File:Discrete Gaussian kernel.svg
| Uploaded by | Omegatron |
|---|---|
| Upload date | 2017-10-02T01:29:10Z |
| MIME type | image/svg+xml |
| Dimensions | 450 × 538 px |
| File size | 34.8 KB |
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 |
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Source code
This media was created with Matplotlib (comprehensive library for creating static, animated, and interactive visualizations in Python)
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
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- 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.