Gaussian filtering an image with NaN in Python Matplotlib

Gaussian filtering is a common image processing technique that smooths images by applying a Gaussian kernel. However, when an image contains NaN (Not a Number) values, standard Gaussian filtering propagates these NaN values throughout the filtered result, making the entire output matrix NaN.

Understanding the Problem

When you apply a Gaussian filter to data containing NaN values, the convolution operation spreads these NaN values to neighboring pixels. This happens because any mathematical operation involving NaN returns NaN.

Example with NaN Propagation

Let's see how NaN values affect Gaussian filtering ?

import numpy as np
import matplotlib.pyplot as plt
from scipy.ndimage import gaussian_filter

# Create figure with subplots
plt.rcParams["figure.figsize"] = [10.00, 5.00]
fig, axes = plt.subplots(1, 2, figsize=(10, 4))

# Create data with NaN values
data = np.array([[1.0, 1.2, 0.89, np.nan],
                 [1.2, np.nan, 1.89, 2.09],
                 [0.78, 0.67, np.nan, 1.78],
                 [np.nan, 1.56, 1.89, 2.78]])

# Display original data
im1 = axes[0].imshow(data, cmap="cubehelix_r")
axes[0].set_title("Original Data with NaN")

# Apply Gaussian filter
gaussian_filtered = gaussian_filter(data, sigma=1)

# Display filtered data
im2 = axes[1].imshow(gaussian_filtered, cmap="cubehelix_r")
axes[1].set_title("After Gaussian Filter")

plt.tight_layout()
plt.show()

print("Original data shape:", data.shape)
print("Filtered data contains NaN:", np.isnan(gaussian_filtered).any())
print("Number of NaN values:", np.isnan(gaussian_filtered).sum())

Original data shape: (4, 4)
Filtered data contains NaN: True
Number of NaN values: 16

Solutions for Handling NaN Values

Method 1: Using astropy's convolution

The astropy library provides NaN-aware convolution functions ?

from astropy.convolution import Gaussian2DKernel, convolve

# Create Gaussian kernel
kernel = Gaussian2DKernel(x_stddev=1)

# Apply NaN-aware convolution
filtered_astropy = convolve(data, kernel, boundary='extend')

Method 2: Manual NaN Handling

Replace NaN values with interpolated values before filtering ?

import numpy as np
from scipy.ndimage import gaussian_filter
import matplotlib.pyplot as plt

# Original data with NaN
data = np.array([[1.0, 1.2, 0.89, np.nan],
                 [1.2, np.nan, 1.89, 2.09],
                 [0.78, 0.67, np.nan, 1.78],
                 [np.nan, 1.56, 1.89, 2.78]])

# Create a mask for valid (non-NaN) values
mask = ~np.isnan(data)

# Replace NaN with mean of valid values
data_filled = data.copy()
data_filled[np.isnan(data)] = np.nanmean(data)

# Apply Gaussian filter
filtered_result = gaussian_filter(data_filled, sigma=1)

# Display results
fig, axes = plt.subplots(1, 3, figsize=(12, 4))

axes[0].imshow(data, cmap="cubehelix_r")
axes[0].set_title("Original with NaN")

axes[1].imshow(data_filled, cmap="cubehelix_r")
axes[1].set_title("NaN Replaced with Mean")

axes[2].imshow(filtered_result, cmap="cubehelix_r")
axes[2].set_title("Gaussian Filtered")

plt.tight_layout()
plt.show()

print("Mean of valid values:", np.nanmean(data))
print("Filtered result has NaN:", np.isnan(filtered_result).any())

Mean of valid values: 1.4052631578947367
Filtered result has NaN: False

Comparison of Approaches

Conclusion

Standard Gaussian filtering propagates NaN values throughout the result. Use astropy's convolution for NaN-aware filtering or manually handle NaN values by replacement before applying the filter.