Module gaussian_blur 

Gaussian blur filter implementation using multi-scale separable convolution.

This implementation uses a multi-scale approach for efficient blurring:

• Small blurs (σ ≤ 2): Direct separable convolution at full resolution
• Large blurs (σ > 2): Iterative downsample → blur → upsample pyramid

The algorithm automatically determines the optimal number of decimation levels using variance analysis. Each 2× decimation applies a [1,3,3,1]/8 binomial filter (adding variance = 3.0), then downsamples, reducing the remaining blur work needed. This exploits the variance additivity property: σ²_total = σ²_downsample + σ²_blur.

Variance Addition Reference: The convolution of two Gaussians with variances σ₁² and σ₂² produces a Gaussian with variance σ₁² + σ₂². This fundamental property comes from probability theory and applies to Gaussian convolution in image processing. See:

• Torralba & Freeman, “Foundations of Computer Vision” (MIT Press), Section 2.2: https://visionbook.mit.edu/blurring_2.html#properties-of-the-continuous-gaussian

Constants

TRANSPARENT_BLACK 🔒

Transparent black pixel constant.

Functions

apply_blur 🔒

Apply Gaussian blur using multi-scale decimation and upsampling.

convolve 🔒

Apply separable Gaussian convolution with logical dimensions.

convolve_x 🔒

Apply horizontal blur pass (1D convolution along x-axis).

convolve_y 🔒

Apply vertical blur pass (1D convolution along y-axis).

decimate_weighted 🔒

Blend 4 RGBA pixels using [1,3,3,1]/8 binomial weights.

downscale 🔒

Downsample image by 2x using separable [1,3,3,1]/8 binomial filter.

downscale_x 🔒

Horizontal decimation pass using [1,3,3,1]/8 filter.

downscale_y 🔒

Vertical decimation pass using [1,3,3,1]/8 filter.

extend 🔒

Extend a coordinate beyond image boundaries according to the edge mode.

interpolate_25_75 🔒

Blend 2 RGBA pixels using [0.25, 0.75] weights (right-weighted interpolation).

interpolate_75_25 🔒

Blend 2 RGBA pixels using [0.75, 0.25] weights.

sample 🔒

Sample a pixel with edge mode handling (generic implementation).

sample_x 🔒

Sample a pixel with edge mode handling for horizontal sampling.

sample_y 🔒

Sample a pixel with edge mode handling for vertical sampling.

upscale 🔒

Upsample a pixmap by 2x using linear interpolation with [0.75, 0.25] weights.

upscale_x 🔒

Horizontal upsampling pass using [0.75, 0.25] interpolation with logical dimensions.

upscale_y 🔒

Vertical upsampling pass using [0.75, 0.25] interpolation with logical dimensions.