File:Discrete Gaussian kernel.svg
Summary
| Description |
English: Comparison of ideal discrete Gaussians based on Bessel functions (solid) versus sampled Gaussian (dashed), for scales values t = 0.5, 1, 2, 4; see Scale space implementation. |
| Date | |
| Source | Own work |
| Author | Omegatron |
| Other versions |
|
Source code
This media was created with Matplotlib (comprehensive library for creating static, animated, and interactive visualizations in Python)Category:Images with Matplotlib source code
Here is a listing of the source used to create this file.
Here is a listing of the source used to create this file.
from scipy.special import iv
import numpy as np
def discrete_gaussian_kernel(n, t):
T = np.exp(-t) * iv(n, t)
return T
def sampled_gaussian_kernel(n, t):
G = 1/np.sqrt(2*np.pi*t) * np.exp(-n**2/(2*t))
return G
if __name__ == '__main__':
import matplotlib.pyplot as plt
plt.figure(figsize=(5, 6))
for t in (0.5, 1, 2, 4):
N = 6
n = np.arange(-N, N+1)
p = plt.plot(n, discrete_gaussian_kernel(n, t), '.-',
label=f'$t={t:.1f}$')[0]
plt.plot(n, sampled_gaussian_kernel(n, t), ':', color=p.get_color())
plt.grid(True)
plt.ylim(0, 0.7)
plt.xlim(-6, 6)
plt.legend()
plt.xlabel('$n$')
plt.ylabel('$T(n,t)$')
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
