70 lines
2.5 KiB
Python
70 lines
2.5 KiB
Python
import numpy as np
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def sigma_matrix2(sig_x, sig_y, theta):
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"""Calculate the rotated sigma matrix (two dimensional matrix).
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Args:
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sig_x (float):
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sig_y (float):
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theta (float): Radian measurement.
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Returns:
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ndarray: Rotated sigma matrix.
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"""
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d_matrix = np.array([[sig_x**2, 0], [0, sig_y**2]])
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u_matrix = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]])
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return np.dot(u_matrix, np.dot(d_matrix, u_matrix.T))
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def mesh_grid(kernel_size):
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"""Generate the mesh grid, centering at zero.
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Args:
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kernel_size (int):
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Returns:
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xy (ndarray): with the shape (kernel_size, kernel_size, 2)
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xx (ndarray): with the shape (kernel_size, kernel_size)
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yy (ndarray): with the shape (kernel_size, kernel_size)
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"""
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ax = np.arange(-kernel_size // 2 + 1., kernel_size // 2 + 1.)
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xx, yy = np.meshgrid(ax, ax)
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xy = np.hstack((xx.reshape((kernel_size * kernel_size, 1)), yy.reshape(kernel_size * kernel_size,
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1))).reshape(kernel_size, kernel_size, 2)
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return xy, xx, yy
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def pdf2(sigma_matrix, grid):
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"""Calculate PDF of the bivariate Gaussian distribution.
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Args:
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sigma_matrix (ndarray): with the shape (2, 2)
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grid (ndarray): generated by :func:`mesh_grid`,
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with the shape (K, K, 2), K is the kernel size.
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Returns:
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kernel (ndarrray): un-normalized kernel.
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"""
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inverse_sigma = np.linalg.inv(sigma_matrix)
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kernel = np.exp(-0.5 * np.sum(np.dot(grid, inverse_sigma) * grid, 2))
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return kernel
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def bivariate_Gaussian(kernel_size, sig_x, sig_y, theta, grid=None, isotropic=True):
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"""Generate a bivariate isotropic or anisotropic Gaussian kernel.
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In the isotropic mode, only `sig_x` is used. `sig_y` and `theta` is ignored.
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Args:
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kernel_size (int):
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sig_x (float):
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sig_y (float):
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theta (float): Radian measurement.
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grid (ndarray, optional): generated by :func:`mesh_grid`,
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with the shape (K, K, 2), K is the kernel size. Default: None
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isotropic (bool):
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Returns:
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kernel (ndarray): normalized kernel.
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"""
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if grid is None:
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grid, _, _ = mesh_grid(kernel_size)
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if isotropic:
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sigma_matrix = np.array([[sig_x**2, 0], [0, sig_x**2]])
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else:
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sigma_matrix = sigma_matrix2(sig_x, sig_y, theta)
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kernel = pdf2(sigma_matrix, grid)
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kernel = kernel / np.sum(kernel)
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return kernel
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