - 1]
            mu[:, sr.start + y - 1, sc.start + x - 1] = np.stack((dy, dx))
            meds.append([ymed - 1, xmed - 1])

    # new normalization
    mu /= (1e-60 + (mu**2).sum(axis=0)**0.5)

    return mu, meds


def masks_to_flows(masks, device=torch.device("cpu"), niter=None):
    """Convert masks to flows using diffusion from center pixel.

    Center of masks where diffusion starts is defined to be the closest pixel to the mean of all pixels that is inside the mask.
    Result of diffusion is converted into flows by computing the gradients of the diffusion density map.

    Args:
        masks (int, 2D or 3D array): Labelled masks 0=NO masks; 1,2,...=mask labels

    Returns:
        np.ndarray: mu is float 3D or 4D array of flows in (Z)XY.
    """
    if masks.max() == 0:
        dynamics_logger.warning("empty masks!")
        return np.zeros((2, *masks.shape), "float32")

    if device.type == "cuda" or device.type == "mps":
        masks_to_flows_device = masks_to_flows_gpu
    else:
        masks_to_flows_device = masks_to_flows_cpu
    
    if masks.ndim == 3:
        Lz, Ly, Lx = masks.shape
        mu = np.zeros((3, Lz, Ly, Lx), np.float32)
        for z in range(Lz):
            mu0 = masks_to_flows_device(masks[z], device=device, niter=niter)[0]
            mu[[1, 2], z] += mu0
        for y in range(Ly):
            mu0 = masks_to_flows_device(masks[:, y], device=device, niter=niter)[0]
            mu[[0, 2], :, y] += mu0
        for x in range(Lx):
            mu0 = masks_to_flows_device(masks[:, :, x], device=device, niter=niter)[0]
            mu[[0, 1], :, :, x] += mu0
        return mu
    elif masks.ndim == 2:
        mu, mu_c = masks_to_flows_device(masks, device=device, niter=niter)
        return mu

    else:
        raise ValueError("masks_to_flows only takes 2D or 3D arrays")


def labels_to_flows(labels, files=None, device=None, redo_flows=False, niter=None,
                    return_flows=True):
    """Converts labels (list of masks or flows) to flows for training model.

    Args:
        labels (list of ND-arrays): The labels to convert. labels[k] can be 2D or 3D. If [3 x Ly x Lx], 
            it is assumed that flows were precomputed. Otherwise, labels[k][0] or labels[k] (if 2D) 
            is used to create flows and cell probabilities.
        files (list of str, optional): The files to save the flows to. If provided, flows are saved to 
            files to be reused. Defaults to None.
        device (str, optional): The device to use for computation. Defaults to None.
        redo_flows (bool, optional): Whether to recompute the flows. Defaults to False.
        niter (int, optional): The number of iterations for computing flows. Defaults to None.

    Returns:
        list of [4 x Ly x Lx] arrays: The flows for training the model. flows[k][0] is labels[k], 
        flows[k][1] is cell distance transform, flows[k][2] is Y flow, flows[k][3] is X flow, 
        and flows[k][4] is heat distribution.
    """
    nimg = len(labels)
    if labels[0].ndim < 3:
        labels = [labels[n][np.newaxis, :, :] for n in range(nimg)]

    flows = []
    # flows need to be recomputed
    if labels[0].shape[0] == 1 or labels[0].ndim < 3 or redo_flows:
        dynamics_logger.info("computing flows for labels")

        # compute flows; labels are fixed here to be unique, so they need to be passed back
        # make sure labels are unique!
        labels = [fastremap.renumber(label, in_place=True)[0] for label in labels]
        iterator = trange if nimg > 1 else range
        for n in iterator(nimg):
            labels[n][0] = fastremap.renumber(labels[n][0], in_place=True)[0]
            vecn = masks_to_flows(labels[n][0].astype(int), device=device, niter=niter)

            # concatenate labels, distance transform, vector flows, heat (boundary and mask are computed in augmentations)
            flow = np.concatenate((labels[n], labels[n] > 0.5, vecn),
                                  axis=0).astype(np.float32)
            if files is not None:
                file_name = os.path.splitext(files[n])[0]
                tifffile.imwrite((file_name + "_flows.tif").replace("/y/", "/flows/"), flow)
            if return_flows:
                flows.append(flow)
    else:
        dynamics_logger.info("flows precomputed")
        if return_flows:
            flows = [labels[n].astype(np.float32) for n in range(nimg)]
    return flows


@njit([
    "(int16[:,:,:], float32[:], float32[:], float32[:,:])",
    "(float32[:,:,:], float32[:], float32[:], float32[:,:])"
], cache=True)
def map_coordinates(I, yc, xc, Y):
    """
    Bilinear interpolation of image "I" in-place with y-coordinates yc and x-coordinates xc to Y.
    
    Args:
        I (numpy.ndarray): Input image of shape (C, Ly, Lx).
        yc (numpy.ndarray): New y-coordinates.
        xc (numpy.ndarray): New x-coordinates.
        Y (numpy.ndarray): Output array of shape (C, ni).
    
    Returns:
        None
    """
    C, Ly, Lx = I.shape
    yc_floor = yc.astype(np.int32)
    xc_floor = xc.astype(np.int32)
    yc = yc - yc_floor
    xc = xc - xc_floor
    for i in range(yc_floor.shape[0]):
        yf = min(Ly - 1, max(0, yc_floor[i]))
        xf = min(Lx - 1, max(0, xc_floor[i]))
        yf1 = min(Ly - 1, yf + 1)
        xf1 = min(Lx - 1, xf + 1)
        y = yc[i]
        x = xc[i]
        for c in range(C):
            Y[c, i] = (np.float32(I[c, yf, xf]) * (1 - y) * (1 - x) +
                       np.float32(I[c, yf, xf1]) * (1 - y) * x +
                       np.float32(I[c, yf1, xf]) * y * (1 - x) +
                       np.float32(I[c, yf1, xf1]) * y * x)


def steps_interp(dP, inds, niter, device=torch.device("cpu")):
    """ Run dynamics of pixels to recover masks in 2D/3D, with interpolation between pixel values.

    Euler integration of dynamics dP for niter steps.

    Args:
        p (numpy.ndarray): Array of shape (n_points, 2 or 3) representing the initial pixel locations.
        dP (numpy.ndarray): Array of shape (2, Ly, Lx) or (3, Lz, Ly, Lx) representing the flow field.
        niter (int): Number of iterations to perform.
        device (torch.device, optional): Device to use for computation. Defaults to None.

    Returns:
        numpy.ndarray: Array of shape (n_points, 2) or (n_points, 3) representing the final pixel locations.

    Raises:
        None

    """
    
    shape = dP.shape[1:]
    ndim = len(shape)
    if (device.type == "cuda" or device.type == "mps") or ndim==3:
        pt = torch.zeros((*[1]*ndim, len(inds[0]), ndim), dtype=torch.float32, device=device)
        im = torch.zeros((1, ndim, *shape), dtype=torch.float32, device=device)
        # Y and X dimensions, flipped X-1, Y-1
        # pt is [1 1 1 3 n_points]
        for n in range(ndim):
            if ndim==3:
                pt[0, 0, 0, :, ndim - n - 1] = torch.from_numpy(inds[n]).to(device, dtype=torch.float32)
            else:
                pt[0, 0, :, ndim - n - 1] = torch.from_numpy(inds[n]).to(device, dtype=torch.float32)
            im[0, ndim - n - 1] = torch.from_numpy(dP[n]).to(device, dtype=torch.float32)
        shape = np.array(shape)[::-1].astype("float") - 1  
        
        # normalize pt between  0 and  1, normalize the flow
        for k in range(ndim):
            im[:, k] *= 2. / shape[k]
            pt[..., k] /= shape[k]

        # normalize to between -1 and 1
        pt *= 2 
        pt -= 1
        
        # dynamics
        for t in range(niter):
            dPt = torch.nn.functional.grid_sample(im, pt, align_corners=False)
            for k in range(ndim):  #clamp the final pixel locations
                pt[..., k] = torch.clamp(pt[..., k] + dPt[:, k], -1., 1.)

        #undo the normalization from before, reverse order of operations
        pt += 1 
        pt *= 0.5
        for k in range(ndim):
            pt[..., k] *= shape[k]

        if ndim==3:
            pt = pt[..., [2, 1, 0]].squeeze()
            pt = pt.unsqueeze(0) if pt.ndim==1 else pt 
            return pt.T
        else:
            pt = pt[..., [1, 0]].squeeze()
            pt = pt.unsqueeze(0) if pt.ndim==1 else pt
            return pt.T

    else:
        p = np.zeros((ndim, len(inds[0])), "float32")
        for n in range(ndim):
            p[n] = inds[n]        
        dPt = np.zeros(p.shape, "float32")
        for t in range(niter):
            map_coordinates(dP, p[0], p[1], dPt)
            for k in range(len(p)):
                p[k] = np.minimum(shape[k] - 1, np.maximum(0, p[k] + dPt[k]))
        return p

@njit("(float32[:,:],float32[:,:,:,:], int32)", nogil=True)
def steps3D(p, dP, niter):
    """ Run dynamics of pixels to recover masks in 3D.

    Euler integration of dynamics dP for niter steps.

    Args:
        p (np.ndarray): Pixels with cellprob > cellprob_threshold [3 x npts].
        dP (np.ndarray): Flows [3 x Lz x Ly x Lx].
        niter (int): Number of iterations of dynamics to run.

    Returns:
        np.ndarray: Final locations of each pixel after dynamics.
    """
    shape = dP.shape[1:]
    for t in range(niter):
        for j in range(p.shape[1]):
            p0, p1, p2 = int(p[0, j]), int(p[1, j]), int(p[2, j])
            step = dP[:, p0, p1, p2]
            for k in range(3):
                p[k, j] = min(shape[k] - 1, max(0, p[k, j] + step[k]))
    return p

@njit("(float32[:,:], float32[:,:,:], int32)", nogil=True)
def steps2D(p, dP, niter):
    """Run dynamics of pixels to recover masks in 2D.

    Euler integration of dynamics dP for niter steps.

    Args:
        p (np.ndarray): Pixels with cellprob > cellprob_threshold [2 x npts].
        dP (np.ndarray): Flows [2 x Ly x Lx].
        niter (int): Number of iterations of dynamics to run.

    Returns:
        np.ndarray: Final locations of each pixel after dynamics.
    """
    shape = dP.shape[1:]
    for t in range(niter):
        for j in range(p.shape[1]):
            # starting coordinates
            p0, p1 = int(p[0, j]), int(p[1, j])
            step = dP[:, p0, p1]
            for k in range(p.shape[0]):
                p[k, j] = min(shape[k] - 1, max(0, p[k, j] + step[k]))
    return p

def follow_flows(dP, inds, niter=200, interp=True, device=torch.device("cpu")):
    """ Run dynamics to recover masks in 2D or 3D.

    Pixels are represented as a meshgrid. Only pixels with non-zero cell-probability
    are used (as defined by inds).

    Args:
        dP (np.ndarray): Flows [axis x Ly x Lx] or [axis x Lz x Ly x Lx].
        mask (np.ndarray, optional): Pixel mask to seed masks. Useful when flows have low magnitudes.
        niter (int, optional): Number of iterations of dynamics to run. Default is 200.
        interp (bool, optional): Interpolate during 2D dynamics (not available in 3D). Default is True.
        device (torch.device, optional): Device to use for computation. Default is None.

    Returns:
        A tuple containing (p, inds): p (np.ndarray): Final locations of each pixel after dynamics; [axis x Ly x Lx] or [axis x Lz x Ly x Lx]; 
        inds (np.ndarray): Indices of pixels used for dynamics; [axis x Ly x Lx] or [axis x Lz x Ly x Lx].
    """
    shape = np.array(dP.shape[1:]).astype(np.int32)
    ndim = len(inds)
    niter = np.uint32(niter)

    if interp:
        p = steps_interp(dP, inds, niter, device=device)
    else:
        p = np.zeros((ndim, len(inds[0])), "float32")
        for n in range(ndim):
            p[n] = inds[n]        
        steps_fcn = steps2D if ndim == 2 else steps3D
        p = steps_fcn(p, dP, niter)
        
    return p


def remove_bad_flow_masks(masks, flows, threshold=0.4, device=torch.device("cpu")):
    """Remove masks which have inconsistent flows.

    Uses metrics.flow_error to compute flows from predicted masks 
    and compare flows to predicted flows from the network. Discards 
    masks with flow errors greater than the threshold.

    Args:
        masks (int, 2D or 3D array): Labelled masks, 0=NO masks; 1,2,...=mask labels,
            size [Ly x Lx] or [Lz x Ly x Lx].
        flows (float, 3D or 4D array): Flows [axis x Ly x Lx] or [axis x Lz x Ly x Lx].
        threshold (float, optional): Masks with flow error greater than threshold are discarded.
            Default is 0.4.

    Returns:
        masks (int, 2D or 3D array): Masks with inconsistent flow masks removed,
            0=NO masks; 1,2,...=mask labels, size [Ly x Lx] or [Lz x Ly x Lx].
    """
    device0 = device
    if masks.size > 10000 * 10000 and (device is not None and device.type == "cuda"):

        major_version, minor_version = torch.__version__.split(".")[:2]
        torch.cuda.empty_cache()
        if major_version == "1" and int(minor_version) < 10:
            # for PyTorch version lower than 1.10
            def mem_info():
                total_mem = torch.cuda.get_device_properties(device0.index).total_memory
                used_mem = torch.cuda.memory_allocated(device0.index)
                free_mem = total_mem - used_mem
                return total_mem, free_mem
        else:
            # for PyTorch version 1.10 and above
            def mem_info():
                free_mem, total_mem = torch.cuda.mem_get_info(device0.index)
                return total_mem, free_mem
        total_mem, free_mem = mem_info()
        if masks.size * 32 > free_mem:
            dynamics_logger.warning(
                "WARNING: image is very large, not using gpu to compute flows from masks for QC step flow_threshold"
            )
            dynamics_logger.info("turn off QC step with flow_threshold=0 if too slow")
            device0 = torch.device("cpu")

    merrors, _ = metrics.flow_error(masks, flows, device0)
    badi = 1 + (merrors > threshold).nonzero()[0]
    masks[np.isin(masks, badi)] = 0
    return masks


def max_pool3d(h, kernel_size=5):
    """ memory efficient max_pool thanks to Mark Kittisopikul 
    
    for stride=1, padding=kernel_size//2, requires odd kernel_size >= 3
    
    """
    _, nd, ny, nx = h.shape
    m = h.clone().detach()
    kruns, k0 = kernel_size // 2, 1
    for k in range(kruns):
        for d in range(-k0, k0+1):
            for y in range(-k0, k0+1):
                for x in range(-k0, k0+1):
                    mv = m[:, max(-d,0):min(nd-d,nd), max(-y,0):min(ny-y,ny), max(-x,0):min(nx-x,nx)]
                    hv = h[:,  max(d,0):min(nd+d,nd),  max(y,0):min(ny+y,ny),  max(x,0):min(nx+x,nx)]
                    torch.maximum(mv, hv, out=mv)
    return m

def max_pool2d(h, kernel_size=5):
    """ memory efficient max_pool thanks to Mark Kittisopikul """
    _, ny, nx = h.shape
    m = h.clone().detach()
    k0 = kernel_size // 2
    for y in range(-k0, k0+1):
        for x in range(-k0, k0+1):
            mv = m[:, max(-y,0):min(ny-y,ny), max(-x,0):min(nx-x,nx)]
            hv = h[:, max(y,0):min(ny+y,ny),  max(x,0):min(nx+x,nx)]
            torch.maximum(mv, hv, out=mv)
    return m

def max_pool1d(h, kernel_size=5, axis=1, out=None):
    """ memory efficient max_pool thanks to Mark Kittisopikul 
    
    for stride=1, padding=kernel_size//2, requires odd kernel_size >= 3

    """
    if out is None:
        out = h.clone()
    else:
        out.copy_(h)

    nd = h.shape[axis]    
    k0 = kernel_size // 2
    for d in range(-k0, k0+1):
        if axis==1:
            mv = out[:, max(-d,0):min(nd-d,nd)]
            hv = h[:, max(d,0):min(nd+d,nd)]
        elif axis==2:
            mv = out[:, :, max(-d,0):min(nd-d,nd)]
            hv = h[:,  :, max(d,0):min(nd+d,nd)]
        elif axis==3:
            mv = out[:, :, :, max(-d,0):min(nd-d,nd)]
            hv = h[:, :,  :, max(d,0):min(nd+d,nd)]
        torch.maximum(mv, hv, out=mv)
    return out

def max_pool_nd(h, kernel_size=5):
    """ memory efficient max_pool in 2d or 3d """
    ndim = h.ndim - 1
    hmax = max_pool1d(h, kernel_size=kernel_size, axis=1)
    hmax2 = max_pool1d(hmax, kernel_size=kernel_size, axis=2)
    if ndim==2:
        del hmax
        return hmax2
    else:
        hmax = max_pool1d(hmax2, kernel_size=kernel_size, axis=3, out=hmax)
        del hmax2 
        return hmax

# from torch.nn.functional import max_pool2d
def get_masks_torch(pt, inds, shape0, rpad=20, max_size_fraction=0.4):
    """Create masks using pixel convergence after running dynamics.

    Makes a histogram of final pixel locations p, initializes masks 
    at peaks of histogram and extends the masks from the peaks so that
    they include all pixels with more than 2 final pixels p. Discards 
    masks with flow errors greater than the threshold. 

    Parameters:
        p (float32, 3D or 4D array): Final locations of each pixel after dynamics,
            size [axis x Ly x Lx] or [axis x Lz x Ly x Lx].
        iscell (bool, 2D or 3D array): If iscell is not None, set pixels that are 
            iscell False to stay in their original location.
        rpad (int, optional): Histogram edge padding. Default is 20.
        max_size_fraction (float, optional): Masks larger than max_size_fraction of
            total image size are removed. Default is 0.4.

    Returns:
        M0 (int, 2D or 3D array): Masks with inconsistent flow masks removed, 
            0=NO masks; 1,2,...=mask labels, size [Ly x Lx] or [Lz x Ly x Lx].
    """
    
    ndim = len(shape0)
    device = pt.device
    
    rpad = 20
    pt += rpad
    pt = torch.clamp(pt, min=0)
    for i in range(len(pt)):
        pt[i] = torch.clamp(pt[i], max=shape0[i]+rpad-1)

    # # add extra padding to make divisible by 5
    # shape = tuple((np.ceil((shape0 + 2*rpad)/5) * 5).astype(int))
    shape = tuple(np.array(shape0) + 2*rpad)

    # sparse coo torch
    coo = torch.sparse_coo_tensor(pt, torch.ones(pt.shape[1], device=pt.device, dtype=torch.int), 
                                shape)
    h1 = coo.to_dense()
    del coo

    hmax1 = max_pool_nd(h1.unsqueeze(0), kernel_size=5)
    hmax1 = hmax1.squeeze()
    seeds1 = torch.nonzero((h1 - hmax1 > -1e-6) * (h1 > 10))
    del hmax1
    if len(seeds1) == 0:
        dynamics_logger.warning("no seeds found in get_masks_torch - no masks found.")
        return np.zeros(shape0, dtype="uint16")
    
    npts = h1[tuple(seeds1.T)]
    isort1 = npts.argsort()
    seeds1 = seeds1[isort1]

    n_seeds = len(seeds1)
    h_slc = torch.zeros((n_seeds, *[11]*ndim), device=seeds1.device)
    for k in range(n_seeds):
        slc = tuple([slice(seeds1[k][j]-5, seeds1[k][j]+6) for j in range(ndim)])
        h_slc[k] = h1[slc]
    del h1
    seed_masks = torch.zeros((n_seeds, *[11]*ndim), device=seeds1.device)
    if ndim==2:
        seed_masks[:,5,5] = 1
    else:
        seed_masks[:,5,5,5] = 1
    
    for iter in range(5):
        # extend
        seed_masks = max_pool_nd(seed_masks, kernel_size=3)
        seed_masks *= h_slc > 2
    del h_slc 
    seeds_new = [tuple((torch.nonzero(seed_masks[k]) + seeds1[k] - 5).T) 
            for k in range(n_seeds)]
    del seed_masks 
    
    dtype = torch.int32 if n_seeds < 2**16 else torch.int64
    M1 = torch.zeros(shape, dtype=dtype, device=device)
    for k in range(n_seeds):
        M1[seeds_new[k]] = 1 + k

    M1 = M1[tuple(pt.long())]
    M1 = M1.cpu().numpy()

    dtype = "uint16" if n_seeds < 2**16 else "uint32"
    M0 = np.zeros(shape0, dtype=dtype)
    M0[inds] = M1
        
    # remove big masks
    uniq, counts = fastremap.unique(M0, return_counts=True)
    big = np.prod(shape0) * max_size_fraction
    bigc = uniq[counts > big]
    if len(bigc) > 0 and (len(bigc) > 1 or bigc[0] != 0):
        M0 = fastremap.mask(M0, bigc)
    fastremap.renumber(M0, in_place=True)  #convenient to guarantee non-skipped labels
    M0 = M0.reshape(tuple(shape0))
    
    #print(f"mem used: {torch.cuda.memory_allocated()/1e9:.3f} gb, max mem used: {torch.cuda.max_memory_allocated()/1e9:.3f} gb")
    return M0


def resize_and_compute_masks(dP, cellprob, niter=200, cellprob_threshold=0.0,
                             flow_threshold=0.4, interp=True, do_3D=False, min_size=15,
                             max_size_fraction=0.4, resize=None, device=torch.device("cpu")):
    """Compute masks using dynamics from dP and cellprob, and resizes masks if resize is not None.

    Args:
        dP (numpy.ndarray): The dynamics flow field array.
        cellprob (numpy.ndarray): The cell probability array.
        p (numpy.ndarray, optional): The pixels on which to run dynamics. Defaults to None
        niter (int, optional): The number of iterations for mask computation. Defaults to 200.
        cellprob_threshold (float, optional): The threshold for cell probability. Defaults to 0.0.
        flow_threshold (float, optional): The threshold for quality control metrics. Defaults to 0.4.
        interp (bool, optional): Whether to interpolate during dynamics computation. Defaults to True.
        do_3D (bool, optional): Whether to perform mask computation in 3D. Defaults to False.
        min_size (int, optional): The minimum size of the masks. Defaults to 15.
        max_size_fraction (float, optional): Masks larger than max_size_fraction of
            total image size are removed. Default is 0.4.
        resize (tuple, optional): The desired size for resizing the masks. Defaults to None.
        device (torch.device, optional): The device to use for computation. Defaults to torch.device("cpu").

    Returns:
        tuple: A tuple containing the computed masks and the final pixel locations.
    """
    mask = compute_masks(dP, cellprob, niter=niter,
                            cellprob_threshold=cellprob_threshold,
                            flow_threshold=flow_threshold, interp=interp, do_3D=do_3D,
                            max_size_fraction=max_size_fraction, 
                            device=device)

    if resize is not None:
        if len(resize) == 2:
            mask = transforms.resize_image(mask, resize[0], resize[1], no_channels=True,
                                           interpolation=cv2.INTER_NEAREST)
        else:
            Lz, Ly, Lx = resize
            if mask.shape[0] != Lz or mask.shape[1] != Ly:
                dynamics_logger.info("resizing 3D masks to original image size")
                if mask.shape[1] != Ly:
                    mask = transforms.resize_image(mask, Ly=Ly, Lx=Lx,
                                                no_channels=True, 
                                                interpolation=cv2.INTER_NEAREST)
                if mask.shape[0] != Lz:
                    mask = transforms.resize_image(mask.transpose(1,0,2),
                                                    Ly=Lz, Lx=Lx,
                                                    no_channels=True, 
                                                    interpolation=cv2.INTER_NEAREST).transpose(1,0,2)

    mask = utils.fill_holes_and_remove_small_masks(mask, min_size=min_size)

    return mask

def compute_masks(dP, cellprob, p=None, niter=200, cellprob_threshold=0.0,
                  flow_threshold=0.4, interp=True, do_3D=False, min_size=-1,
                  max_size_fraction=0.4, device=torch.device("cpu")):
    """Compute masks using dynamics from dP and cellprob.

    Args:
        dP (numpy.ndarray): The dynamics flow field array.
        cellprob (numpy.ndarray): The cell probability array.
        p (numpy.ndarray, optional): The pixels on which to run dynamics. Defaults to None
        niter (int, optional): The number of iterations for mask computation. Defaults to 200.
        cellprob_threshold (float, optional): The threshold for cell probability. Defaults to 0.0.
        flow_threshold (float, optional): The threshold for quality control metrics. Defaults to 0.4.
        interp (bool, optional): Whether to interpolate during dynamics computation. Defaults to True.
        do_3D (bool, optional): Whether to perform mask computation in 3D. Defaults to False.
        min_size (int, optional): The minimum size of the masks. Defaults to 15.
        max_size_fraction (float, optional): Masks larger than max_size_fraction of
            total image size are removed. Default is 0.4.
        device (torch.device, optional): The device to use for computation. Defaults to torch.device("cpu").

    Returns:
        tuple: A tuple containing the computed masks and the final pixel locations.
    """
    
    if (cellprob > cellprob_threshold).sum():  #mask at this point is a cell cluster binary map, not labels
        inds = np.nonzero(cellprob > cellprob_threshold)
        if len(inds[0]) == 0:
            dynamics_logger.info("No cell pixels found.")
            shape = cellprob.shape
            mask = np.zeros(shape, "uint16")
            return mask

        p_final = follow_flows(dP * (cellprob > cellprob_threshold) / 5., 
                               inds=inds, niter=niter, interp=interp,
                                device=device)
        if not torch.is_tensor(p_final):
            p_final = torch.from_numpy(p_final).to(device, dtype=torch.int)
        else:
            p_final = p_final.int()
        # calculate masks
        if device.type == "mps":
            p_final = p_final.to(torch.device("cpu"))
        mask = get_masks_torch(p_final, inds, dP.shape[1:], 
                               max_size_fraction=max_size_fraction)
        del p_final
        # flow thresholding factored out of get_masks
        if not do_3D:
            if mask.max() > 0 and flow_threshold is not None and flow_threshold > 0:
                # make sure labels are unique at output of get_masks
                mask = remove_bad_flow_masks(mask, dP, threshold=flow_threshold,
                                             device=device)

        if mask.max() < 2**16 and mask.dtype != "uint16":
            mask = mask.astype("uint16")

    else:  # nothing to compute, just make it compatible
        dynamics_logger.info("No cell pixels found.")
        shape = cellprob.shape
        mask = np.zeros(cellprob.shape, "uint16")
        return mask
    
    if min_size > 0:
        mask = utils.fill_holes_and_remove_small_masks(mask, min_size=min_size)

    if mask.dtype == np.uint32:
        dynamics_logger.warning(
            "more than 65535 masks in image, masks returned as np.uint32")

    return mask

def get_masks_orig(p, iscell=None, rpad=20, max_size_fraction=0.4):
    """Create masks using pixel convergence after running dynamics.

    Original implementation on CPU with histogramdd
    (histogramdd uses excessive memory with large images)

    Makes a histogram of final pixel locations p, initializes masks 
    at peaks of histogram and extends the masks from the peaks so that
    they include all pixels with more than 2 final pixels p. Discards 
    masks with flow errors greater than the threshold. 

    Parameters:
        p (float32, 3D or 4D array): Final locations of each pixel after dynamics,
            size [axis x Ly x Lx] or [axis x Lz x Ly x Lx].
        iscell (bool, 2D or 3D array): If iscell is not None, set pixels that are 
            iscell False to stay in their original location.
        rpad (int, optional): Histogram edge padding. Default is 20.
        max_size_fraction (float, optional): Masks larger than max_size_fraction of
            total image size are removed. Default is 0.4.

    Returns:
        M0 (int, 2D or 3D array): Masks with inconsistent flow masks removed, 
            0=NO masks; 1,2,...=mask labels, size [Ly x Lx] or [Lz x Ly x Lx].
    """
    pflows = []
    edges = []
    shape0 = p.shape[1:]
    dims = len(p)
    if iscell is not None:
        if dims == 3:
            inds = np.meshgrid(np.arange(shape0[0]), np.arange(shape0[1]),
                               np.arange(shape0[2]), indexing="ij")
        elif dims == 2:
            inds = np.meshgrid(np.arange(shape0[0]), np.arange(shape0[1]),
                               indexing="ij")
        for i in range(dims):
            p[i, ~iscell] = inds[i][~iscell]

    for i in range(dims):
        pflows.append(p[i].flatten().astype("int32"))
        edges.append(np.arange(-.5 - rpad, shape0[i] + .5 + rpad, 1))

    h, _ = np.histogramdd(tuple(pflows), bins=edges)
    hmax = h.copy()
    for i in range(dims):
        hmax = maximum_filter1d(hmax, 5, axis=i)

    seeds = np.nonzero(np.logical_and(h - hmax > -1e-6, h > 10))
    Nmax = h[seeds]
    isort = np.argsort(Nmax)[::-1]
    for s in seeds:
        s[:] = s[isort]

    pix = list(np.array(seeds).T)

    shape = h.shape
    if dims == 3:
        expand = np.nonzero(np.ones((3, 3, 3)))
    else:
        expand = np.nonzero(np.ones((3, 3)))

    for iter in range(5):
        for k in range(len(pix)):
            if iter == 0:
                pix[k] = list(pix[k])
            newpix = []
            iin = []
            for i, e in enumerate(expand):
                epix = e[:, np.newaxis] + np.expand_dims(pix[k][i], 0) - 1
                epix = epix.flatten()
                iin.append(np.logical_and(epix >= 0, epix < shape[i]))
                newpix.append(epix)
            iin = np.all(tuple(iin), axis=0)
            for p in newpix:
                p = p[iin]
            newpix = tuple(newpix)
            igood = h[newpix] > 2
            for i in range(dims):
                pix[k][i] = newpix[i][igood]
            if iter == 4:
                pix[k] = tuple(pix[k])

    M = np.zeros(h.shape, np.uint32)
    for k in range(len(pix)):
        M[pix[k]] = 1 + k

    for i in range(dims):
        pflows[i] = pflows[i] + rpad
    M0 = M[tuple(pflows)]

    # remove big masks
    uniq, counts = fastremap.unique(M0, return_counts=True)
    big = np.prod(shape0) * max_size_fraction
    bigc = uniq[counts > big]
    if len(bigc) > 0 and (len(bigc) > 1 or bigc[0] != 0):
        M0 = fastremap.mask(M0, bigc)
    fastremap.renumber(M0, in_place=True)  #convenient to guarantee non-skipped labels
    M0 = np.reshape(M0, shape0)
    return M0