slic_superpixels.py

import math
from collections.abc import Iterable
from warnings import warn

import numpy as np
from numpy import random
from scipy.cluster.vq import kmeans2
from scipy.spatial.distance import pdist, squareform

from .._shared import utils
from .._shared.filters import gaussian
from ..color import rgb2lab
from ..util import img_as_float, regular_grid
from ._slic import _enforce_label_connectivity_cython, _slic_cython


def _get_mask_centroids(mask, n_centroids, multichannel):
    """Find regularly spaced centroids on a mask.

    Parameters
    ----------
    mask : 3D ndarray
        The mask within which the centroids must be positioned.
    n_centroids : int
        The number of centroids to be returned.

    Returns
    -------
    centroids : 2D ndarray
        The coordinates of the centroids with shape (n_centroids, 3).
    steps : 1D ndarray
        The approximate distance between two seeds in all dimensions.

    """

    # Get tight ROI around the mask to optimize
    coord = np.array(np.nonzero(mask), dtype=float).T
    # Fix random seed to ensure repeatability
    # Keep old-style RandomState here as expected results in tests depend on it
    rng = random.RandomState(123)

    # select n_centroids randomly distributed points from within the mask
    idx_full = np.arange(len(coord), dtype=int)
    idx = np.sort(rng.choice(idx_full, min(n_centroids, len(coord)), replace=False))

    # To save time, when n_centroids << len(coords), use only a subset of the
    # coordinates when calling k-means. Rather than the full set of coords,
    # we will use a substantially larger subset than n_centroids. Here we
    # somewhat arbitrarily choose dense_factor=10 to make the samples
    # 10 times closer together along each axis than the n_centroids samples.
    dense_factor = 10
    ndim_spatial = mask.ndim - 1 if multichannel else mask.ndim
    n_dense = int((dense_factor**ndim_spatial) * n_centroids)
    if len(coord) > n_dense:
        # subset of points to use for the k-means calculation
        # (much denser than idx, but less than the full set)
        idx_dense = np.sort(rng.choice(idx_full, n_dense, replace=False))
    else:
        idx_dense = Ellipsis
    centroids, _ = kmeans2(coord[idx_dense], coord[idx], iter=5)

    # Compute the minimum distance of each centroid to the others
    dist = squareform(pdist(centroids))
    np.fill_diagonal(dist, np.inf)
    closest_pts = dist.argmin(-1)
    steps = abs(centroids - centroids[closest_pts, :]).mean(0)

    return centroids, steps


def _get_grid_centroids(image, n_centroids):
    """Find regularly spaced centroids on the image.

    Parameters
    ----------
    image : 2D, 3D or 4D ndarray
        Input image, which can be 2D or 3D, and grayscale or
        multichannel.
    n_centroids : int
        The (approximate) number of centroids to be returned.

    Returns
    -------
    centroids : 2D ndarray
        The coordinates of the centroids with shape (~n_centroids, 3).
    steps : 1D ndarray
        The approximate distance between two seeds in all dimensions.

    """
    d, h, w = image.shape[:3]

    grid_z, grid_y, grid_x = np.mgrid[:d, :h, :w]
    slices = regular_grid(image.shape[:3], n_centroids)

    centroids_z = grid_z[slices].ravel()[..., np.newaxis]
    centroids_y = grid_y[slices].ravel()[..., np.newaxis]
    centroids_x = grid_x[slices].ravel()[..., np.newaxis]

    centroids = np.concatenate([centroids_z, centroids_y, centroids_x], axis=-1)

    steps = np.asarray([float(s.step) if s.step is not None else 1.0 for s in slices])
    return centroids, steps


@utils.channel_as_last_axis(multichannel_output=False)
def slic(
    image,
    n_segments=100,
    compactness=10.0,
    max_num_iter=10,
    sigma=0,
    spacing=None,
    convert2lab=None,
    enforce_connectivity=True,
    min_size_factor=0.5,
    max_size_factor=3,
    slic_zero=False,
    start_label=1,
    mask=None,
    *,
    channel_axis=-1,
):
    """Segments image using k-means clustering in Color-(x,y,z) space.

    Parameters
    ----------
    image : (M, N[, P][, C]) ndarray
        Input image. Can be 2D or 3D, and grayscale or multichannel
        (see `channel_axis` parameter).
        Input image must either be NaN-free or the NaN's must be masked out.
    n_segments : int, optional
        The (approximate) number of labels in the segmented output image.
    compactness : float, optional
        Balances color proximity and space proximity. Higher values give
        more weight to space proximity, making superpixel shapes more
        square/cubic. In SLICO mode, this is the initial compactness.
        This parameter depends strongly on image contrast and on the
        shapes of objects in the image. We recommend exploring possible
        values on a log scale, e.g., 0.01, 0.1, 1, 10, 100, before
        refining around a chosen value.
    max_num_iter : int, optional
        Maximum number of iterations of k-means.
    sigma : float or array-like of floats, optional
        Width of Gaussian smoothing kernel for pre-processing for each
        dimension of the image. The same sigma is applied to each dimension in
        case of a scalar value. Zero means no smoothing.
        Note that `sigma` is automatically scaled if it is scalar and
        if a manual voxel spacing is provided (see Notes section). If
        sigma is array-like, its size must match ``image``'s number
        of spatial dimensions.
    spacing : array-like of floats, optional
        The voxel spacing along each spatial dimension. By default,
        `slic` assumes uniform spacing (same voxel resolution along
        each spatial dimension).
        This parameter controls the weights of the distances along the
        spatial dimensions during k-means clustering.
    convert2lab : bool, optional
        Whether the input should be converted to Lab colorspace prior to
        segmentation. The input image *must* be RGB. Highly recommended.
        This option defaults to ``True`` when ``channel_axis` is not None *and*
        ``image.shape[-1] == 3``.
    enforce_connectivity : bool, optional
        Whether the generated segments are connected or not
    min_size_factor : float, optional
        Proportion of the minimum segment size to be removed with respect
        to the supposed segment size ```depth*width*height/n_segments```
    max_size_factor : float, optional
        Proportion of the maximum connected segment size. A value of 3 works
        in most of the cases.
    slic_zero : bool, optional
        Run SLIC-zero, the zero-parameter mode of SLIC. [2]_
    start_label : int, optional
        The labels' index start. Should be 0 or 1.

        .. versionadded:: 0.17
           ``start_label`` was introduced in 0.17
    mask : ndarray, optional
        If provided, superpixels are computed only where mask is True,
        and seed points are homogeneously distributed over the mask
        using a k-means clustering strategy. Mask number of dimensions
        must be equal to image number of spatial dimensions.

        .. versionadded:: 0.17
           ``mask`` was introduced in 0.17
    channel_axis : int or None, optional
        If None, the image is assumed to be a grayscale (single channel) image.
        Otherwise, this parameter indicates which axis of the array corresponds
        to channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    labels : 2D or 3D array
        Integer mask indicating segment labels.

    Raises
    ------
    ValueError
        If ``convert2lab`` is set to ``True`` but the last array
        dimension is not of length 3.
    ValueError
        If ``start_label`` is not 0 or 1.
    ValueError
        If ``image`` contains unmasked NaN values.
    ValueError
        If ``image`` contains unmasked infinite values.
    ValueError
        If ``image`` is 2D but ``channel_axis`` is -1 (the default).

    Notes
    -----
    * If `sigma > 0`, the image is smoothed using a Gaussian kernel prior to
      segmentation.

    * If `sigma` is scalar and `spacing` is provided, the kernel width is
      divided along each dimension by the spacing. For example, if ``sigma=1``
      and ``spacing=[5, 1, 1]``, the effective `sigma` is ``[0.2, 1, 1]``. This
      ensures sensible smoothing for anisotropic images.

    * The image is rescaled to be in [0, 1] prior to processing (masked
      values are ignored).

    * Images of shape (M, N, 3) are interpreted as 2D RGB images by default. To
      interpret them as 3D with the last dimension having length 3, use
      `channel_axis=None`.

    * `start_label` is introduced to handle the issue [4]_. Label indexing
      starts at 1 by default.

    References
    ----------
    .. [1] Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi,
        Pascal Fua, and Sabine Süsstrunk, SLIC Superpixels Compared to
        State-of-the-art Superpixel Methods, TPAMI, May 2012.
        :DOI:`10.1109/TPAMI.2012.120`
    .. [2] https://www.epfl.ch/labs/ivrl/research/slic-superpixels/#SLICO
    .. [3] Irving, Benjamin. "maskSLIC: regional superpixel generation with
           application to local pathology characterisation in medical images.",
           2016, :arXiv:`1606.09518`
    .. [4] https://github.com/scikit-image/scikit-image/issues/3722

    Examples
    --------
    >>> from skimage.segmentation import slic
    >>> from skimage.data import astronaut
    >>> img = astronaut()
    >>> segments = slic(img, n_segments=100, compactness=10)

    Increasing the compactness parameter yields more square regions:

    >>> segments = slic(img, n_segments=100, compactness=20)

    """
    if image.ndim == 2 and channel_axis is not None:
        raise ValueError(
            f"channel_axis={channel_axis} indicates multichannel, which is not "
            "supported for a two-dimensional image; use channel_axis=None if "
            "the image is grayscale"
        )

    image = img_as_float(image)
    float_dtype = utils._supported_float_type(image.dtype)
    # copy=True so subsequent in-place operations do not modify the
    # function input
    image = image.astype(float_dtype, copy=True)

    if mask is not None:
        # Create masked_image to rescale while ignoring masked values
        mask = np.ascontiguousarray(mask, dtype=bool)
        if channel_axis is not None:
            mask_ = np.expand_dims(mask, axis=channel_axis)
            mask_ = np.broadcast_to(mask_, image.shape)
        else:
            mask_ = mask
        image_values = image[mask_]
    else:
        image_values = image

    # Rescale image to [0, 1] to make choice of compactness insensitive to
    # input image scale.
    imin = image_values.min()
    imax = image_values.max()
    if np.isnan(imin):
        raise ValueError("unmasked NaN values in image are not supported")
    if np.isinf(imin) or np.isinf(imax):
        raise ValueError("unmasked infinite values in image are not supported")
    image -= imin
    if imax != imin:
        image /= imax - imin

    use_mask = mask is not None
    dtype = image.dtype

    is_2d = False

    multichannel = channel_axis is not None
    if image.ndim == 2:
        # 2D grayscale image
        image = image[np.newaxis, ..., np.newaxis]
        is_2d = True
    elif image.ndim == 3 and multichannel:
        # Make 2D multichannel image 3D with depth = 1
        image = image[np.newaxis, ...]
        is_2d = True
    elif image.ndim == 3 and not multichannel:
        # Add channel as single last dimension
        image = image[..., np.newaxis]

    if multichannel and (convert2lab or convert2lab is None):
        if image.shape[channel_axis] != 3 and convert2lab:
            raise ValueError("Lab colorspace conversion requires a RGB image.")
        elif image.shape[channel_axis] == 3:
            image = rgb2lab(image)

    if start_label not in [0, 1]:
        raise ValueError("start_label should be 0 or 1.")

    # initialize cluster centroids for desired number of segments
    update_centroids = False
    if use_mask:
        mask = mask.view('uint8')
        if mask.ndim == 2:
            mask = np.ascontiguousarray(mask[np.newaxis, ...])
        if mask.shape != image.shape[:3]:
            raise ValueError("image and mask should have the same shape.")
        centroids, steps = _get_mask_centroids(mask, n_segments, multichannel)
        update_centroids = True
    else:
        centroids, steps = _get_grid_centroids(image, n_segments)

    if spacing is None:
        spacing = np.ones(3, dtype=dtype)
    elif isinstance(spacing, Iterable):
        spacing = np.asarray(spacing, dtype=dtype)
        if is_2d:
            if spacing.size != 2:
                if spacing.size == 3:
                    warn(
                        "Input image is 2D: spacing number of "
                        "elements must be 2. In the future, a ValueError "
                        "will be raised.",
                        FutureWarning,
                        stacklevel=2,
                    )
                else:
                    raise ValueError(
                        f"Input image is 2D, but spacing has "
                        f"{spacing.size} elements (expected 2)."
                    )
            else:
                spacing = np.insert(spacing, 0, 1)
        elif spacing.size != 3:
            raise ValueError(
                f"Input image is 3D, but spacing has "
                f"{spacing.size} elements (expected 3)."
            )
        spacing = np.ascontiguousarray(spacing, dtype=dtype)
    else:
        raise TypeError("spacing must be None or iterable.")

    if np.isscalar(sigma):
        sigma = np.array([sigma, sigma, sigma], dtype=dtype)
        sigma /= spacing
    elif isinstance(sigma, Iterable):
        sigma = np.asarray(sigma, dtype=dtype)
        if is_2d:
            if sigma.size != 2:
                if spacing.size == 3:
                    warn(
                        "Input image is 2D: sigma number of "
                        "elements must be 2. In the future, a ValueError "
                        "will be raised.",
                        FutureWarning,
                        stacklevel=2,
                    )
                else:
                    raise ValueError(
                        f"Input image is 2D, but sigma has "
                        f"{sigma.size} elements (expected 2)."
                    )
            else:
                sigma = np.insert(sigma, 0, 0)
        elif sigma.size != 3:
            raise ValueError(
                f"Input image is 3D, but sigma has "
                f"{sigma.size} elements (expected 3)."
            )

    if (sigma > 0).any():
        # add zero smoothing for channel dimension
        sigma = list(sigma) + [0]
        image = gaussian(image, sigma=sigma, mode='reflect')

    n_centroids = centroids.shape[0]
    segments = np.ascontiguousarray(
        np.concatenate([centroids, np.zeros((n_centroids, image.shape[3]))], axis=-1),
        dtype=dtype,
    )

    # Scaling of ratio in the same way as in the SLIC paper so the
    # values have the same meaning
    step = max(steps)
    ratio = 1.0 / compactness

    image = np.ascontiguousarray(image * ratio, dtype=dtype)

    if update_centroids:
        # Step 2 of the algorithm [3]_
        _slic_cython(
            image,
            mask,
            segments,
            step,
            max_num_iter,
            spacing,
            slic_zero,
            ignore_color=True,
            start_label=start_label,
        )

    labels = _slic_cython(
        image,
        mask,
        segments,
        step,
        max_num_iter,
        spacing,
        slic_zero,
        ignore_color=False,
        start_label=start_label,
    )

    if enforce_connectivity:
        if use_mask:
            segment_size = mask.sum() / n_centroids
        else:
            segment_size = math.prod(image.shape[:3]) / n_centroids
        min_size = int(min_size_factor * segment_size)
        max_size = int(max_size_factor * segment_size)
        labels = _enforce_label_connectivity_cython(
            labels, min_size, max_size, start_label=start_label
        )

    if is_2d:
        labels = labels[0]

    return labels