utils.py

# Copyright (c) MONAI Consortium
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#     http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import warnings
from typing import Any, Callable, Dict, List, Mapping, Sequence, Tuple, Union

import cv2
import math
import numpy as np
import torch
import torch.nn.functional as F
import colorsys
import itertools
import matplotlib.pyplot as plt
from matplotlib import cm

from monai.data.meta_tensor import MetaTensor
from monai.data.utils import compute_importance_map, dense_patch_slices, get_valid_patch_size
from monai.transforms import Resize
from monai.utils import (
    BlendMode,
    PytorchPadMode,
    convert_data_type,
    convert_to_dst_type,
    ensure_tuple,
    fall_back_tuple,
    look_up_option,
    optional_import,
)

from scipy import ndimage
from scipy.ndimage.filters import gaussian_filter
from scipy.ndimage.interpolation import affine_transform, map_coordinates

from skimage import morphology as morph
from scipy.ndimage import filters, measurements
from scipy.ndimage.morphology import (
    binary_dilation,
    binary_fill_holes,
    distance_transform_cdt,
    distance_transform_edt,
)

from skimage.segmentation import watershed
from skimage.exposure import rescale_intensity
from skimage.filters import sobel_h, sobel_v, gaussian
from skimage.morphology import disk, binary_opening

tqdm, _ = optional_import("tqdm", name="tqdm")

__all__ = ["sliding_window_inference"]

####
def normalize(mask, dtype=np.uint8):
    return (255 * mask / np.amax(mask)).astype(dtype)

def fix_mirror_padding(ann):
    """Deal with duplicated instances due to mirroring in interpolation
    during shape augmentation (scale, rotation etc.).

    """
    current_max_id = np.amax(ann)
    inst_list = list(np.unique(ann))
    if 0 in inst_list:
        inst_list.remove(0)  # 0 is background
    for inst_id in inst_list:
        inst_map = np.array(ann == inst_id, np.uint8)
        remapped_ids = measurements.label(inst_map)[0]
        remapped_ids[remapped_ids > 1] += current_max_id
        ann[remapped_ids > 1] = remapped_ids[remapped_ids > 1]
        current_max_id = np.amax(ann)
    return ann

####
def get_bounding_box(img):
    """Get bounding box coordinate information."""
    rows = np.any(img, axis=1)
    cols = np.any(img, axis=0)
    rmin, rmax = np.where(rows)[0][[0, -1]]
    cmin, cmax = np.where(cols)[0][[0, -1]]
    # due to python indexing, need to add 1 to max
    # else accessing will be 1px in the box, not out
    rmax += 1
    cmax += 1
    return [rmin, rmax, cmin, cmax]


####
def cropping_center(x, crop_shape, batch=False):
    """Crop an input image at the centre.

    Args:
        x: input array
        crop_shape: dimensions of cropped array
    
    Returns:
        x: cropped array
    
    """
    orig_shape = x.shape
    if not batch:
        h0 = int((orig_shape[0] - crop_shape[0]) * 0.5)
        w0 = int((orig_shape[1] - crop_shape[1]) * 0.5)
        x = x[h0 : h0 + crop_shape[0], w0 : w0 + crop_shape[1]]
    else:
        h0 = int((orig_shape[1] - crop_shape[0]) * 0.5)
        w0 = int((orig_shape[2] - crop_shape[1]) * 0.5)
        x = x[:, h0 : h0 + crop_shape[0], w0 : w0 + crop_shape[1]]
    return x

def gen_instance_hv_map(ann, crop_shape):
    """Input annotation must be of original shape.
    
    The map is calculated only for instances within the crop portion
    but based on the original shape in original image.

    Perform following operation:
    Obtain the horizontal and vertical distance maps for each
    nuclear instance.

    """
    orig_ann = ann.copy()  # instance ID map
    fixed_ann = fix_mirror_padding(orig_ann)
    # re-cropping with fixed instance id map
    crop_ann = cropping_center(fixed_ann, crop_shape)
    # TODO: deal with 1 label warning
    crop_ann = morph.remove_small_objects(crop_ann, min_size=30)

    x_map = np.zeros(orig_ann.shape[:2], dtype=np.float32)
    y_map = np.zeros(orig_ann.shape[:2], dtype=np.float32)

    inst_list = list(np.unique(crop_ann))
    if 0 in inst_list:
        inst_list.remove(0)  # 0 is background
    for inst_id in inst_list:
        inst_map = np.array(fixed_ann == inst_id, np.uint8)
        inst_box = get_bounding_box(inst_map) # rmin, rmax, cmin, cmax

        # expand the box by 2px
        # Because we first pad the ann at line 207, the bboxes
        # will remain valid after expansion
        inst_box[0] -= 2
        inst_box[2] -= 2
        inst_box[1] += 2
        inst_box[3] += 2
        
        # fix inst_box
        inst_box[0] = max(inst_box[0], 0)
        inst_box[2] = max(inst_box[2], 0)
        # inst_box[1] = min(inst_box[1], fixed_ann.shape[0]) 
        # inst_box[3] = min(inst_box[3], fixed_ann.shape[1])

        inst_map = inst_map[inst_box[0] : inst_box[1], inst_box[2] : inst_box[3]]

        if inst_map.shape[0] < 2 or inst_map.shape[1] < 2:
            print(f'inst_map.shape < 2: {inst_map.shape}, {inst_box}, {get_bounding_box(np.array(fixed_ann == inst_id, np.uint8))}')
            continue

        # instance center of mass, rounded to nearest pixel
        inst_com = list(measurements.center_of_mass(inst_map))
        if np.isnan(measurements.center_of_mass(inst_map)).any():
            print(inst_id, fixed_ann.shape, np.array(fixed_ann == inst_id, np.uint8).shape)
            print(get_bounding_box(np.array(fixed_ann == inst_id, np.uint8)))
            print(inst_map)
            print(inst_list)
            print(inst_box)
            print(np.count_nonzero(np.array(fixed_ann == inst_id, np.uint8)))

        inst_com[0] = int(inst_com[0] + 0.5)
        inst_com[1] = int(inst_com[1] + 0.5)

        inst_x_range = np.arange(1, inst_map.shape[1] + 1)
        inst_y_range = np.arange(1, inst_map.shape[0] + 1)
        # shifting center of pixels grid to instance center of mass
        inst_x_range -= inst_com[1]
        inst_y_range -= inst_com[0]

        inst_x, inst_y = np.meshgrid(inst_x_range, inst_y_range)

        # remove coord outside of instance
        inst_x[inst_map == 0] = 0
        inst_y[inst_map == 0] = 0
        inst_x = inst_x.astype("float32")
        inst_y = inst_y.astype("float32")

        # normalize min into -1 scale
        if np.min(inst_x) < 0:
            inst_x[inst_x < 0] /= -np.amin(inst_x[inst_x < 0])
        if np.min(inst_y) < 0:
            inst_y[inst_y < 0] /= -np.amin(inst_y[inst_y < 0])
        # normalize max into +1 scale
        if np.max(inst_x) > 0:
            inst_x[inst_x > 0] /= np.amax(inst_x[inst_x > 0])
        if np.max(inst_y) > 0:
            inst_y[inst_y > 0] /= np.amax(inst_y[inst_y > 0])

        ####
        x_map_box = x_map[inst_box[0] : inst_box[1], inst_box[2] : inst_box[3]]
        x_map_box[inst_map > 0] = inst_x[inst_map > 0]

        y_map_box = y_map[inst_box[0] : inst_box[1], inst_box[2] : inst_box[3]]
        y_map_box[inst_map > 0] = inst_y[inst_map > 0]

    hv_map = np.dstack([x_map, y_map])
    return hv_map

def remove_small_objects(pred, min_size=64, connectivity=1):
    """Remove connected components smaller than the specified size.

    This function is taken from skimage.morphology.remove_small_objects, but the warning
    is removed when a single label is provided.

    Args:
        pred: input labelled array
        min_size: minimum size of instance in output array
        connectivity: The connectivity defining the neighborhood of a pixel.

    Returns:
        out: output array with instances removed under min_size

    """
    out = pred

    if min_size == 0:  # shortcut for efficiency
        return out

    if out.dtype == bool:
        selem = ndimage.generate_binary_structure(pred.ndim, connectivity)
        ccs = np.zeros_like(pred, dtype=np.int32)
        ndimage.label(pred, selem, output=ccs)
    else:
        ccs = out

    try:
        component_sizes = np.bincount(ccs.ravel())
    except ValueError:
        raise ValueError(
            "Negative value labels are not supported. Try "
            "relabeling the input with `scipy.ndimage.label` or "
            "`skimage.morphology.label`."
        )

    too_small = component_sizes < min_size
    too_small_mask = too_small[ccs]
    out[too_small_mask] = 0

    return out

####
def gen_targets(ann, crop_shape, **kwargs):
    """Generate the targets for the network."""
    hv_map = gen_instance_hv_map(ann, crop_shape)
    np_map = ann.copy()
    np_map[np_map > 0] = 1

    hv_map = cropping_center(hv_map, crop_shape)
    np_map = cropping_center(np_map, crop_shape)

    target_dict = {
        "hv_map": hv_map,
        "np_map": np_map,
    }

    return target_dict

####
def xentropy_loss(true, pred, reduction="mean"):
    """Cross entropy loss. Assumes NHWC!

    Args:
        pred: prediction array
        true: ground truth array
    
    Returns:
        cross entropy loss

    """
    epsilon = 10e-8
    # scale preds so that the class probs of each sample sum to 1
    pred = pred / torch.sum(pred, -1, keepdim=True)
    # manual computation of crossentropy
    pred = torch.clamp(pred, epsilon, 1.0 - epsilon)
    loss = -torch.sum((true * torch.log(pred)), -1, keepdim=True)
    loss = loss.mean() if reduction == "mean" else loss.sum()
    return loss


####
def dice_loss(true, pred, smooth=1e-3):
    """`pred` and `true` must be of torch.float32. Assuming of shape NxHxWxC."""
    inse = torch.sum(pred * true, (0, 1, 2))
    l = torch.sum(pred, (0, 1, 2))
    r = torch.sum(true, (0, 1, 2))
    loss = 1.0 - (2.0 * inse + smooth) / (l + r + smooth)
    loss = torch.sum(loss)
    return loss


####
def mse_loss(true, pred):
    """Calculate mean squared error loss.

    Args:
        true: ground truth of combined horizontal
              and vertical maps
        pred: prediction of combined horizontal
              and vertical maps 
    
    Returns:
        loss: mean squared error

    """
    loss = pred - true
    loss = (loss * loss).mean()
    return loss


####
def msge_loss(true, pred, focus):
    """Calculate the mean squared error of the gradients of 
    horizontal and vertical map predictions. Assumes 
    channel 0 is Vertical and channel 1 is Horizontal.

    Args:
        true:  ground truth of combined horizontal
               and vertical maps
        pred:  prediction of combined horizontal
               and vertical maps 
        focus: area where to apply loss (we only calculate
                the loss within the nuclei)
    
    Returns:
        loss:  mean squared error of gradients

    """

    def get_sobel_kernel(size):
        """Get sobel kernel with a given size."""
        assert size % 2 == 1, "Must be odd, get size=%d" % size

        h_range = torch.arange(
            -size // 2 + 1,
            size // 2 + 1,
            dtype=torch.float32,
            device="cuda",
            requires_grad=False,
        )
        v_range = torch.arange(
            -size // 2 + 1,
            size // 2 + 1,
            dtype=torch.float32,
            device="cuda",
            requires_grad=False,
        )
        h, v = torch.meshgrid(h_range, v_range)
        kernel_h = h / (h * h + v * v + 1.0e-15)
        kernel_v = v / (h * h + v * v + 1.0e-15)
        return kernel_h, kernel_v

    ####
    def get_gradient_hv(hv):
        """For calculating gradient."""
        kernel_h, kernel_v = get_sobel_kernel(5)
        kernel_h = kernel_h.view(1, 1, 5, 5)  # constant
        kernel_v = kernel_v.view(1, 1, 5, 5)  # constant

        h_ch = hv[..., 0].unsqueeze(1)  # Nx1xHxW
        v_ch = hv[..., 1].unsqueeze(1)  # Nx1xHxW

        # can only apply in NCHW mode
        h_dh_ch = F.conv2d(h_ch, kernel_h, padding=2)
        v_dv_ch = F.conv2d(v_ch, kernel_v, padding=2)
        dhv = torch.cat([h_dh_ch, v_dv_ch], dim=1)
        dhv = dhv.permute(0, 2, 3, 1).contiguous()  # to NHWC
        return dhv

    focus = (focus[..., None]).float()  # assume input NHW
    focus = torch.cat([focus, focus], axis=-1)
    true_grad = get_gradient_hv(true)
    pred_grad = get_gradient_hv(pred)
    loss = pred_grad - true_grad
    loss = focus * (loss * loss)
    # artificial reduce_mean with focused region
    loss = loss.sum() / (focus.sum() + 1.0e-8)
    return loss


def __proc_np_hv(pred, np_thres, ksize, overall_thres, obj_size_thres):
    """Process Nuclei Prediction with XY Coordinate Map.

    Args:
        pred: prediction output, assuming
              channel 0 contain probability map of nuclei
              channel 1 containing the regressed X-map
              channel 2 containing the regressed Y-map

    """
    pred = np.array(pred, dtype=np.float32)

    blb_raw = pred[..., 0]
    h_dir_raw = pred[..., 1]
    v_dir_raw = pred[..., 2]

    # processing
    blb = np.array(blb_raw >= np_thres, dtype=np.int32)

    blb = measurements.label(blb)[0]
    blb = remove_small_objects(blb, min_size=10)
    blb[blb > 0] = 1  # background is 0 already

    h_dir = cv2.normalize(
        h_dir_raw, None, alpha=0, beta=1, norm_type=cv2.NORM_MINMAX, dtype=cv2.CV_32F
    )
    v_dir = cv2.normalize(
        v_dir_raw, None, alpha=0, beta=1, norm_type=cv2.NORM_MINMAX, dtype=cv2.CV_32F
    )

    sobelh = cv2.Sobel(h_dir, cv2.CV_64F, 1, 0, ksize=ksize)
    sobelv = cv2.Sobel(v_dir, cv2.CV_64F, 0, 1, ksize=ksize)

    sobelh = 1 - (
        cv2.normalize(
            sobelh, None, alpha=0, beta=1, norm_type=cv2.NORM_MINMAX, dtype=cv2.CV_32F
        )
    )
    sobelv = 1 - (
        cv2.normalize(
            sobelv, None, alpha=0, beta=1, norm_type=cv2.NORM_MINMAX, dtype=cv2.CV_32F
        )
    )

    overall = np.maximum(sobelh, sobelv)
    overall = overall - (1 - blb)
    overall[overall < 0] = 0

    dist = (1.0 - overall) * blb
    ## nuclei values form mountains so inverse to get basins
    dist = -cv2.GaussianBlur(dist, (3, 3), 0)

    overall = np.array(overall >= overall_thres, dtype=np.int32)

    marker = blb - overall
    marker[marker < 0] = 0
    marker = binary_fill_holes(marker).astype("uint8")
    kernel = cv2.getStructuringElement(cv2.MORPH_ELLIPSE, (5, 5))
    marker = cv2.morphologyEx(marker, cv2.MORPH_OPEN, kernel)
    marker = measurements.label(marker)[0]
    marker = remove_small_objects(marker, min_size=obj_size_thres)

    proced_pred = watershed(dist, markers=marker, mask=blb)

    return proced_pred

def __proc_np_hv_2(pred, np_thres=0.5, ksize=21, overall_thres=0.4, obj_size_thres=10):
    """Process Nuclei Prediction with XY Coordinate Map.

    Args:
        pred: prediction output, assuming
              channel 0 contain probability map of nuclei
              channel 1 containing the regressed X-map
              channel 2 containing the regressed Y-map

    """
    pred = np.array(pred, dtype=np.float32)

    blb_raw = pred[..., 0]
    h_dir_raw = pred[..., 1]
    v_dir_raw = pred[..., 2]

    # processing
    blb = np.array(blb_raw >= np_thres, dtype=np.int32)

    blb = measurements.label(blb)[0]
    blb = remove_small_objects(blb, min_size=10)
    blb[blb > 0] = 1  # background is 0 already

    h_dir = rescale_intensity(h_dir_raw, out_range=(0, 1)).astype('float32')
    v_dir = rescale_intensity(v_dir_raw, out_range=(0, 1)).astype('float32')

    sobelh = sobel_v(h_dir).astype('float64')
    sobelv = sobel_h(v_dir).astype('float64')

    sobelh = 1 - rescale_intensity(sobelh, out_range=(0, 1)).astype('float32')
    sobelv = 1 - rescale_intensity(sobelv, out_range=(0, 1)).astype('float32')

    overall = np.maximum(sobelh, sobelv)
    overall = overall - (1 - blb)
    overall[overall < 0] = 0

    dist = (1.0 - overall) * blb
    ## nuclei values form mountains so inverse to get basins
    dist = - gaussian(dist, sigma=0.8)

    overall = np.array(overall >= overall_thres, dtype=np.int32)

    marker = blb - overall
    marker[marker < 0] = 0
    marker = binary_fill_holes(marker).astype("uint8")
    kernel = disk(2)
    marker = binary_opening(marker, kernel)
    marker = measurements.label(marker)[0]
    marker = remove_small_objects(marker, min_size=obj_size_thres)

    proced_pred = watershed(dist, markers=marker, mask=blb)

    return proced_pred


####
def colorize(ch, vmin, vmax):
    """Will clamp value value outside the provided range to vmax and vmin."""
    cmap = plt.get_cmap("jet")
    ch = np.squeeze(ch.astype("float32"))
    vmin = vmin if vmin is not None else ch.min()
    vmax = vmax if vmax is not None else ch.max()
    ch[ch > vmax] = vmax  # clamp value
    ch[ch < vmin] = vmin
    ch = (ch - vmin) / (vmax - vmin + 1.0e-16)
    # take RGB from RGBA heat map
    ch_cmap = (cmap(ch)[..., :3] * 255).astype("uint8")
    return ch_cmap


####
def random_colors(N, bright=True):
    """Generate random colors.

    To get visually distinct colors, generate them in HSV space then
    convert to RGB.
    """
    brightness = 1.0 if bright else 0.7
    hsv = [(i / N, 1, brightness) for i in range(N)]
    colors = list(map(lambda c: colorsys.hsv_to_rgb(*c), hsv))
    random.shuffle(colors)
    return colors


####
def visualize_instances_map(
    input_image, inst_map, type_map=None, type_colour=None, line_thickness=2
):
    """Overlays segmentation results on image as contours.

    Args:
        input_image: input image
        inst_map: instance mask with unique value for every object
        type_map: type mask with unique value for every class
        type_colour: a dict of {type : colour} , `type` is from 0-N
                     and `colour` is a tuple of (R, G, B)
        line_thickness: line thickness of contours

    Returns:
        overlay: output image with segmentation overlay as contours
    """
    overlay = np.copy((input_image).astype(np.uint8))

    inst_list = list(np.unique(inst_map))  # get list of instances
    inst_list.remove(0)  # remove background

    inst_rng_colors = random_colors(len(inst_list))
    inst_rng_colors = np.array(inst_rng_colors) * 255
    inst_rng_colors = inst_rng_colors.astype(np.uint8)

    for inst_idx, inst_id in enumerate(inst_list):
        inst_map_mask = np.array(inst_map == inst_id, np.uint8)  # get single object
        y1, y2, x1, x2 = get_bounding_box(inst_map_mask)
        y1 = y1 - 2 if y1 - 2 >= 0 else y1
        x1 = x1 - 2 if x1 - 2 >= 0 else x1
        x2 = x2 + 2 if x2 + 2 <= inst_map.shape[1] - 1 else x2
        y2 = y2 + 2 if y2 + 2 <= inst_map.shape[0] - 1 else y2
        inst_map_crop = inst_map_mask[y1:y2, x1:x2]
        contours_crop = cv2.findContours(
            inst_map_crop, cv2.RETR_TREE, cv2.CHAIN_APPROX_SIMPLE
        )
        # only has 1 instance per map, no need to check #contour detected by opencv
        contours_crop = np.squeeze(
            contours_crop[0][0].astype("int32")
        )  # * opencv protocol format may break
        contours_crop += np.asarray([[x1, y1]])  # index correction
        if type_map is not None:
            type_map_crop = type_map[y1:y2, x1:x2]
            type_id = np.unique(type_map_crop).max()  # non-zero
            inst_colour = type_colour[type_id]
        else:
            inst_colour = (inst_rng_colors[inst_idx]).tolist()
        cv2.drawContours(overlay, [contours_crop], -1, inst_colour, line_thickness)
    return overlay


def sliding_window_inference(
    inputs: torch.Tensor,
    roi_size: Union[Sequence[int], int],
    sw_batch_size: int,
    predictor: Callable[..., Union[torch.Tensor, Sequence[torch.Tensor], Dict[Any, torch.Tensor]]],
    overlap: float = 0.25,
    mode: Union[BlendMode, str] = BlendMode.CONSTANT,
    sigma_scale: Union[Sequence[float], float] = 0.125,
    padding_mode: Union[PytorchPadMode, str] = PytorchPadMode.CONSTANT,
    cval: float = 0.0,
    sw_device: Union[torch.device, str, None] = None,
    device: Union[torch.device, str, None] = None,
    progress: bool = False,
    roi_weight_map: Union[torch.Tensor, None] = None,
    *args: Any,
    **kwargs: Any,
) -> Union[torch.Tensor, Tuple[torch.Tensor, ...], Dict[Any, torch.Tensor]]:
    """
    Sliding window inference on `inputs` with `predictor`.

    The outputs of `predictor` could be a tensor, a tuple, or a dictionary of tensors.
    Each output in the tuple or dict value is allowed to have different resolutions with respect to the input.
    e.g., the input patch spatial size is [128,128,128], the output (a tuple of two patches) patch sizes
    could be ([128,64,256], [64,32,128]).
    In this case, the parameter `overlap` and `roi_size` need to be carefully chosen to ensure the output ROI is still
    an integer. If the predictor's input and output spatial sizes are not equal, we recommend choosing the parameters
    so that `overlap*roi_size*output_size/input_size` is an integer (for each spatial dimension).

    When roi_size is larger than the inputs' spatial size, the input image are padded during inference.
    To maintain the same spatial sizes, the output image will be cropped to the original input size.

    Args:
        inputs: input image to be processed (assuming NCHW[D])
        roi_size: the spatial window size for inferences.
            When its components have None or non-positives, the corresponding inputs dimension will be used.
            if the components of the `roi_size` are non-positive values, the transform will use the
            corresponding components of img size. For example, `roi_size=(32, -1)` will be adapted
            to `(32, 64)` if the second spatial dimension size of img is `64`.
        sw_batch_size: the batch size to run window slices.
        predictor: given input tensor ``patch_data`` in shape NCHW[D],
            The outputs of the function call ``predictor(patch_data)`` should be a tensor, a tuple, or a dictionary
            with Tensor values. Each output in the tuple or dict value should have the same batch_size, i.e. NM'H'W'[D'];
            where H'W'[D'] represents the output patch's spatial size, M is the number of output channels,
            N is `sw_batch_size`, e.g., the input shape is (7, 1, 128,128,128),
            the output could be a tuple of two tensors, with shapes: ((7, 5, 128, 64, 256), (7, 4, 64, 32, 128)).
            In this case, the parameter `overlap` and `roi_size` need to be carefully chosen
            to ensure the scaled output ROI sizes are still integers.
            If the `predictor`'s input and output spatial sizes are different,
            we recommend choosing the parameters so that ``overlap*roi_size*zoom_scale`` is an integer for each dimension.
        overlap: Amount of overlap between scans.
        mode: {``"constant"``, ``"gaussian"``}
            How to blend output of overlapping windows. Defaults to ``"constant"``.

            - ``"constant``": gives equal weight to all predictions.
            - ``"gaussian``": gives less weight to predictions on edges of windows.

        sigma_scale: the standard deviation coefficient of the Gaussian window when `mode` is ``"gaussian"``.
            Default: 0.125. Actual window sigma is ``sigma_scale`` * ``dim_size``.
            When sigma_scale is a sequence of floats, the values denote sigma_scale at the corresponding
            spatial dimensions.
        padding_mode: {``"constant"``, ``"reflect"``, ``"replicate"``, ``"circular"``}
            Padding mode for ``inputs``, when ``roi_size`` is larger than inputs. Defaults to ``"constant"``
            See also: https://pytorch.org/docs/stable/generated/torch.nn.functional.pad.html
        cval: fill value for 'constant' padding mode. Default: 0
        sw_device: device for the window data.
            By default the device (and accordingly the memory) of the `inputs` is used.
            Normally `sw_device` should be consistent with the device where `predictor` is defined.
        device: device for the stitched output prediction.
            By default the device (and accordingly the memory) of the `inputs` is used. If for example
            set to device=torch.device('cpu') the gpu memory consumption is less and independent of the
            `inputs` and `roi_size`. Output is on the `device`.
        progress: whether to print a `tqdm` progress bar.
        roi_weight_map: pre-computed (non-negative) weight map for each ROI.
            If not given, and ``mode`` is not `constant`, this map will be computed on the fly.
        args: optional args to be passed to ``predictor``.
        kwargs: optional keyword args to be passed to ``predictor``.

    Note:
        - input must be channel-first and have a batch dim, supports N-D sliding window.

    """
    compute_dtype = inputs.dtype
    num_spatial_dims = len(inputs.shape) - 2
    if overlap < 0 or overlap >= 1:
        raise ValueError("overlap must be >= 0 and < 1.")

    # determine image spatial size and batch size
    # Note: all input images must have the same image size and batch size
    batch_size, _, *image_size_ = inputs.shape

    if device is None:
        device = inputs.device
    if sw_device is None:
        sw_device = inputs.device

    roi_size = fall_back_tuple(roi_size, image_size_)
    # in case that image size is smaller than roi size
    image_size = tuple(max(image_size_[i], roi_size[i]) for i in range(num_spatial_dims))
    pad_size = []
    for k in range(len(inputs.shape) - 1, 1, -1):
        diff = max(roi_size[k - 2] - inputs.shape[k], 0)
        half = diff // 2
        pad_size.extend([half, diff - half])
    inputs = F.pad(inputs, pad=pad_size, mode=look_up_option(padding_mode, PytorchPadMode), value=cval)

    scan_interval = _get_scan_interval(image_size, roi_size, num_spatial_dims, overlap)

    # Store all slices in list
    slices = dense_patch_slices(image_size, roi_size, scan_interval)
    num_win = len(slices)  # number of windows per image
    total_slices = num_win * batch_size  # total number of windows

    # Create window-level importance map
    valid_patch_size = get_valid_patch_size(image_size, roi_size)
    if valid_patch_size == roi_size and (roi_weight_map is not None):
        importance_map = roi_weight_map
    else:
        try:
            importance_map = compute_importance_map(valid_patch_size, mode=mode, sigma_scale=sigma_scale, device=device)
        except BaseException as e:
            raise RuntimeError(
                "Seems to be OOM. Please try smaller patch size or mode='constant' instead of mode='gaussian'."
            ) from e
    importance_map = convert_data_type(importance_map, torch.Tensor, device, compute_dtype)[0]  # type: ignore
    # handle non-positive weights
    min_non_zero = max(importance_map[importance_map != 0].min().item(), 1e-3)
    importance_map = torch.clamp(importance_map.to(torch.float32), min=min_non_zero).to(compute_dtype)

    # Perform predictions
    dict_key, output_image_list, count_map_list = None, [], []
    _initialized_ss = -1
    is_tensor_output = True  # whether the predictor's output is a tensor (instead of dict/tuple)

    # for each patch
    for slice_g in tqdm(range(0, total_slices, sw_batch_size)) if progress else range(0, total_slices, sw_batch_size):
        slice_range = range(slice_g, min(slice_g + sw_batch_size, total_slices))
        unravel_slice = [
            [slice(int(idx / num_win), int(idx / num_win) + 1), slice(None)] + list(slices[idx % num_win])
            for idx in slice_range
        ]
        window_data = torch.cat(
            [convert_data_type(inputs[win_slice], torch.Tensor)[0] for win_slice in unravel_slice]
        ).to(sw_device)
        seg_prob_out = predictor(window_data, *args, **kwargs)  # batched patch segmentation

        # convert seg_prob_out to tuple seg_prob_tuple, this does not allocate new memory.
        seg_prob_tuple: Tuple[torch.Tensor, ...]
        if isinstance(seg_prob_out, torch.Tensor):
            seg_prob_tuple = (seg_prob_out,)
        elif isinstance(seg_prob_out, Mapping):
            if dict_key is None:
                dict_key = sorted(seg_prob_out.keys())  # track predictor's output keys
            seg_prob_tuple = tuple(seg_prob_out[k] for k in dict_key)
            is_tensor_output = False
        else:
            seg_prob_tuple = ensure_tuple(seg_prob_out)
            is_tensor_output = False

        # for each output in multi-output list
        for ss, seg_prob in enumerate(seg_prob_tuple):
            seg_prob = seg_prob.to(device)  # BxCxMxNxP or BxCxMxN

            # compute zoom scale: out_roi_size/in_roi_size
            zoom_scale = []
            for axis, (img_s_i, out_w_i, in_w_i) in enumerate(
                zip(image_size, seg_prob.shape[2:], window_data.shape[2:])
            ):
                _scale = out_w_i / float(in_w_i)
                if not (img_s_i * _scale).is_integer():
                    warnings.warn(
                        f"For spatial axis: {axis}, output[{ss}] will have non-integer shape. Spatial "
                        f"zoom_scale between output[{ss}] and input is {_scale}. Please pad inputs."
                    )
                zoom_scale.append(_scale)

            if _initialized_ss < ss:  # init. the ss-th buffer at the first iteration
                # construct multi-resolution outputs
                output_classes = seg_prob.shape[1]
                output_shape = [batch_size, output_classes] + [
                    int(image_size_d * zoom_scale_d) for image_size_d, zoom_scale_d in zip(image_size, zoom_scale)
                ]
                # allocate memory to store the full output and the count for overlapping parts
                output_image_list.append(torch.zeros(output_shape, dtype=compute_dtype, device='cpu'))
                count_map_list.append(torch.zeros([1, 1] + output_shape[2:], dtype=compute_dtype, device='cpu'))
                _initialized_ss += 1

            # resizing the importance_map
            resizer = Resize(spatial_size=seg_prob.shape[2:], mode="nearest", anti_aliasing=False)

            # store the result in the proper location of the full output. Apply weights from importance map.
            for idx, original_idx in zip(slice_range, unravel_slice):
                # zoom roi
                original_idx_zoom = list(original_idx)  # 4D for 2D image, 5D for 3D image
                for axis in range(2, len(original_idx_zoom)):
                    zoomed_start = original_idx[axis].start * zoom_scale[axis - 2]
                    zoomed_end = original_idx[axis].stop * zoom_scale[axis - 2]
                    if not zoomed_start.is_integer() or (not zoomed_end.is_integer()):
                        warnings.warn(
                            f"For axis-{axis-2} of output[{ss}], the output roi range is not int. "
                            f"Input roi range is ({original_idx[axis].start}, {original_idx[axis].stop}). "
                            f"Spatial zoom_scale between output[{ss}] and input is {zoom_scale[axis - 2]}. "
                            f"Corresponding output roi range is ({zoomed_start}, {zoomed_end}).\n"
                            f"Please change overlap ({overlap}) or roi_size ({roi_size[axis-2]}) for axis-{axis-2}. "
                            "Tips: if overlap*roi_size*zoom_scale is an integer, it usually works."
                        )
                    original_idx_zoom[axis] = slice(int(zoomed_start), int(zoomed_end), None)
                importance_map_zoom = resizer(importance_map.unsqueeze(0))[0].to(compute_dtype)
                # store results and weights
                #print(output_image_list[ss][original_idx_zoom].device,importance_map_zoom.cpu().device,seg_prob.cpu().device)
                output_image_list[ss][original_idx_zoom] += importance_map_zoom.cpu() * seg_prob[idx - slice_g].cpu()
                count_map_list[ss][original_idx_zoom] += (
                    importance_map_zoom.unsqueeze(0).unsqueeze(0).expand(count_map_list[ss][original_idx_zoom].shape).cpu()
                )

    # account for any overlapping sections
    for ss in range(len(output_image_list)):
        output_image_list[ss] = (output_image_list[ss] / count_map_list.pop(0)).to(compute_dtype)

    # remove padding if image_size smaller than roi_size
    for ss, output_i in enumerate(output_image_list):
        if torch.isnan(output_i).any() or torch.isinf(output_i).any():
            warnings.warn("Sliding window inference results contain NaN or Inf.")

        zoom_scale = [
            seg_prob_map_shape_d / roi_size_d for seg_prob_map_shape_d, roi_size_d in zip(output_i.shape[2:], roi_size)
        ]

        final_slicing: List[slice] = []
        for sp in range(num_spatial_dims):
            slice_dim = slice(pad_size[sp * 2], image_size_[num_spatial_dims - sp - 1] + pad_size[sp * 2])
            slice_dim = slice(
                int(round(slice_dim.start * zoom_scale[num_spatial_dims - sp - 1])),
                int(round(slice_dim.stop * zoom_scale[num_spatial_dims - sp - 1])),
            )
            final_slicing.insert(0, slice_dim)
        while len(final_slicing) < len(output_i.shape):
            final_slicing.insert(0, slice(None))
        output_image_list[ss] = output_i[final_slicing]

    if dict_key is not None:  # if output of predictor is a dict
        final_output = dict(zip(dict_key, output_image_list))
    else:
        final_output = tuple(output_image_list)  # type: ignore
    final_output = final_output[0] if is_tensor_output else final_output  # type: ignore
    if isinstance(inputs, MetaTensor):
        final_output = convert_to_dst_type(final_output, inputs)[0]  # type: ignore
    return final_output


def _get_scan_interval(
    image_size: Sequence[int], roi_size: Sequence[int], num_spatial_dims: int, overlap: float
) -> Tuple[int, ...]:
    """
    Compute scan interval according to the image size, roi size and overlap.
    Scan interval will be `int((1 - overlap) * roi_size)`, if interval is 0,
    use 1 instead to make sure sliding window works.

    """
    if len(image_size) != num_spatial_dims:
        raise ValueError("image coord different from spatial dims.")
    if len(roi_size) != num_spatial_dims:
        raise ValueError("roi coord different from spatial dims.")

    scan_interval = []
    for i in range(num_spatial_dims):
        if roi_size[i] == image_size[i]:
            scan_interval.append(int(roi_size[i]))
        else:
            interval = int(roi_size[i] * (1 - overlap))
            scan_interval.append(interval if interval > 0 else 1)
    return tuple(scan_interval)