Median and uniform filters in SciPy - Step-by-Step Execution

Concept Flow - Median and uniform filters

Start with input data array

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Choose filter type: median or uniform

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Apply filter over sliding window

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For each window position:

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Median filter

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Sort values in window

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Pick middle value

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Replace center element with filtered value

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Move window to next position

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Repeat until entire array filtered

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Output filtered array

The filter slides a window over data. Median filter picks the middle value in the window. Uniform filter replaces with the average. This smooths or cleans data.

Execution Sample

SciPy

import numpy as np
from scipy.ndimage import median_filter, uniform_filter

arr = np.array([1, 2, 80, 4, 5])
med = median_filter(arr, size=3, mode='nearest')
uni = uniform_filter(arr, size=3, mode='nearest')

This code applies median and uniform filters with window size 3 on a 1D array.

Execution Table

Step	Window Position	Window Values	Median Filter Output	Uniform Filter Output
1	Indices 0-2	[1, 2, 80]	2	27.6667
2	Indices 1-3	[2, 80, 4]	4	28.6667
3	Indices 2-4	[80, 4, 5]	5	29.6667
4	Edges handled by padding	N/A	1 (left), 5 (right)	1.3333 (left), 4.6667 (right)
5	Final filtered arrays	N/A	[1, 2, 4, 5, 5]	[1.3333, 27.6667, 28.6667, 29.6667, 4.6667]

💡 All window positions processed; edges handled by padding; final filtered arrays produced.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
arr	[1, 2, 80, 4, 5]	[1, 2, 80, 4, 5]	[1, 2, 80, 4, 5]	[1, 2, 80, 4, 5]	[1, 2, 80, 4, 5]
median_filter output	N/A	[?, 2, ?, ?, ?]	[?, 2, 4, ?, ?]	[?, 2, 4, 5, ?]	[1, 2, 4, 5, 5]
uniform_filter output	N/A	[?, 27.6667, ?, ?, ?]	[?, 27.6667, 28.6667, ?, ?]	[?, 27.6667, 28.6667, 29.6667, ?]	[1.3333, 27.6667, 28.6667, 29.6667, 4.6667]

Key Moments - 2 Insights

Why does the median filter output at the edges differ from the middle?

Edges have fewer neighbors, so padding is used. This means the window includes repeated edge values, affecting the median. See execution_table row 4.

Why is the uniform filter output a decimal while the median filter output is an integer?

Uniform filter calculates the average, which can be a decimal. Median filter picks a middle value from the window, which is an existing integer from the array. See execution_table rows 1-3.

Visual Quiz - 3 Questions

Look at the execution table, what is the median filter output at window position indices 1-3?

A 2

B 4

C 5

D 80

💡 Hint

Check execution_table row 2 under 'Median Filter Output'

At which step does the uniform filter output first include the value 28.6667?

A Step 1

B Step 3

C Step 2

D Step 4

💡 Hint

Look at execution_table rows 1-3 under 'Uniform Filter Output'

If the window size changes from 3 to 5, how would the median filter output change?

A It would use a larger window, so median values might smooth more

B It would produce the same output as size 3

C It would only affect uniform filter, not median

D It would cause an error

💡 Hint

Window size controls how many neighbors are considered, see concept_flow

Concept Snapshot

Median and uniform filters smooth data by sliding a window.
Median filter picks the middle value in the window.
Uniform filter replaces with the average of values.
Edges are handled by padding.
Window size controls smoothing strength.

Full Transcript

Median and uniform filters work by sliding a window over data. For each window, median filter sorts values and picks the middle one, while uniform filter calculates the average. This helps reduce noise or smooth data. Edges are handled by padding to keep window size consistent. The example code applies both filters on a small array with window size 3. The execution table shows how the window moves, what values it sees, and what outputs it produces. Median filter outputs integers from the data, uniform filter outputs averages which can be decimals. Beginners often wonder why edges differ and why outputs differ in type; this is due to padding and calculation methods. Changing window size changes smoothing effect. This visual trace helps understand step-by-step how these filters work.