Overview
Gaussian blur replaces each pixel with a weighted neighborhood average where nearby pixels receive more weight. It suppresses high-frequency noise and is separable into horizontal and vertical passes.
CoreSource checked
Gaussian Blur
Smooths an image by convolving it with a Gaussian kernel.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Image Processing
- Difficulty
- Beginner
- Family
- Smoothing Filter
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 17
- Code example
- Ready
- Visualization
- Ready
Core Concepts
Gaussian kernelweighted averageseparable filternoise smoothingpixel operationfilter kernelsmoothing filterpixel neighborhood
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(w h k)
Average
O(w h k)
Worst
O(w h k)
Space
O(w h)
When to Use
- Use when local averaging should favor nearby pixels smoothly.
- Use when a separable, predictable low-pass filter is appropriate.
When Not to Use
- Avoid when preserving sharp edges is more important than noise reduction.
- Avoid when blur radius and border behavior cannot be chosen consistently.
What It Does
- Builds or samples a Gaussian kernel
- Convolves the image with normalized weights
- Reduces noise and fine detail
Use Cases
- Preprocessing before edge or feature detection
- Scale-space construction
- Softening images or suppressing pixel noise
Inputs
- Image
- Blur radius or sigma
Outputs
- Blurred image
Key Formulas (1)
Gaussian weight
G(x) = exp(−(x2) / (2 · σ2))
G(x) = exp(-(x^2) / (2 * sigma^2))Assigns stronger weight to nearby samples than distant samples.
Pseudocode
- 1.Choose sigma and kernel radius
- 2.Compute normalized Gaussian weights
- 3.Convolve each row with the 1D kernel
- 4.Convolve each column with the same 1D kernel
- 5.Return the smoothed image
Canonical Example
- Input
- 1D row [0, 0, 10, 0, 0] with a small Gaussian kernel
- Output
- a row where the central spike is spread into neighboring pixels
- Explanation
- The Gaussian weights distribute the spike while preserving the total intensity when normalized.
Implementation Notes
- Normalize kernel weights so they sum to one.
- Use separable horizontal and vertical convolution for performance.
- Test with an impulse image to verify kernel shape and centering.
Common Pitfalls
- Forgetting to normalize the kernel changes image brightness.
- Using inconsistent border handling changes edge pixels.
- Large kernels are expensive unless separability or approximation is used.
Interactive Mechanism Walkthrough
Spatial Primitive & Sweep-Line CanvasShow a weighted kernel softening sharp pixel changes.
Step 1 of 5: Choose sigma and kernel radius
blur-kernelNotes
Gaussian blur is often used as a controlled low-pass filter before measuring gradients.
Sources (1)
What each reference supports for this entry.
Digital Image Processing
BookImage-processing textbook support for Gaussian Blur's pixel-neighborhood operations, filtering rules, and image-analysis role.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
AlternativesAdaptive Thresholding
Image Processing · Core
Adaptive Thresholding extracts or transforms image evidence differently than Gaussian Blur.
Compare with thisAlternativesK-Means Image Segmentation
Image Processing · Core
K-Means Image Segmentation extracts or transforms image evidence differently than Gaussian Blur.
Compare with thisAlternativesMedian Filter
Signal Processing · Core
Median filters suppress impulse noise, while Gaussian blur averages local neighborhoods.
Compare with thisAlternativesOtsu Thresholding
Image Processing · Core
Otsu Thresholding extracts or transforms image evidence differently than Gaussian Blur.
Compare with thisRelationships
View full relationship pageOften paired withCanny Edge Detection
Canny uses Gaussian smoothing before edge-gradient measurement.
Conceptual neighborImage Pyramid
Image pyramids often combine smoothing with downsampling.
Related Algorithms
Tags
Image ProcessingSmoothingFiltering