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Add function to build gaussian and laplacian pyramids
This commit is contained in:
Johannes Schönberger
@@ -4,7 +4,8 @@ from .finite_radon_transform import *
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from .integral import *
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from ._geometric import (warp, warp_coords, estimate_transform,
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SimilarityTransform, AffineTransform,
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ProjectiveTransform, PolynomialTransform,
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ProjectiveTransform, PolynomialTransform,
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PiecewiseAffineTransform)
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from ._warps import swirl, homography, resize, rotate
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from .pyramid import (pyramid_reduce, pyramid_expand,
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build_gaussian_pyramid, build_laplacian_pyramid)
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@@ -0,0 +1,292 @@
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import math
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import numpy as np
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from scipy import ndimage
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from skimage.transform import resize
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from skimage.util import img_as_float
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def _smooth(image, sigma, mode, cval):
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# allocate output array
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smoothed = np.empty(image.shape, dtype=np.double)
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if image.ndim == 3: # apply gaussian filter to all dimensions independently
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for dim in range(image.shape[2]):
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ndimage.gaussian_filter(image[..., dim], sigma,
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output=smoothed[..., dim],
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mode=mode, cval=cval)
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else:
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ndimage.gaussian_filter(image, sigma, output=smoothed,
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mode=mode, cval=cval)
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return smoothed
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def _check_factor(factor):
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if factor <= 1:
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raise ValueError('scale factor must be greater than 1')
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def pyramid_reduce(image, factor=2, sigma=None, order=1,
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mode='reflect', cval=0):
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"""Smooth and then downsample image.
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Parameters
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----------
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image : array
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Input image.
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factor : float, optional
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Downscale factor. Default is 2.
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sigma : float, optional
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Sigma for gaussian filter. Default is `2 * factor / 6.0` which
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corresponds to a filter mask twice the size of the scale factor that
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covers more than 99% of the gaussian distribution.
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order : int, optional
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Order of splines used in interpolation of downsampling. See
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`scipy.ndimage.map_coordinates` for detail. Default is 1.
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mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
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The mode parameter determines how the array borders are handled, where
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cval is the value when mode is equal to 'constant'.
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Default is 'reflect'.
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cval : float, optional
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Value to fill past edges of input if mode is 'constant'. Default is 0.
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Returns
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-------
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out : array
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Smoothed and downsampled image.
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References
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----------
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..[1] http://web.mit.edu/persci/people/adelson/pub_pdfs/pyramid83.pdf
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"""
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_check_factor(factor)
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image = img_as_float(image)
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rows = image.shape[0]
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cols = image.shape[1]
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out_rows = math.ceil(rows / float(factor))
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out_cols = math.ceil(cols / float(factor))
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if sigma is None:
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# automatically determine sigma which covers > 99% of distribution
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sigma = 2 * factor / 6.0
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smoothed = _smooth(image, sigma, mode, cval)
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out = resize(smoothed, (out_rows, out_cols), order=order,
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mode=mode, cval=cval)
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return out
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def pyramid_expand(image, factor=2, sigma=None, order=1,
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mode='reflect', cval=0):
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"""Upsample and then smooth image.
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Parameters
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----------
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image : array
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Input image.
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factor : float, optional
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Upscale factor. Default is 2.
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sigma : float, optional
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Sigma for gaussian filter. Default is `2 * factor / 6.0` which
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corresponds to a filter mask twice the size of the scale factor that
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covers more than 99% of the gaussian distribution.
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order : int, optional
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Order of splines used in interpolation of downsampling. See
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`scipy.ndimage.map_coordinates` for detail. Default is 1.
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mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
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The mode parameter determines how the array borders are handled, where
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cval is the value when mode is equal to 'constant'.
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Default is 'reflect'.
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cval : float, optional
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Value to fill past edges of input if mode is 'constant'. Default is 0.
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Returns
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-------
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out : array
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Upsampled and smoothed image.
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References
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----------
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..[1] http://web.mit.edu/persci/people/adelson/pub_pdfs/pyramid83.pdf
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"""
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_check_factor(factor)
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rows = image.shape[0]
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cols = image.shape[1]
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out_rows = 2 * rows
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out_cols = 2 * cols
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if sigma is None:
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# automatically determine sigma which covers > 99% of distribution
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sigma = 2 * factor / 6.0
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resized = resize(image, (out_rows, out_cols), order=order,
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mode=mode, cval=cval)
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out = _smooth(resized, sigma, mode, cval)
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return out
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def build_gaussian_pyramid(image, max_layer=-1, factor=2, sigma=None, order=1,
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mode='reflect', cval=0):
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"""Build gaussian pyramid.
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Recursively applies the `pyramid_reduce` function to the image.
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Parameters
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----------
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image : array
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Input image.
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max_layer : int
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Number of layers for the pyramid. 0th layer is the original image.
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Default is -1 which builds all possible layers.
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factor : float, optional
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Downscale factor. Default is 2.
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sigma : float, optional
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Sigma for gaussian filter. Default is `2 * factor / 6.0` which
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corresponds to a filter mask twice the size of the scale factor that
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covers more than 99% of the gaussian distribution.
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order : int, optional
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Order of splines used in interpolation of downsampling. See
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`scipy.ndimage.map_coordinates` for detail. Default is 1.
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mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
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The mode parameter determines how the array borders are handled, where
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cval is the value when mode is equal to 'constant'.
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Default is 'reflect'.
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cval : float, optional
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Value to fill past edges of input if mode is 'constant'. Default is 0.
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Returns
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-------
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pyramid : list of arrays
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"""
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_check_factor(factor)
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pyramid = []
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pyramid.append(image)
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layer = 0
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rows = image.shape[0]
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cols = image.shape[1]
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# build downsampled images until max_layer is reached or downsampled image
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# has size of 1 in one direction
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while True:
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layer += 1
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layer_image = pyramid_reduce(pyramid[-1], factor, sigma, order,
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mode, cval)
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# image degraded to 1px
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if layer_image.ndim == 1:
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break
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prev_rows = rows
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prev_cols = cols
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rows = layer_image.shape[0]
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cols = layer_image.shape[1]
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# no change to previous pyramid layer
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if prev_rows == rows and prev_cols == cols:
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break
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pyramid.append(layer_image)
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if layer == max_layer:
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break
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return pyramid
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def build_laplacian_pyramid(image, max_layer=-1, factor=2, sigma=None, order=1,
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mode='reflect', cval=0):
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"""Build laplacian pyramid.
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Each layer contains the difference between the downsampled and the
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downsampled plus smoothed image.
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Parameters
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----------
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image : array
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Input image.
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max_layer : int
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Number of layers for the pyramid. 0th layer is the original image.
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Default is -1 which builds all possible layers.
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factor : float, optional
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Downscale factor. Default is 2.
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sigma : float, optional
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Sigma for gaussian filter. Default is `2 * factor / 6.0` which
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corresponds to a filter mask twice the size of the scale factor that
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covers more than 99% of the gaussian distribution.
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order : int, optional
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Order of splines used in interpolation of downsampling. See
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`scipy.ndimage.map_coordinates` for detail. Default is 1.
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mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
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The mode parameter determines how the array borders are handled, where
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cval is the value when mode is equal to 'constant'.
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Default is 'reflect'.
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cval : float, optional
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Value to fill past edges of input if mode is 'constant'. Default is 0.
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Returns
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-------
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pyramid : list of arrays
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"""
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_check_factor(factor)
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if sigma is None:
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# automatically determine sigma which covers > 99% of distribution
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sigma = 2 * factor / 6.0
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pyramid = []
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pyramid.append(image - _smooth(image, sigma, mode, cval))
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layer = 0
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rows = image.shape[0]
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cols = image.shape[1]
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# build downsampled images until max_layer is reached or downsampled image
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# has size of 1 in one direction
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while True:
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layer += 1
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rows = pyramid[-1].shape[0]
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cols = pyramid[-1].shape[1]
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out_rows = math.ceil(rows / float(factor))
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out_cols = math.ceil(cols / float(factor))
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resized = resize(pyramid[-1], (out_rows, out_cols), order=order,
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mode=mode, cval=cval)
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layer_image = _smooth(resized, sigma, mode, cval)
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# image degraded to 1px
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if layer_image.ndim == 1:
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break
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prev_rows = rows
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prev_cols = cols
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rows = layer_image.shape[0]
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cols = layer_image.shape[1]
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# no change to previous pyramid layer
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if prev_rows == rows and prev_cols == cols:
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break
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pyramid.append(layer_image)
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if layer == max_layer:
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break
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return pyramid
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