# Effective Gaussian Filtering of Images with NaNs in Python using Matplotlib

π‘ Problem Formulation: When processing images, NaN (Not a Number) values can pose a problem, especially during Gaussian filteringβa common image smoothing technique. These NaN values may arise from invalid operations or missing data within an image array. The conventional Gaussian filtering functions do not handle NaNs, often resulting in distorted output. In this article, we explore reliable methods to perform Gaussian filtering on images with NaN values in Python using Matplotlib, ensuring that the presence of NaNs does not compromise the smoothing process. Imagine converting an image loaded as a NumPy array filled with floating-point values, where some are NaNs, into a smoothly filtered image without NaN distortions.

## Method 1: Masked Array Filtering

This method involves creating a masked array that ignores NaN values during the filtering process. The `numpy.ma.masked_array` function is used to represent the NaNs as a mask, and then filtering is applied using `scipy.ndimage.gaussian_filter` on the unmasked values. This technique maintains the NaN values’ positions while smoothing other data points.

Here’s an example:

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

# Create a sample image with NaNs
image_with_nans = np.random.rand(10, 10)
image_with_nans[5, 5] = np.nan

# Create a masked array, ignoring NaNs

# Apply Gaussian filter

# Plot the filtered image
plt.imshow(filtered_image, cmap='gray')
plt.colorbar()
plt.show()```

The output will be an image displayed in a Matplotlib window, where the NaN values are retained but the valid data points are smoothed.

This method keeps the original NaN values intact and smooths other pixels effectively. However, NaNs might still affect the filtering close to their location, resulting in less-than-ideal smoothing around those areas. Furthermore, applications using the output might need to account for the masked values separately.

## Method 2: Nearest Neighbors NaN Interpolation

Before applying the Gaussian filter, NaN values can be replaced by interpolating from nearest neighbors. This approach uses the `scipy.interpolate.griddata` function, which interpolates the NaN locations based on valid neighboring pixels. After interpolation, a standard Gaussian filter is applied to the interpolated image.

Here’s an example:

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

def interpolate_nans(image):
x, y = np.indices(image.shape)
valid_points = np.isfinite(image)
coordinates = np.column_stack((x[valid_points], y[valid_points]))
values = image[valid_points]
grid_z2 = interpolate.griddata(coordinates, values, (x, y), method='nearest')
return grid_z2

# Create sample image with NaNs
image_with_nans = np.random.rand(10, 10)
image_with_nans[:2,:] = np.nan

# Interpolate NaNs
interpolated_image = interpolate_nans(image_with_nans)

# Apply Gaussian Filter
filtered_image = gaussian_filter(interpolated_image, sigma=1)

# Display results
plt.imshow(filtered_image, cmap='gray')
plt.colorbar()
plt.show()```

The output will be an image displayed in a Matplotlib window showing the interpolation of NaN areas and the subsequent Gaussian smoothing.

This method provides a practical way to treat NaNs by estimating their values from the surroundings. However, it may not always be suitable if NaNs represent crucial features that should not be altered.

## Method 3: Modify Gaussian Filter to Ignore NaNs

In this method, we modify the Gaussian filter itself to skip NaN values during the convolution. We achieve this by using a custom filtering function that first masks out NaNs and then convolves with a Gaussian kernel manually recalculating the normalization for each window.

Here’s an example:

```import numpy as np
import scipy.ndimage as nd
import matplotlib.pyplot as plt

def nan_gaussian_filter(image, sigma=1):
V = np.where(np.isnan(image), 0, image)  # Values (with NaNs to 0)
V[np.isnan(image)] = 0  # Ignore NaNs
VV = nd.gaussian_filter(V, sigma=sigma)

W = np.where(np.isnan(image), 0, 1)  # Weights
WW = nd.gaussian_filter(W, sigma=sigma)

return VV/WW

# Create a sample image with NaNs
image_with_nans = np.random.rand(10, 10)
image_with_nans[5, 5] = np.nan

# Apply the custom nan_gaussian_filter
filtered_image = nan_gaussian_filter(image_with_nans, sigma=1)

# Display the filtered image
plt.imshow(filtered_image, cmap='gray')
plt.colorbar()
plt.show()```

The output will be a Matplotlib window displaying the image with NaN values avoided during the Gaussian filter process.

This custom filter treats NaNs transparently and avoids the need for interpolation, maintaining the integrity of non-NaN data. Nevertheless, this approach might be computationally more intensive than standard filtering methods.

## Bonus One-Liner Method 5: Pandas DataFrame with interpolate and apply

For a quick solution, converting the image to a Pandas DataFrame and using its `interpolate` and `apply` functionality can be handy. This method allows for simple and concise NaN interpolation.

Here’s an example:

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

# Create a sample image with NaNs
image_with_nans = np.random.rand(10, 10)
image_with_nans[[5, 7], [2, 8]] = np.nan

# Convert to DataFrame
df = pd.DataFrame(image_with_nans)

# Interpolate NaNs
df_interpolated = df.interpolate(method='nearest', axis=0).interpolate(method='nearest', axis=1)

# Apply Gaussian Filter using DataFrame's applymap method
filtered_image = df_interpolated.applymap(lambda x: gaussian_filter(x, sigma=1))

# Display the filtered image
plt.imshow(filtered_image, cmap='gray')
plt.colorbar()
plt.show()```

The output is a smoothed image displayed using Matplotlib, where NaNs have been interpolated using DataFrame operations before Gaussian filtering.

This method leverages the high-level data manipulation capabilities of Pandas. However, it may be less efficient and provide less control over the interpolation process given the DataFrame conversion overhead.

## Summary/Discussion

• Method 1: Masked Array Filtering. It is robust and retains NaN positions effectively. Its weakness lies in handling the areas close to NaN values.
• Method 2: Nearest Neighbors NaN Interpolation. It fills in NaNs with plausible values before smoothing, making it best for generalized smoothing but may alter important NaN features.
• Method 3: Modify Gaussian Filter to Ignore NaNs. Custom filter that maintains data integrity, especially where NaN values are important. This method might be slower than others due to its more complex calculations.
• Method 5: Pandas DataFrame with interpolate and apply. Quickest and most straightforward, suitable for rapid prototyping. It compromises fine-grained control and performance.