# Licensed under a 3-clause BSD style license - see LICENSE.rst from __future__ import (absolute_import, division, print_function, unicode_literals) import numpy as np from .core import Kernel1D, Kernel2D, Kernel from .utils import KernelSizeError from ..modeling import models from ..modeling.core import Fittable1DModel, Fittable2DModel __all__ = sorted(['Gaussian1DKernel', 'Gaussian2DKernel', 'CustomKernel', 'Box1DKernel', 'Box2DKernel', 'Tophat2DKernel', 'Trapezoid1DKernel', 'MexicanHat1DKernel', 'MexicanHat2DKernel', 'AiryDisk2DKernel', 'Model1DKernel', 'Model2DKernel', 'TrapezoidDisk2DKernel', 'Ring2DKernel']) def _round_up_to_odd_integer(value): i = int(np.ceil(value)) if i % 2 == 0: return i + 1 else: return i class Gaussian1DKernel(Kernel1D): """ 1D Gaussian filter kernel. The Gaussian filter is a filter with great smoothing properties. It is isotropic and does not produce artifacts. Parameters ---------- stddev : number Standard deviation of the Gaussian kernel. x_size : odd int, optional Size of the kernel array. Default = 8 * stddev mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by linearly interpolating between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. Very slow. factor : number, optional Factor of oversampling. Default factor = 10. If the factor is too large, evaluation can be very slow. See Also -------- Box1DKernel, Trapezoid1DKernel, MexicanHat1DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import Gaussian1DKernel gauss_1D_kernel = Gaussian1DKernel(10) plt.plot(gauss_1D_kernel, drawstyle='steps') plt.xlabel('x [pixels]') plt.ylabel('value') plt.show() """ _separable = True _is_bool = False def __init__(self, stddev, **kwargs): self._model = models.Gaussian1D(1. / (np.sqrt(2 * np.pi) * stddev), 0, stddev) self._default_size = _round_up_to_odd_integer(8 * stddev) super(Gaussian1DKernel, self).__init__(**kwargs) self._truncation = np.abs(1. - 1 / self._normalization) class Gaussian2DKernel(Kernel2D): """ 2D Gaussian filter kernel. The Gaussian filter is a filter with great smoothing properties. It is isotropic and does not produce artifacts. Parameters ---------- stddev : number Standard deviation of the Gaussian kernel. x_size : odd int, optional Size in x direction of the kernel array. Default = 8 * stddev. y_size : odd int, optional Size in y direction of the kernel array. Default = 8 * stddev. mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by performing a bilinear interpolation between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Box2DKernel, Tophat2DKernel, MexicanHat2DKernel, Ring2DKernel, TrapezoidDisk2DKernel, AiryDisk2DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import Gaussian2DKernel gaussian_2D_kernel = Gaussian2DKernel(10) plt.imshow(gaussian_2D_kernel, interpolation='none', origin='lower') plt.xlabel('x [pixels]') plt.ylabel('y [pixels]') plt.colorbar() plt.show() """ _separable = True _is_bool = False def __init__(self, stddev, **kwargs): self._model = models.Gaussian2D(1. / (2 * np.pi * stddev ** 2), 0, 0, stddev, stddev) self._default_size = _round_up_to_odd_integer(8 * stddev) super(Gaussian2DKernel, self).__init__(**kwargs) self._truncation = np.abs(1. - 1 / self._normalization) class Box1DKernel(Kernel1D): """ 1D Box filter kernel. The Box filter or running mean is a smoothing filter. It is not isotropic and can produce artifacts, when applied repeatedly to the same data. By default the Box kernel uses the ``linear_interp`` discretization mode, which allows non-shifting, even-sized kernels. This is achieved by weighting the edge pixels with 1/2. E.g a Box kernel with an effective smoothing of 4 pixel would have the following array: [0.5, 1, 1, 1, 0.5]. Parameters ---------- width : number Width of the filter kernel. mode : str, optional One of the following discretization modes: * 'center' Discretize model by taking the value at the center of the bin. * 'linear_interp' (default) Discretize model by linearly interpolating between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Gaussian1DKernel, Trapezoid1DKernel, MexicanHat1DKernel Examples -------- Kernel response function: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import Box1DKernel box_1D_kernel = Box1DKernel(9) plt.plot(box_1D_kernel, drawstyle='steps') plt.xlim(-1, 9) plt.xlabel('x [pixels]') plt.ylabel('value') plt.show() """ _separable = True _is_bool = True def __init__(self, width, **kwargs): self._model = models.Box1D(1. / width, 0, width) self._default_size = _round_up_to_odd_integer(width) kwargs['mode'] = 'linear_interp' super(Box1DKernel, self).__init__(**kwargs) self._truncation = 0 self.normalize() class Box2DKernel(Kernel2D): """ 2D Box filter kernel. The Box filter or running mean is a smoothing filter. It is not isotropic and can produce artifact, when applied repeatedly to the same data. By default the Box kernel uses the ``linear_interp`` discretization mode, which allows non-shifting, even-sized kernels. This is achieved by weighting the edge pixels with 1/2. Parameters ---------- width : number Width of the filter kernel. mode : str, optional One of the following discretization modes: * 'center' Discretize model by taking the value at the center of the bin. * 'linear_interp' (default) Discretize model by performing a bilinear interpolation between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Box2DKernel, Tophat2DKernel, MexicanHat2DKernel, Ring2DKernel, TrapezoidDisk2DKernel, AiryDisk2DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import Box2DKernel box_2D_kernel = Box2DKernel(9) plt.imshow(box_2D_kernel, interpolation='none', origin='lower', vmin=0.0, vmax=0.015) plt.xlim(-1, 9) plt.ylim(-1, 9) plt.xlabel('x [pixels]') plt.ylabel('y [pixels]') plt.colorbar() plt.show() """ _separable = True _is_bool = True def __init__(self, width, **kwargs): self._model = models.Box2D(1. / width ** 2, 0, 0, width, width) self._default_size = _round_up_to_odd_integer(width) kwargs['mode'] = 'linear_interp' super(Box2DKernel, self).__init__(**kwargs) self._truncation = 0 self.normalize() class Tophat2DKernel(Kernel2D): """ 2D Tophat filter kernel. The Tophat filter is an isotropic smoothing filter. It can produce artifacts when applied repeatedly on the same data. Parameters ---------- radius : int Radius of the filter kernel. mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by performing a bilinear interpolation between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Box2DKernel, Tophat2DKernel, MexicanHat2DKernel, Ring2DKernel, TrapezoidDisk2DKernel, AiryDisk2DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import Tophat2DKernel tophat_2D_kernel = Tophat2DKernel(40) plt.imshow(tophat_2D_kernel, interpolation='none', origin='lower') plt.xlabel('x [pixels]') plt.ylabel('y [pixels]') plt.colorbar() plt.show() """ def __init__(self, radius, **kwargs): self._model = models.Disk2D(1. / (np.pi * radius ** 2), 0, 0, radius) self._default_size = _round_up_to_odd_integer(2 * radius) super(Tophat2DKernel, self).__init__(**kwargs) self._truncation = 0 class Ring2DKernel(Kernel2D): """ 2D Ring filter kernel. The Ring filter kernel is the difference between two Tophat kernels of different width. This kernel is useful for, e.g., background estimation. Parameters ---------- radius_in : number Inner radius of the ring kernel. width : number Width of the ring kernel. mode: str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by performing a bilinear interpolation between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Box2DKernel, Gaussian2DKernel, MexicanHat2DKernel, Tophat2DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import Ring2DKernel ring_2D_kernel = Ring2DKernel(9, 8) plt.imshow(ring_2D_kernel, interpolation='none', origin='lower') plt.xlabel('x [pixels]') plt.ylabel('y [pixels]') plt.colorbar() plt.show() """ def __init__(self, radius_in, width, **kwargs): radius_out = radius_in + width self._model = models.Ring2D(1. / (np.pi * (radius_out ** 2 - radius_in ** 2)), 0, 0, radius_in, width) self._default_size = _round_up_to_odd_integer(2 * radius_out) super(Ring2DKernel, self).__init__(**kwargs) self._truncation = 0 class Trapezoid1DKernel(Kernel1D): """ 1D trapezoid kernel. Parameters ---------- width : number Width of the filter kernel, defined as the width of the constant part, before it begins to slope down. slope : number Slope of the filter kernel's tails mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by linearly interpolating between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Box1DKernel, Gaussian1DKernel, MexicanHat1DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import Trapezoid1DKernel trapezoid_1D_kernel = Trapezoid1DKernel(17, slope=0.2) plt.plot(trapezoid_1D_kernel, drawstyle='steps') plt.xlabel('x [pixels]') plt.ylabel('amplitude') plt.xlim(-1, 28) plt.show() """ _is_bool = False def __init__(self, width, slope=1., **kwargs): self._model = models.Trapezoid1D(1, 0, width, slope) self._default_size = _round_up_to_odd_integer(width + 2. / slope) super(Trapezoid1DKernel, self).__init__(**kwargs) self._truncation = 0 self.normalize() class TrapezoidDisk2DKernel(Kernel2D): """ 2D trapezoid kernel. Parameters ---------- radius : number Width of the filter kernel, defined as the width of the constant part, before it begins to slope down. slope : number Slope of the filter kernel's tails mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by performing a bilinear interpolation between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Box2DKernel, Tophat2DKernel, MexicanHat2DKernel, Ring2DKernel, TrapezoidDisk2DKernel, AiryDisk2DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import TrapezoidDisk2DKernel trapezoid_2D_kernel = TrapezoidDisk2DKernel(20, slope=0.2) plt.imshow(trapezoid_2D_kernel, interpolation='none', origin='lower') plt.xlabel('x [pixels]') plt.ylabel('y [pixels]') plt.colorbar() plt.show() """ _is_bool = False def __init__(self, radius, slope=1., **kwargs): self._model = models.TrapezoidDisk2D(1, 0, 0, radius, slope) self._default_size = _round_up_to_odd_integer(2 * radius + 2. / slope) super(TrapezoidDisk2DKernel, self).__init__(**kwargs) self._truncation = 0 self.normalize() class MexicanHat1DKernel(Kernel1D): """ 1D Mexican hat filter kernel. The Mexican Hat, or inverted Gaussian-Laplace filter, is a bandpass filter. It smoothes the data and removes slowly varying or constant structures (e.g. Background). It is useful for peak or multi-scale detection. This kernel is derived from a normalized Gaussian function, by computing the second derivative. This results in an amplitude at the kernels center of 1. / (sqrt(2 * pi) * width ** 3). The normalization is the same as for `scipy.ndimage.filters.gaussian_laplace`, except for a minus sign. Parameters ---------- width : number Width of the filter kernel, defined as the standard deviation of the Gaussian function from which it is derived. x_size : odd int, optional Size in x direction of the kernel array. Default = 8 * width. mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by linearly interpolating between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Box1DKernel, Gaussian1DKernel, Trapezoid1DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import MexicanHat1DKernel mexicanhat_1D_kernel = MexicanHat1DKernel(10) plt.plot(mexicanhat_1D_kernel, drawstyle='steps') plt.xlabel('x [pixels]') plt.ylabel('value') plt.show() """ _is_bool = True def __init__(self, width, **kwargs): amplitude = 1.0 / (np.sqrt(2 * np.pi) * width ** 3) self._model = models.MexicanHat1D(amplitude, 0, width) self._default_size = _round_up_to_odd_integer(8 * width) super(MexicanHat1DKernel, self).__init__(**kwargs) self._truncation = np.abs(self._array.sum() / self._array.size) class MexicanHat2DKernel(Kernel2D): """ 2D Mexican hat filter kernel. The Mexican Hat, or inverted Gaussian-Laplace filter, is a bandpass filter. It smoothes the data and removes slowly varying or constant structures (e.g. Background). It is useful for peak or multi-scale detection. This kernel is derived from a normalized Gaussian function, by computing the second derivative. This results in an amplitude at the kernels center of 1. / (pi * width ** 4). The normalization is the same as for `scipy.ndimage.filters.gaussian_laplace`, except for a minus sign. Parameters ---------- width : number Width of the filter kernel, defined as the standard deviation of the Gaussian function from which it is derived. x_size : odd int, optional Size in x direction of the kernel array. Default = 8 * width. y_size : odd int, optional Size in y direction of the kernel array. Default = 8 * width. mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by performing a bilinear interpolation between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Box2DKernel, Tophat2DKernel, MexicanHat2DKernel, Ring2DKernel, TrapezoidDisk2DKernel, AiryDisk2DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import MexicanHat2DKernel mexicanhat_2D_kernel = MexicanHat2DKernel(10) plt.imshow(mexicanhat_2D_kernel, interpolation='none', origin='lower') plt.xlabel('x [pixels]') plt.ylabel('y [pixels]') plt.colorbar() plt.show() """ _is_bool = False def __init__(self, width, **kwargs): amplitude = 1.0 / (np.pi * width ** 4) self._model = models.MexicanHat2D(amplitude, 0, 0, width) self._default_size = _round_up_to_odd_integer(8 * width) super(MexicanHat2DKernel, self).__init__(**kwargs) self._truncation = np.abs(self._array.sum() / self._array.size) class AiryDisk2DKernel(Kernel2D): """ 2D Airy disk kernel. This kernel models the diffraction pattern of a circular aperture. This kernel is normalized to a peak value of 1. Parameters ---------- radius : float The radius of the Airy disk kernel (radius of the first zero). x_size : odd int, optional Size in x direction of the kernel array. Default = 8 * radius. y_size : odd int, optional Size in y direction of the kernel array. Default = 8 * radius. mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by performing a bilinear interpolation between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Box2DKernel, Tophat2DKernel, MexicanHat2DKernel, Ring2DKernel, TrapezoidDisk2DKernel, AiryDisk2DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import AiryDisk2DKernel airydisk_2D_kernel = AiryDisk2DKernel(10) plt.imshow(airydisk_2D_kernel, interpolation='none', origin='lower') plt.xlabel('x [pixels]') plt.ylabel('y [pixels]') plt.colorbar() plt.show() """ _is_bool = False def __init__(self, radius, **kwargs): self._model = models.AiryDisk2D(1, 0, 0, radius) self._default_size = _round_up_to_odd_integer(8 * radius) super(AiryDisk2DKernel, self).__init__(**kwargs) self.normalize() self._truncation = None class Model1DKernel(Kernel1D): """ Create kernel from 1D model. The model has to be centered on x = 0. Parameters ---------- model : `~astropy.modeling.Fittable1DModel` Kernel response function model x_size : odd int, optional Size in x direction of the kernel array. Default = 8 * width. mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by linearly interpolating between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. Raises ------ TypeError If model is not an instance of `~astropy.modeling.Fittable1DModel` See also -------- Model2DKernel : Create kernel from `~astropy.modeling.Fittable2DModel` CustomKernel : Create kernel from list or array Examples -------- Define a Gaussian1D model: >>> from astropy.modeling.models import Gaussian1D >>> from astropy.convolution.kernels import Model1DKernel >>> gauss = Gaussian1D(1, 0, 2) And create a custom one dimensional kernel from it: >>> gauss_kernel = Model1DKernel(gauss, x_size=9) This kernel can now be used like a usual Astropy kernel. """ _separable = False _is_bool = False def __init__(self, model, **kwargs): if isinstance(model, Fittable1DModel): self._model = model else: raise TypeError("Must be Fittable1DModel") super(Model1DKernel, self).__init__(**kwargs) class Model2DKernel(Kernel2D): """ Create kernel from 2D model. The model has to be centered on x = 0 and y = 0. Parameters ---------- model : `~astropy.modeling.Fittable2DModel` Kernel response function model x_size : odd int, optional Size in x direction of the kernel array. Default = 8 * width. y_size : odd int, optional Size in y direction of the kernel array. Default = 8 * width. mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by performing a bilinear interpolation between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. Raises ------ TypeError If model is not an instance of `~astropy.modeling.Fittable2DModel` See also -------- Model1DKernel : Create kernel from `~astropy.modeling.Fittable1DModel` CustomKernel : Create kernel from list or array Examples -------- Define a Gaussian2D model: >>> from astropy.modeling.models import Gaussian2D >>> from astropy.convolution.kernels import Model2DKernel >>> gauss = Gaussian2D(1, 0, 0, 2, 2) And create a custom two dimensional kernel from it: >>> gauss_kernel = Model2DKernel(gauss, x_size=9) This kernel can now be used like a usual astropy kernel. """ _is_bool = False _separable = False def __init__(self, model, **kwargs): self._separable = False if isinstance(model, Fittable2DModel): self._model = model else: raise TypeError("Must be Fittable2DModel") super(Model2DKernel, self).__init__(**kwargs) class PSFKernel(Kernel2D): """ Initialize filter kernel from astropy PSF instance. """ _separable = False def __init__(self): raise NotImplementedError('Not yet implemented') class CustomKernel(Kernel): """ Create filter kernel from list or array. Parameters ---------- array : list or array Filter kernel array. Size must be odd. Raises ------ TypeError If array is not a list or array. KernelSizeError If array size is even. See also -------- Model2DKernel, Model1DKernel Examples -------- Define one dimensional array: >>> from astropy.convolution.kernels import CustomKernel >>> import numpy as np >>> array = np.array([1, 2, 3, 2, 1]) >>> kernel = CustomKernel(array) >>> kernel.dimension 1 Define two dimensional array: >>> array = np.array([[1, 1, 1], [1, 2, 1], [1, 1, 1]]) >>> kernel = CustomKernel(array) >>> kernel.dimension 2 """ def __init__(self, array): self.array = array super(CustomKernel, self).__init__(self._array) @property def array(self): """ Filter kernel array. """ return self._array @array.setter def array(self, array): """ Filter kernel array setter """ if isinstance(array, np.ndarray): self._array = array.astype(np.float64) elif isinstance(array, list): self._array = np.array(array, dtype=np.float64) else: raise TypeError("Must be list or array.") # Check if array is odd in all axes odd = np.all([axes_size % 2 != 0 for axes_size in self.shape]) if not odd: raise KernelSizeError("Kernel size must be odd in all axes.") # Check if array is bool ones = self._array == 1. zeros = self._array == 0 self._is_bool = np.all(np.logical_or(ones, zeros)) self._truncation = 0.0