1€ Filter (One Euro Filter)

A Python implementation of the 1€ Filter for numpy vector (1e filter, 1 euro filter, One Euro Filter). The original code is also available in jaantollander. The code in one_euro_filter.py can be used as numpy vector for implementing the real-time deep learning algorithm in python. Detailed pseudocode about the underlying mathematics of the algorithm and sources can be found in a blog post that jaantollander wrote about it, Noise Filtering Using 1€ Filter.

Source code

import numpy as np
from time import time

def smoothing_factor(t_e, cutoff):
    r = 2 * np.pi * cutoff * t_e
    return r / (r + 1)


def exponential_smoothing(a, x, x_prev):
    return a * x + (1 - a) * x_prev


class OneEuroFilter:
    def __init__(self, x0, dx0=0.0, min_cutoff=1.0, beta=0.0,
                 d_cutoff=1.0):
        """Initialize the one euro filter."""
        # The parameters.
        self.data_shape = x0.shape
        self.min_cutoff = np.full(x0.shape, min_cutoff)
        self.beta = np.full(x0.shape, beta)
        self.d_cutoff = np.full(x0.shape, d_cutoff)
        # Previous values.
        self.x_prev = x0.astype(np.float)
        self.dx_prev = np.full(x0.shape, dx0)
        self.t_prev = time()

    def __call__(self, x):
        """Compute the filtered signal."""
        assert x.shape == self.data_shape

        t = time()
        t_e = t - self.t_prev
        t_e = np.full(x.shape, t_e)

        # The filtered derivative of the signal.
        a_d = smoothing_factor(t_e, self.d_cutoff)
        dx = (x - self.x_prev) / t_e
        dx_hat = exponential_smoothing(a_d, dx, self.dx_prev)

        # The filtered signal.
        cutoff = self.min_cutoff + self.beta * np.abs(dx_hat)
        a = smoothing_factor(t_e, cutoff)
        x_hat = exponential_smoothing(a, x, self.x_prev)

        # Memorize the previous values.
        self.x_prev = x_hat
        self.dx_prev = dx_hat
        self.t_prev = t

        return x_hat

Example code results.

pip install seaborn
python example.py

Cursor event example use

pip install tk
python cursor_example.py