Overview
A median filter slides a window over a signal or image and outputs the median value in that window. It reduces impulse noise while preserving sharper edges better than simple averaging.
CoreSource checked
Median Filter
Replaces each sample or pixel with the median of a local neighborhood.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Signal Processing
- Difficulty
- Beginner
- Family
- Nonlinear Filter
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 2
- Code example
- Not ready
- Visualization
- Ready
Core Concepts
signal samplesranked neighborhoodfilter kernelnoise smoothingnonlinear filtersample windowsignal transformnoise handling
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n k log k)
Worst
O(n k log k)
Space
O(k)
When to Use
- Use when outlier samples should be suppressed without averaging across edges too much.
- Use when the window size can be chosen relative to feature size.
When Not to Use
- Avoid when Gaussian-like noise is better handled by linear filters.
- Avoid with windows so large that real features are erased.
What It Does
- Collects values in a local window
- Sorts or selects the median value
- Outputs the median as the filtered sample
Use Cases
- Removing salt-and-pepper noise
- Robust smoothing for images or signals
- Preprocessing before thresholding or edge detection
Inputs
- Signal or image
- Window size
Outputs
- Filtered signal or image
Key Formulas (1)
Median replacement
output[i] = median(values in local window around i)
output[i] = median(values in local window around i)Replaces each sample with the middle-ranked value from its neighborhood.
Pseudocode
- 1.Choose a local window size and boundary policy
- 2.For each output position
- 3.Collect neighboring samples inside the window
- 4.Select the median value
- 5.Write the median to the output
Canonical Example
- Input
- window [2, 100, 3]
- Output
- 3
- Explanation
- The outlier 100 is ignored because the median is the middle sorted value.
Implementation Notes
- Use odd window sizes unless an even-window policy is explicitly needed.
- Test impulse-noise examples and edge-preservation examples.
- For images with small integer ranges, histogram-based median updates can be faster.
Common Pitfalls
- Even-sized windows need a defined median convention.
- Boundary padding choices change output near edges.
- Large naive windows can be expensive without incremental histograms or selection structures.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow an outlier removed by choosing the middle value in a window.
Step 1 of 5: Choose a local window size and boundary policy
median-windowNotes
Median filtering is nonlinear; it does not have the same frequency response interpretation as linear filters.
Sources (1)
What each reference supports for this entry.
Digital Image Processing
BookImage-processing reference for nonlinear filters such as median filtering and practical neighborhood operations.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toGaussian Blur
Median filters suppress impulse noise, while Gaussian blur averages local neighborhoods.
Conceptual neighborMorphological Dilation
Both are local-window image operations but use different order statistics.
Related Algorithms
Tags
Signal ProcessingMedian FilterFilteringSmoothing