Gaussian Blur

The Gaussian Blur command smooths the image using a Gaussian-weighted kernel. Compared to plain Blur, the Gaussian falloff preserves edges more faithfully and avoids the ringing artefacts of a hard box kernel.

When to use

Gaussian Blur is the preferred noise-reduction step for fluorescence images before threshold segmentation.

Parameters

Parameter	Description
Kernel size	Side length of the kernel in pixels (must be odd; range 3–27)
Sigma	Standard deviation of the Gaussian distribution (controls the spread)

Choosing sigma

A good rule of thumb is sigma ≈ kernel_size / 6. A smaller sigma relative to the kernel size produces a sharper result; a larger sigma increases smoothing towards a flat box filter.

Notes

The Gaussian function weights pixels by their distance from the centre:

$$G(x, y) = \frac{1}{2\pi\sigma^2} e^{-\frac{x^2+y^2}{2\sigma^2}}$$

Larger kernel sizes or higher sigma values remove more noise but also blur small objects.

Background

Gaussian smoothing is the foundation of scale-space theory in computer vision - the idea that an image can be analyzed at multiple levels of detail by convolving it with Gaussians of increasing $\sigma$, from fine noise-level detail up to coarse structure. See Witkin, “Scale-Space Filtering” (IJCAI, 1983) and Lindeberg, “Scale-Space Theory in Computer Vision” (Springer, 1994) for the underlying theory.