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Thomas Rouch ThomasParistech

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Computer Vision Engineer | MINES Paristech | ENS Paris-Saclay

ThomasParistech / density_cut_and_normalize.py

Last active July 17, 2024 14:26

	# Normalize the density by the disk/kernel convolution
	density /= gaussian_blurred

ThomasParistech / gaussian_blur.py

Created July 17, 2024 13:58

	import cv2

	def ceil_odd(x: float) -> int:
	"""Round float to nearest odd integer."""
	return 1 + 2math.ceil(0.5(x-1.0))

	# Perform KDE and retrieve the bandwidth
	kde = gaussian_kde(disk_xy.T)
	sigma = np.sqrt(kde.covariance[0, 0])

ThomasParistech / scikit_kde.py

Created July 15, 2024 17:33

	from sklearn.neighbors import KernelDensity

	kde = KernelDensity(kernel='linear', bandwidth="silverman")
	kde.fit(input_xy)
	density = np.exp(kde.score_samples(pred_xy))

ThomasParistech / reflection_radius.py

Last active July 10, 2024 07:47

ThomasParistech / reflected_kde.py

Last active July 7, 2024 18:58

	... # Generate disk_xy

	# Compute radius
	r = np.linalg.norm(disk_xy, axis=-1)

	# Change radius
	new_radius = 2 - r
	reflected_disk_xy = np.multiply((new_radius/r)[:, None],
	disk_xy)

ThomasParistech / base_kde.py

Created July 6, 2024 13:43

Boundary bias in Basic KDE on unit disk

	import numpy as np
	import matplotlib.pyplot as plt
	from scipy.stats import gaussian_kde

	# Generate a uniform grid of points in [-1, 1] x [-1, 1]
	n_rows = 100
	grid_xy = np.stack(np.meshgrid(np.linspace(-1, 1, n_rows),
	np.linspace(-1, 1, n_rows),
	indexing="xy"),
	axis=-1).reshape(-1, 2)

ThomasParistech / weighted_kde.py

Created February 26, 2024 16:20

	import numpy as np
	from scipy.stats import norm

	def weighted_kde(x_data: np.ndarray, x_prediction: np.ndarray) -> np.ndarray:
	h = silverman_bandwidth(x_data) # Required to evaluate CDF
	area_values = norm.cdf(1.0, x_prediction, h) - norm.cdf(0.0, x_prediction, h)
	basic_densities = basic_kde(x_data, x_prediction, h)
	return basic_densities / area_values

ThomasParistech / reflective_kde.py

Last active April 8, 2024 20:27

	import numpy as np

	def reflective_kde(x_data: np.ndarray, x_prediction: np.ndarray) -> np.ndarray:
	h = silverman_bandwidth(x_data) # Compute before adding reflected data
	x_data_augmented = np.stack((-x_data, x_data, 2-x_data))
	reflective_densities = basic_kde(x_data_augmented, x_prediction, h)
	# Discard left and right reflected samples and normalize density by 1/3
	return 3 * reflective_densities

ThomasParistech / transformed_kde.py

Last active February 26, 2024 17:35

	import numpy as np
	from scipy.special import logit

	def transformed_kde(x_data: np.ndarray, x_prediction: np.ndarray) -> np.ndarray:
	x_data_logit = logit(x_data)
	x_prediction_logit = logit(x_prediction)
	densities_logit = basic_kde(x_data_logit, x_prediction_logit)
	return densities_logit / (x_prediction * (1.0-x_prediction))

ThomasParistech / basic_kde.py

Last active February 25, 2024 23:05

basic_kde

	import numpy as np
	from scipy.stats import norm


	def silverman_bandwidth(x_data: np.ndarray) -> float:
	return (4/(3x_data.shape[0]))0.2 np.std(x_data)


	def basic_kde(x_data: np.ndarray, x_prediction: np.ndarray) -> np.ndarray:
	"""Perform Gaussian Kernel Density Estimation.