Convolution Mechanics
The kernel slides across the image. At each position, the output pixel is the sum of the kernel coefficients times the pixel values beneath them: g(x,y) = Σ w(s,t) · f(x+s, y+t). For the Gaussian, the coefficients come from the Gaussian function, normalized to sum to 1.
Comparison with Other Smoothing Filters
The box (averaging) filter sets all coefficients equal. It is simpler and faster, but it blurs edges aggressively and produces frequency-domain ringing. Objects smaller than half the mask area disappear entirely.
A weighted average gives the center the highest weight, for example a 3×3 kernel with center 4, orthogonal neighbors 2 and diagonals 1, all divided by 16. It approximates the Gaussian for small kernels.
The Gaussian takes its coefficients from exp(-D²/2σ²). Of the three, it is the standard choice for noise reduction.
Border Handling
At the image border, the kernel extends past the edge. In the BOM Options tab, Border Input can build a border from real pixels of the neighboring fields of view, and Border Option sets how the image is padded: Fill with black, Fill with white, Mirror, or Copy last pixels. These are module options; the Gauss filter has no border setting of its own.
Relationship to PSF
Because the fluorescence PSF is approximately Gaussian, convolving with a Gaussian kernel models the blurring the optics already apply. That connection helps you choose sigma relative to the optical resolution of your system.
Among smoothing filters, the Gaussian blurs most smoothly. A simple average (box filter) treats all neighbors equally and leaves blocky artifacts, while the Gaussian weights neighbors by distance, so the result looks natural. In general it can also be computed quickly, because a square Gaussian kernel splits into two 1D passes instead of one 2D pass.
