Smooth a bumpy circle

Question

I am detecting edges of round objects and am obtaining "bumpy" irregular edges. Is there away to smooth the edges so that I have a more uniform shape?

For example, in the code below I generate a "bumpy" circle (left). Is there a smoothing or moving average kind of function I could use to obtain or approximate the "smooth" circle (right). Preferably with some sort of parameter I can control as my actual images arn't perfectly circular.

import numpy as np
import matplotlib.pyplot as plt

fig, (bumpy, smooth) = plt.subplots(ncols=2, figsize=(14, 7))

an = np.linspace(0, 2 * np.pi, 100) 

bumpy.plot(3 * np.cos(an) + np.random.normal(0,.03,100), 3 * np.sin(an) + np.random.normal(0,.03,100))

smooth.plot(3 * np.cos(an), 3 * np.sin(an))

Answer 1

You can do this in frequency domain. Take the (x,y) coordinates of the points of your curve and construct the signal as signal = x + yj, then take the Fourier transform of this signal. Filter out the high frequency components, then take the inverse Fourier transform and you'll get a smooth curve. You can control the smoothness by adjusting the cutoff frequency.

Here's an example:

import numpy as np
from matplotlib import pyplot as plt

r = 3
theta = np.linspace(0, 2 * np.pi, 100) 
noise_level = 2
# construct the signal
x = r *  np.cos(theta) + noise_level * np.random.normal(0,.03,100)
y = r *  np.sin(theta) + noise_level * np.random.normal(0,.03,100)
signal = x + 1j*y
# FFT and frequencies
fft = np.fft.fft(signal)
freq = np.fft.fftfreq(signal.shape[-1])
# filter
cutoff = 0.1
fft[np.abs(freq) > cutoff] = 0
# IFFT
signal_filt = np.fft.ifft(fft)

plt.figure()
plt.subplot(121)
plt.axis('equal')
plt.plot(x, y, label='Noisy')
plt.subplot(122)
plt.axis('equal')
plt.plot(signal_filt.real, signal_filt.imag, label='Smooth')