import numpy as np from scipy import ndimage as ndi from ._geometric import (SimilarityTransform, AffineTransform, ProjectiveTransform) from ._warps_cy import _warp_fast from ..measure import block_reduce from .._shared.utils import (get_bound_method_class, safe_as_int, warn, convert_to_float, _to_ndimage_mode, _validate_interpolation_order, channel_as_last_axis) HOMOGRAPHY_TRANSFORMS = ( SimilarityTransform, AffineTransform, ProjectiveTransform ) def _preprocess_resize_output_shape(image, output_shape): """Validate resize output shape according to input image. Parameters ---------- image: ndarray Image to be resized. output_shape: iterable Size of the generated output image `(rows, cols[, ...][, dim])`. If `dim` is not provided, the number of channels is preserved. Returns ------- image: ndarray The input image, but with additional singleton dimensions appended in the case where ``len(output_shape) > input.ndim``. output_shape: tuple The output image converted to tuple. Raises ------ ValueError: If output_shape length is smaller than the image number of dimensions Notes ----- The input image is reshaped if its number of dimensions is not equal to output_shape_length. """ output_shape = tuple(output_shape) output_ndim = len(output_shape) input_shape = image.shape if output_ndim > image.ndim: # append dimensions to input_shape input_shape += (1, ) * (output_ndim - image.ndim) image = np.reshape(image, input_shape) elif output_ndim == image.ndim - 1: # multichannel case: append shape of last axis output_shape = output_shape + (image.shape[-1], ) elif output_ndim < image.ndim: raise ValueError("output_shape length cannot be smaller than the " "image number of dimensions") return image, output_shape def resize(image, output_shape, order=None, mode='reflect', cval=0, clip=True, preserve_range=False, anti_aliasing=None, anti_aliasing_sigma=None): """Resize image to match a certain size. Performs interpolation to up-size or down-size N-dimensional images. Note that anti-aliasing should be enabled when down-sizing images to avoid aliasing artifacts. For downsampling with an integer factor also see `skimage.transform.downscale_local_mean`. Parameters ---------- image : ndarray Input image. output_shape : iterable Size of the generated output image `(rows, cols[, ...][, dim])`. If `dim` is not provided, the number of channels is preserved. In case the number of input channels does not equal the number of output channels a n-dimensional interpolation is applied. Returns ------- resized : ndarray Resized version of the input. Other parameters ---------------- order : int, optional The order of the spline interpolation, default is 0 if image.dtype is bool and 1 otherwise. The order has to be in the range 0-5. See `skimage.transform.warp` for detail. mode : {'constant', 'edge', 'symmetric', 'reflect', 'wrap'}, optional Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of `numpy.pad`. cval : float, optional Used in conjunction with mode 'constant', the value outside the image boundaries. clip : bool, optional Whether to clip the output to the range of values of the input image. This is enabled by default, since higher order interpolation may produce values outside the given input range. preserve_range : bool, optional Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of `img_as_float`. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html anti_aliasing : bool, optional Whether to apply a Gaussian filter to smooth the image prior to downsampling. It is crucial to filter when downsampling the image to avoid aliasing artifacts. If not specified, it is set to True when downsampling an image whose data type is not bool. It is also set to False when using nearest neighbor interpolation (``order`` == 0) with integer input data type. anti_aliasing_sigma : {float, tuple of floats}, optional Standard deviation for Gaussian filtering used when anti-aliasing. By default, this value is chosen as (s - 1) / 2 where s is the downsampling factor, where s > 1. For the up-size case, s < 1, no anti-aliasing is performed prior to rescaling. Notes ----- Modes 'reflect' and 'symmetric' are similar, but differ in whether the edge pixels are duplicated during the reflection. As an example, if an array has values [0, 1, 2] and was padded to the right by four values using symmetric, the result would be [0, 1, 2, 2, 1, 0, 0], while for reflect it would be [0, 1, 2, 1, 0, 1, 2]. Examples -------- >>> from skimage import data >>> from skimage.transform import resize >>> image = data.camera() >>> resize(image, (100, 100)).shape (100, 100) """ image, output_shape = _preprocess_resize_output_shape(image, output_shape) input_shape = image.shape input_type = image.dtype if input_type == np.float16: image = image.astype(np.float32) if anti_aliasing is None: anti_aliasing = ( not input_type == bool and not (np.issubdtype(input_type, np.integer) and order == 0) and any(x < y for x, y in zip(output_shape, input_shape))) if input_type == bool and anti_aliasing: raise ValueError("anti_aliasing must be False for boolean images") factors = np.divide(input_shape, output_shape) order = _validate_interpolation_order(input_type, order) if order > 0: image = convert_to_float(image, preserve_range) # Save input value range for clip img_bounds = np.array([image.min(), image.max()]) if clip else None # Translate modes used by np.pad to those used by scipy.ndimage ndi_mode = _to_ndimage_mode(mode) if anti_aliasing: if anti_aliasing_sigma is None: anti_aliasing_sigma = np.maximum(0, (factors - 1) / 2) else: anti_aliasing_sigma = \ np.atleast_1d(anti_aliasing_sigma) * np.ones_like(factors) if np.any(anti_aliasing_sigma < 0): raise ValueError("Anti-aliasing standard deviation must be " "greater than or equal to zero") elif np.any((anti_aliasing_sigma > 0) & (factors <= 1)): warn("Anti-aliasing standard deviation greater than zero but " "not down-sampling along all axes") image = ndi.gaussian_filter(image, anti_aliasing_sigma, cval=cval, mode=ndi_mode) zoom_factors = [1 / f for f in factors] out = ndi.zoom(image, zoom_factors, order=order, mode=ndi_mode, cval=cval, grid_mode=True) _clip_warp_output(img_bounds, out, mode, cval, clip) return out @channel_as_last_axis() def rescale(image, scale, order=None, mode='reflect', cval=0, clip=True, preserve_range=False, anti_aliasing=None, anti_aliasing_sigma=None, *, channel_axis=None): """Scale image by a certain factor. Performs interpolation to up-scale or down-scale N-dimensional images. Note that anti-aliasing should be enabled when down-sizing images to avoid aliasing artifacts. For down-sampling with an integer factor also see `skimage.transform.downscale_local_mean`. Parameters ---------- image : ndarray Input image. scale : {float, tuple of floats} Scale factors. Separate scale factors can be defined as `(rows, cols[, ...][, dim])`. Returns ------- scaled : ndarray Scaled version of the input. Other parameters ---------------- order : int, optional The order of the spline interpolation, default is 0 if image.dtype is bool and 1 otherwise. The order has to be in the range 0-5. See `skimage.transform.warp` for detail. mode : {'constant', 'edge', 'symmetric', 'reflect', 'wrap'}, optional Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of `numpy.pad`. cval : float, optional Used in conjunction with mode 'constant', the value outside the image boundaries. clip : bool, optional Whether to clip the output to the range of values of the input image. This is enabled by default, since higher order interpolation may produce values outside the given input range. preserve_range : bool, optional Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of `img_as_float`. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html anti_aliasing : bool, optional Whether to apply a Gaussian filter to smooth the image prior to down-scaling. It is crucial to filter when down-sampling the image to avoid aliasing artifacts. If input image data type is bool, no anti-aliasing is applied. anti_aliasing_sigma : {float, tuple of floats}, optional Standard deviation for Gaussian filtering to avoid aliasing artifacts. By default, this value is chosen as (s - 1) / 2 where s is the down-scaling factor. 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. Notes ----- Modes 'reflect' and 'symmetric' are similar, but differ in whether the edge pixels are duplicated during the reflection. As an example, if an array has values [0, 1, 2] and was padded to the right by four values using symmetric, the result would be [0, 1, 2, 2, 1, 0, 0], while for reflect it would be [0, 1, 2, 1, 0, 1, 2]. Examples -------- >>> from skimage import data >>> from skimage.transform import rescale >>> image = data.camera() >>> rescale(image, 0.1).shape (51, 51) >>> rescale(image, 0.5).shape (256, 256) """ scale = np.atleast_1d(scale) multichannel = channel_axis is not None if len(scale) > 1: if ((not multichannel and len(scale) != image.ndim) or (multichannel and len(scale) != image.ndim - 1)): raise ValueError("Supply a single scale, or one value per spatial " "axis") if multichannel: scale = np.concatenate((scale, [1])) orig_shape = np.asarray(image.shape) output_shape = np.maximum(np.round(scale * orig_shape), 1) if multichannel: # don't scale channel dimension output_shape[-1] = orig_shape[-1] return resize(image, output_shape, order=order, mode=mode, cval=cval, clip=clip, preserve_range=preserve_range, anti_aliasing=anti_aliasing, anti_aliasing_sigma=anti_aliasing_sigma) def rotate(image, angle, resize=False, center=None, order=None, mode='constant', cval=0, clip=True, preserve_range=False): """Rotate image by a certain angle around its center. Parameters ---------- image : ndarray Input image. angle : float Rotation angle in degrees in counter-clockwise direction. resize : bool, optional Determine whether the shape of the output image will be automatically calculated, so the complete rotated image exactly fits. Default is False. center : iterable of length 2 The rotation center. If ``center=None``, the image is rotated around its center, i.e. ``center=(cols / 2 - 0.5, rows / 2 - 0.5)``. Please note that this parameter is (cols, rows), contrary to normal skimage ordering. Returns ------- rotated : ndarray Rotated version of the input. Other parameters ---------------- order : int, optional The order of the spline interpolation, default is 0 if image.dtype is bool and 1 otherwise. The order has to be in the range 0-5. See `skimage.transform.warp` for detail. mode : {'constant', 'edge', 'symmetric', 'reflect', 'wrap'}, optional Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of `numpy.pad`. cval : float, optional Used in conjunction with mode 'constant', the value outside the image boundaries. clip : bool, optional Whether to clip the output to the range of values of the input image. This is enabled by default, since higher order interpolation may produce values outside the given input range. preserve_range : bool, optional Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of `img_as_float`. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html Notes ----- Modes 'reflect' and 'symmetric' are similar, but differ in whether the edge pixels are duplicated during the reflection. As an example, if an array has values [0, 1, 2] and was padded to the right by four values using symmetric, the result would be [0, 1, 2, 2, 1, 0, 0], while for reflect it would be [0, 1, 2, 1, 0, 1, 2]. Examples -------- >>> from skimage import data >>> from skimage.transform import rotate >>> image = data.camera() >>> rotate(image, 2).shape (512, 512) >>> rotate(image, 2, resize=True).shape (530, 530) >>> rotate(image, 90, resize=True).shape (512, 512) """ rows, cols = image.shape[0], image.shape[1] if image.dtype == np.float16: image = image.astype(np.float32) # rotation around center if center is None: center = np.array((cols, rows)) / 2. - 0.5 else: center = np.asarray(center) tform1 = SimilarityTransform(translation=center) tform2 = SimilarityTransform(rotation=np.deg2rad(angle)) tform3 = SimilarityTransform(translation=-center) tform = tform3 + tform2 + tform1 output_shape = None if resize: # determine shape of output image corners = np.array([ [0, 0], [0, rows - 1], [cols - 1, rows - 1], [cols - 1, 0] ]) corners = tform.inverse(corners) minc = corners[:, 0].min() minr = corners[:, 1].min() maxc = corners[:, 0].max() maxr = corners[:, 1].max() out_rows = maxr - minr + 1 out_cols = maxc - minc + 1 output_shape = np.around((out_rows, out_cols)) # fit output image in new shape translation = (minc, minr) tform4 = SimilarityTransform(translation=translation) tform = tform4 + tform # Make sure the transform is exactly affine, to ensure fast warping. tform.params[2] = (0, 0, 1) return warp(image, tform, output_shape=output_shape, order=order, mode=mode, cval=cval, clip=clip, preserve_range=preserve_range) def downscale_local_mean(image, factors, cval=0, clip=True): """Down-sample N-dimensional image by local averaging. The image is padded with `cval` if it is not perfectly divisible by the integer factors. In contrast to interpolation in `skimage.transform.resize` and `skimage.transform.rescale` this function calculates the local mean of elements in each block of size `factors` in the input image. Parameters ---------- image : ndarray N-dimensional input image. factors : array_like Array containing down-sampling integer factor along each axis. cval : float, optional Constant padding value if image is not perfectly divisible by the integer factors. clip : bool, optional Unused, but kept here for API consistency with the other transforms in this module. (The local mean will never fall outside the range of values in the input image, assuming the provided `cval` also falls within that range.) Returns ------- image : ndarray Down-sampled image with same number of dimensions as input image. For integer inputs, the output dtype will be ``float64``. See :func:`numpy.mean` for details. Examples -------- >>> a = np.arange(15).reshape(3, 5) >>> a array([[ 0, 1, 2, 3, 4], [ 5, 6, 7, 8, 9], [10, 11, 12, 13, 14]]) >>> downscale_local_mean(a, (2, 3)) array([[3.5, 4. ], [5.5, 4.5]]) """ return block_reduce(image, factors, np.mean, cval) def _swirl_mapping(xy, center, rotation, strength, radius): x, y = xy.T x0, y0 = center rho = np.sqrt((x - x0) ** 2 + (y - y0) ** 2) # Ensure that the transformation decays to approximately 1/1000-th # within the specified radius. radius = radius / 5 * np.log(2) theta = rotation + strength * \ np.exp(-rho / radius) + \ np.arctan2(y - y0, x - x0) xy[..., 0] = x0 + rho * np.cos(theta) xy[..., 1] = y0 + rho * np.sin(theta) return xy def swirl(image, center=None, strength=1, radius=100, rotation=0, output_shape=None, order=None, mode='reflect', cval=0, clip=True, preserve_range=False): """Perform a swirl transformation. Parameters ---------- image : ndarray Input image. center : (column, row) tuple or (2,) ndarray, optional Center coordinate of transformation. strength : float, optional The amount of swirling applied. radius : float, optional The extent of the swirl in pixels. The effect dies out rapidly beyond `radius`. rotation : float, optional Additional rotation applied to the image. Returns ------- swirled : ndarray Swirled version of the input. Other parameters ---------------- output_shape : tuple (rows, cols), optional Shape of the output image generated. By default the shape of the input image is preserved. order : int, optional The order of the spline interpolation, default is 0 if image.dtype is bool and 1 otherwise. The order has to be in the range 0-5. See `skimage.transform.warp` for detail. mode : {'constant', 'edge', 'symmetric', 'reflect', 'wrap'}, optional Points outside the boundaries of the input are filled according to the given mode, with 'constant' used as the default. Modes match the behaviour of `numpy.pad`. cval : float, optional Used in conjunction with mode 'constant', the value outside the image boundaries. clip : bool, optional Whether to clip the output to the range of values of the input image. This is enabled by default, since higher order interpolation may produce values outside the given input range. preserve_range : bool, optional Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of `img_as_float`. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html """ if center is None: center = np.array(image.shape)[:2][::-1] / 2 warp_args = {'center': center, 'rotation': rotation, 'strength': strength, 'radius': radius} return warp(image, _swirl_mapping, map_args=warp_args, output_shape=output_shape, order=order, mode=mode, cval=cval, clip=clip, preserve_range=preserve_range) def _stackcopy(a, b): """Copy b into each color layer of a, such that:: a[:,:,0] = a[:,:,1] = ... = b Parameters ---------- a : (M, N) or (M, N, P) ndarray Target array. b : (M, N) Source array. Notes ----- Color images are stored as an ``(M, N, 3)`` or ``(M, N, 4)`` arrays. """ if a.ndim == 3: a[:] = b[:, :, np.newaxis] else: a[:] = b def warp_coords(coord_map, shape, dtype=np.float64): """Build the source coordinates for the output of a 2-D image warp. Parameters ---------- coord_map : callable like GeometricTransform.inverse Return input coordinates for given output coordinates. Coordinates are in the shape (P, 2), where P is the number of coordinates and each element is a ``(row, col)`` pair. shape : tuple Shape of output image ``(rows, cols[, bands])``. dtype : np.dtype or string dtype for return value (sane choices: float32 or float64). Returns ------- coords : (ndim, rows, cols[, bands]) array of dtype `dtype` Coordinates for `scipy.ndimage.map_coordinates`, that will yield an image of shape (orows, ocols, bands) by drawing from source points according to the `coord_transform_fn`. Notes ----- This is a lower-level routine that produces the source coordinates for 2-D images used by `warp()`. It is provided separately from `warp` to give additional flexibility to users who would like, for example, to re-use a particular coordinate mapping, to use specific dtypes at various points along the the image-warping process, or to implement different post-processing logic than `warp` performs after the call to `ndi.map_coordinates`. Examples -------- Produce a coordinate map that shifts an image up and to the right: >>> from skimage import data >>> from scipy.ndimage import map_coordinates >>> >>> def shift_up10_left20(xy): ... return xy - np.array([-20, 10])[None, :] >>> >>> image = data.astronaut().astype(np.float32) >>> coords = warp_coords(shift_up10_left20, image.shape) >>> warped_image = map_coordinates(image, coords) """ shape = safe_as_int(shape) rows, cols = shape[0], shape[1] coords_shape = [len(shape), rows, cols] if len(shape) == 3: coords_shape.append(shape[2]) coords = np.empty(coords_shape, dtype=dtype) # Reshape grid coordinates into a (P, 2) array of (row, col) pairs tf_coords = np.indices((cols, rows), dtype=dtype).reshape(2, -1).T # Map each (row, col) pair to the source image according to # the user-provided mapping tf_coords = coord_map(tf_coords) # Reshape back to a (2, M, N) coordinate grid tf_coords = tf_coords.T.reshape((-1, cols, rows)).swapaxes(1, 2) # Place the y-coordinate mapping _stackcopy(coords[1, ...], tf_coords[0, ...]) # Place the x-coordinate mapping _stackcopy(coords[0, ...], tf_coords[1, ...]) if len(shape) == 3: coords[2, ...] = range(shape[2]) return coords def _clip_warp_output(input_image, output_image, mode, cval, clip): """Clip output image to range of values of input image. Note that this function modifies the values of `output_image` in-place and it is only modified if ``clip=True``. Parameters ---------- input_image : ndarray Input image. output_image : ndarray Output image, which is modified in-place. Other parameters ---------------- mode : {'constant', 'edge', 'symmetric', 'reflect', 'wrap'} Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of `numpy.pad`. cval : float Used in conjunction with mode 'constant', the value outside the image boundaries. clip : bool Whether to clip the output to the range of values of the input image. This is enabled by default, since higher order interpolation may produce values outside the given input range. """ if clip: min_val = np.min(input_image) if np.isnan(min_val): # NaNs detected, use NaN-safe min/max min_func = np.nanmin max_func = np.nanmax min_val = min_func(input_image) else: min_func = np.min max_func = np.max max_val = max_func(input_image) # Check if cval has been used such that it expands the effective input # range preserve_cval = (mode == 'constant' and not min_val <= cval <= max_val and min_func(output_image) <= cval <= max_func(output_image)) # expand min/max range to account for cval if preserve_cval: # cast cval to the same dtype as the input image cval = input_image.dtype.type(cval) min_val = min(min_val, cval) max_val = max(max_val, cval) np.clip(output_image, min_val, max_val, out=output_image) def warp(image, inverse_map, map_args={}, output_shape=None, order=None, mode='constant', cval=0., clip=True, preserve_range=False): """Warp an image according to a given coordinate transformation. Parameters ---------- image : ndarray Input image. inverse_map : transformation object, callable ``cr = f(cr, **kwargs)``, or ndarray Inverse coordinate map, which transforms coordinates in the output images into their corresponding coordinates in the input image. There are a number of different options to define this map, depending on the dimensionality of the input image. A 2-D image can have 2 dimensions for gray-scale images, or 3 dimensions with color information. - For 2-D images, you can directly pass a transformation object, e.g. `skimage.transform.SimilarityTransform`, or its inverse. - For 2-D images, you can pass a ``(3, 3)`` homogeneous transformation matrix, e.g. `skimage.transform.SimilarityTransform.params`. - For 2-D images, a function that transforms a ``(M, 2)`` array of ``(col, row)`` coordinates in the output image to their corresponding coordinates in the input image. Extra parameters to the function can be specified through `map_args`. - For N-D images, you can directly pass an array of coordinates. The first dimension specifies the coordinates in the input image, while the subsequent dimensions determine the position in the output image. E.g. in case of 2-D images, you need to pass an array of shape ``(2, rows, cols)``, where `rows` and `cols` determine the shape of the output image, and the first dimension contains the ``(row, col)`` coordinate in the input image. See `scipy.ndimage.map_coordinates` for further documentation. Note, that a ``(3, 3)`` matrix is interpreted as a homogeneous transformation matrix, so you cannot interpolate values from a 3-D input, if the output is of shape ``(3,)``. See example section for usage. map_args : dict, optional Keyword arguments passed to `inverse_map`. output_shape : tuple (rows, cols), optional Shape of the output image generated. By default the shape of the input image is preserved. Note that, even for multi-band images, only rows and columns need to be specified. order : int, optional The order of interpolation. The order has to be in the range 0-5: - 0: Nearest-neighbor - 1: Bi-linear (default) - 2: Bi-quadratic - 3: Bi-cubic - 4: Bi-quartic - 5: Bi-quintic Default is 0 if image.dtype is bool and 1 otherwise. mode : {'constant', 'edge', 'symmetric', 'reflect', 'wrap'}, optional Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of `numpy.pad`. cval : float, optional Used in conjunction with mode 'constant', the value outside the image boundaries. clip : bool, optional Whether to clip the output to the range of values of the input image. This is enabled by default, since higher order interpolation may produce values outside the given input range. preserve_range : bool, optional Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of `img_as_float`. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html Returns ------- warped : double ndarray The warped input image. Notes ----- - The input image is converted to a `double` image. - In case of a `SimilarityTransform`, `AffineTransform` and `ProjectiveTransform` and `order` in [0, 3] this function uses the underlying transformation matrix to warp the image with a much faster routine. Examples -------- >>> from skimage.transform import warp >>> from skimage import data >>> image = data.camera() The following image warps are all equal but differ substantially in execution time. The image is shifted to the bottom. Use a geometric transform to warp an image (fast): >>> from skimage.transform import SimilarityTransform >>> tform = SimilarityTransform(translation=(0, -10)) >>> warped = warp(image, tform) Use a callable (slow): >>> def shift_down(xy): ... xy[:, 1] -= 10 ... return xy >>> warped = warp(image, shift_down) Use a transformation matrix to warp an image (fast): >>> matrix = np.array([[1, 0, 0], [0, 1, -10], [0, 0, 1]]) >>> warped = warp(image, matrix) >>> from skimage.transform import ProjectiveTransform >>> warped = warp(image, ProjectiveTransform(matrix=matrix)) You can also use the inverse of a geometric transformation (fast): >>> warped = warp(image, tform.inverse) For N-D images you can pass a coordinate array, that specifies the coordinates in the input image for every element in the output image. E.g. if you want to rescale a 3-D cube, you can do: >>> cube_shape = np.array([30, 30, 30]) >>> rng = np.random.default_rng() >>> cube = rng.random(cube_shape) Setup the coordinate array, that defines the scaling: >>> scale = 0.1 >>> output_shape = (scale * cube_shape).astype(int) >>> coords0, coords1, coords2 = np.mgrid[:output_shape[0], ... :output_shape[1], :output_shape[2]] >>> coords = np.array([coords0, coords1, coords2]) Assume that the cube contains spatial data, where the first array element center is at coordinate (0.5, 0.5, 0.5) in real space, i.e. we have to account for this extra offset when scaling the image: >>> coords = (coords + 0.5) / scale - 0.5 >>> warped = warp(cube, coords) """ if image.size == 0: raise ValueError("Cannot warp empty image with dimensions", image.shape) order = _validate_interpolation_order(image.dtype, order) if order > 0: image = convert_to_float(image, preserve_range) if image.dtype == np.float16: image = image.astype(np.float32) input_shape = np.array(image.shape) if output_shape is None: output_shape = input_shape else: output_shape = safe_as_int(output_shape) warped = None if order == 2: # When fixing this issue, make sure to fix the branches further # below in this function warn("Bi-quadratic interpolation behavior has changed due " "to a bug in the implementation of scikit-image. " "The new version now serves as a wrapper " "around SciPy's interpolation functions, which itself " "is not verified to be a correct implementation. Until " "skimage's implementation is fixed, we recommend " "to use bi-linear or bi-cubic interpolation instead.") if order in (1, 3) and not map_args: # use fast Cython version for specific interpolation orders and input matrix = None if isinstance(inverse_map, np.ndarray) and inverse_map.shape == (3, 3): # inverse_map is a transformation matrix as numpy array matrix = inverse_map elif isinstance(inverse_map, HOMOGRAPHY_TRANSFORMS): # inverse_map is a homography matrix = inverse_map.params elif (hasattr(inverse_map, '__name__') and inverse_map.__name__ == 'inverse' and get_bound_method_class(inverse_map) in HOMOGRAPHY_TRANSFORMS): # inverse_map is the inverse of a homography matrix = np.linalg.inv(inverse_map.__self__.params) if matrix is not None: matrix = matrix.astype(image.dtype) ctype = 'float32_t' if image.dtype == np.float32 else 'float64_t' if image.ndim == 2: warped = _warp_fast[ctype](image, matrix, output_shape=output_shape, order=order, mode=mode, cval=cval) elif image.ndim == 3: dims = [] for dim in range(image.shape[2]): dims.append(_warp_fast[ctype](image[..., dim], matrix, output_shape=output_shape, order=order, mode=mode, cval=cval)) warped = np.dstack(dims) if warped is None: # use ndi.map_coordinates if (isinstance(inverse_map, np.ndarray) and inverse_map.shape == (3, 3)): # inverse_map is a transformation matrix as numpy array, # this is only used for order >= 4. inverse_map = ProjectiveTransform(matrix=inverse_map) if isinstance(inverse_map, np.ndarray): # inverse_map is directly given as coordinates coords = inverse_map else: # inverse_map is given as function, that transforms (N, 2) # destination coordinates to their corresponding source # coordinates. This is only supported for 2(+1)-D images. if image.ndim < 2 or image.ndim > 3: raise ValueError("Only 2-D images (grayscale or color) are " "supported, when providing a callable " "`inverse_map`.") def coord_map(*args): return inverse_map(*args, **map_args) if len(input_shape) == 3 and len(output_shape) == 2: # Input image is 2D and has color channel, but output_shape is # given for 2-D images. Automatically add the color channel # dimensionality. output_shape = (output_shape[0], output_shape[1], input_shape[2]) coords = warp_coords(coord_map, output_shape) # Pre-filtering not necessary for order 0, 1 interpolation prefilter = order > 1 ndi_mode = _to_ndimage_mode(mode) warped = ndi.map_coordinates(image, coords, prefilter=prefilter, mode=ndi_mode, order=order, cval=cval) _clip_warp_output(image, warped, mode, cval, clip) return warped def _linear_polar_mapping(output_coords, k_angle, k_radius, center): """Inverse mapping function to convert from cartesian to polar coordinates Parameters ---------- output_coords : ndarray `(M, 2)` array of `(col, row)` coordinates in the output image k_angle : float Scaling factor that relates the intended number of rows in the output image to angle: ``k_angle = nrows / (2 * np.pi)`` k_radius : float Scaling factor that relates the radius of the circle bounding the area to be transformed to the intended number of columns in the output image: ``k_radius = ncols / radius`` center : tuple (row, col) Coordinates that represent the center of the circle that bounds the area to be transformed in an input image. Returns ------- coords : ndarray `(M, 2)` array of `(col, row)` coordinates in the input image that correspond to the `output_coords` given as input. """ angle = output_coords[:, 1] / k_angle rr = ((output_coords[:, 0] / k_radius) * np.sin(angle)) + center[0] cc = ((output_coords[:, 0] / k_radius) * np.cos(angle)) + center[1] coords = np.column_stack((cc, rr)) return coords def _log_polar_mapping(output_coords, k_angle, k_radius, center): """Inverse mapping function to convert from cartesian to polar coordinates Parameters ---------- output_coords : ndarray `(M, 2)` array of `(col, row)` coordinates in the output image k_angle : float Scaling factor that relates the intended number of rows in the output image to angle: ``k_angle = nrows / (2 * np.pi)`` k_radius : float Scaling factor that relates the radius of the circle bounding the area to be transformed to the intended number of columns in the output image: ``k_radius = width / np.log(radius)`` center : tuple (row, col) Coordinates that represent the center of the circle that bounds the area to be transformed in an input image. Returns ------- coords : ndarray `(M, 2)` array of `(col, row)` coordinates in the input image that correspond to the `output_coords` given as input. """ angle = output_coords[:, 1] / k_angle rr = ((np.exp(output_coords[:, 0] / k_radius)) * np.sin(angle)) + center[0] cc = ((np.exp(output_coords[:, 0] / k_radius)) * np.cos(angle)) + center[1] coords = np.column_stack((cc, rr)) return coords @channel_as_last_axis() def warp_polar(image, center=None, *, radius=None, output_shape=None, scaling='linear', channel_axis=None, **kwargs): """Remap image to polar or log-polar coordinates space. Parameters ---------- image : ndarray Input image. Only 2-D arrays are accepted by default. 3-D arrays are accepted if a `channel_axis` is specified. center : tuple (row, col), optional Point in image that represents the center of the transformation (i.e., the origin in cartesian space). Values can be of type `float`. If no value is given, the center is assumed to be the center point of the image. radius : float, optional Radius of the circle that bounds the area to be transformed. output_shape : tuple (row, col), optional scaling : {'linear', 'log'}, optional Specify whether the image warp is polar or log-polar. Defaults to 'linear'. 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. **kwargs : keyword arguments Passed to `transform.warp`. Returns ------- warped : ndarray The polar or log-polar warped image. Examples -------- Perform a basic polar warp on a grayscale image: >>> from skimage import data >>> from skimage.transform import warp_polar >>> image = data.checkerboard() >>> warped = warp_polar(image) Perform a log-polar warp on a grayscale image: >>> warped = warp_polar(image, scaling='log') Perform a log-polar warp on a grayscale image while specifying center, radius, and output shape: >>> warped = warp_polar(image, (100,100), radius=100, ... output_shape=image.shape, scaling='log') Perform a log-polar warp on a color image: >>> image = data.astronaut() >>> warped = warp_polar(image, scaling='log', channel_axis=-1) """ multichannel = channel_axis is not None if image.ndim != 2 and not multichannel: raise ValueError(f'Input array must be 2-dimensional when ' f'`channel_axis=None`, got {image.ndim}') if image.ndim != 3 and multichannel: raise ValueError(f'Input array must be 3-dimensional when ' f'`channel_axis` is specified, got {image.ndim}') if center is None: center = (np.array(image.shape)[:2] / 2) - 0.5 if radius is None: w, h = np.array(image.shape)[:2] / 2 radius = np.sqrt(w ** 2 + h ** 2) if output_shape is None: height = 360 width = int(np.ceil(radius)) output_shape = (height, width) else: output_shape = safe_as_int(output_shape) height = output_shape[0] width = output_shape[1] if scaling == 'linear': k_radius = width / radius map_func = _linear_polar_mapping elif scaling == 'log': k_radius = width / np.log(radius) map_func = _log_polar_mapping else: raise ValueError("Scaling value must be in {'linear', 'log'}") k_angle = height / (2 * np.pi) warp_args = {'k_angle': k_angle, 'k_radius': k_radius, 'center': center} warped = warp(image, map_func, map_args=warp_args, output_shape=output_shape, **kwargs) return warped def _local_mean_weights(old_size, new_size, grid_mode, dtype): """Create a 2D weight matrix for resizing with the local mean. Parameters ---------- old_size: int Old size. new_size: int New size. grid_mode : bool Whether to use grid data model of pixel/voxel model for average weights computation. dtype: dtype Output array data type. Returns ------- weights: (new_size, old_size) array Rows sum to 1. """ if grid_mode: old_breaks = np.linspace(0, old_size, num=old_size + 1, dtype=dtype) new_breaks = np.linspace(0, old_size, num=new_size + 1, dtype=dtype) else: old, new = old_size - 1, new_size - 1 old_breaks = np.pad(np.linspace(0.5, old - 0.5, old, dtype=dtype), 1, 'constant', constant_values=(0, old)) if new == 0: val = np.inf else: val = 0.5 * old / new new_breaks = np.pad(np.linspace(val, old - val, new, dtype=dtype), 1, 'constant', constant_values=(0, old)) upper = np.minimum(new_breaks[1:, np.newaxis], old_breaks[np.newaxis, 1:]) lower = np.maximum(new_breaks[:-1, np.newaxis], old_breaks[np.newaxis, :-1]) weights = np.maximum(upper - lower, 0) weights /= weights.sum(axis=1, keepdims=True) return weights def resize_local_mean(image, output_shape, grid_mode=True, preserve_range=False, *, channel_axis=None): """Resize an array with the local mean / bilinear scaling. Parameters ---------- image : ndarray Input image. If this is a multichannel image, the axis corresponding to channels should be specified using `channel_axis` output_shape : iterable Size of the generated output image. When `channel_axis` is not None, the `channel_axis` should either be omitted from `output_shape` or the ``output_shape[channel_axis]`` must match ``image.shape[channel_axis]``. If the length of `output_shape` exceeds image.ndim, additional singleton dimensions will be appended to the input ``image`` as needed. grid_mode : bool, optional Defines ``image`` pixels position: if True, pixels are assumed to be at grid intersections, otherwise at cell centers. As a consequence, for example, a 1d signal of length 5 is considered to have length 4 when `grid_mode` is False, but length 5 when `grid_mode` is True. See the following visual illustration: .. code-block:: text | pixel 1 | pixel 2 | pixel 3 | pixel 4 | pixel 5 | |<-------------------------------------->| vs. |<----------------------------------------------->| The starting point of the arrow in the diagram above corresponds to coordinate location 0 in each mode. preserve_range : bool, optional Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of `img_as_float`. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html Returns ------- resized : ndarray Resized version of the input. See Also -------- resize, downscale_local_mean Notes ----- This method is sometimes referred to as "area-based" interpolation or "pixel mixing" interpolation [1]_. When `grid_mode` is True, it is equivalent to using OpenCV's resize with `INTER_AREA` interpolation mode. It is commonly used for image downsizing. If the downsizing factors are integers, then `downscale_local_mean` should be preferred instead. References ---------- .. [1] http://entropymine.com/imageworsener/pixelmixing/ Examples -------- >>> from skimage import data >>> from skimage.transform import resize_local_mean >>> image = data.camera() >>> resize_local_mean(image, (100, 100)).shape (100, 100) """ if channel_axis is not None: if channel_axis < -image.ndim or channel_axis >= image.ndim: raise ValueError("invalid channel_axis") # move channels to last position image = np.moveaxis(image, channel_axis, -1) nc = image.shape[-1] output_ndim = len(output_shape) if output_ndim == image.ndim - 1: # insert channels dimension at the end output_shape = output_shape + (nc,) elif output_ndim == image.ndim: if output_shape[channel_axis] != nc: raise ValueError( "Cannot reshape along the channel_axis. Use " "channel_axis=None to reshape along all axes." ) # move channels to last position in output_shape channel_axis = channel_axis % image.ndim output_shape = ( output_shape[:channel_axis] + output_shape[channel_axis:] + (nc,) ) else: raise ValueError( "len(output_shape) must be image.ndim or (image.ndim - 1) " "when a channel_axis is specified." ) resized = image else: resized, output_shape = _preprocess_resize_output_shape(image, output_shape) resized = convert_to_float(resized, preserve_range) dtype = resized.dtype for axis, (old_size, new_size) in enumerate(zip(image.shape, output_shape)): if old_size == new_size: continue weights = _local_mean_weights(old_size, new_size, grid_mode, dtype) product = np.tensordot(resized, weights, [[axis], [-1]]) resized = np.moveaxis(product, -1, axis) if channel_axis is not None: # restore channels to original axis resized = np.moveaxis(resized, -1, channel_axis) return resized