IMG-25

CT windowing

g = clip((HU − WL)/WW + ½). Display grey from window level and width.

Reading speed

DisplayWindowing

Governing equation

g=\mathrm{clip}\left(\dfrac{\mathrm{HU}-WL}{WW}+\tfrac12\right)

$HU \in \left[-1000, 1000\right]$

where

HU: Pixel HU (HU)
WL: Window level (HU)
WW: Window width (HU)
g: Display grey (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

g=\mathrm{clip}\left(\dfrac{\mathrm{HU}-WL}{WW}+\tfrac12\right)

$HU \in \left[-1000, 1000\right]$

$HU = -1000$ $g = 0$

Along the curve

②

Domain of the variable — blue

HU_{\min} = -1000,\quad HU_{\max} = 1000

$HU \in \left[-1000, 1000\right]$

$HU = -1000$ $HU = -1000$

Along the curve

③

Response curve — green

g=\mathrm{clip}\left(\dfrac{\mathrm{HU}-WL}{WW}+\tfrac12\right)

$HU \in \left[-1000, 1000\right]$

$HU = -1000$ $g = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}g}{\mathrm{d}HU}

$HU \in \left[-1000, 1000\right]$

$HU = -987.4$ $g^{\prime} = 0$

Along the curve

Lecture brief

Historical brief

Larmor precession, CT Beer projections, SNR and Nyquist sampling are why MRI and CT images exist as numbers. The lab computes frequency, dose and resolution limits. This sheet (IMG-25 — CT windowing) is the form associated with Windowing. Working symbols: $HU$ , $WL$ , $WW$ $\rightarrow$ $g$ . Lung WW/WL ~ 1500/−600, bone 2000/+300, soft tissue 400/+40. Windowing is not a dose change.

Purpose

Purpose: compute

g

from

HU

WL

WW

in Medical imaging via

g=\mathrm{clip}\left(\dfrac{\mathrm{HU}-WL}{WW}+\tfrac12\right)

g = clip((HU − WL)/WW + ½). Display grey from window level and width. Use it when a real medical imaging question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

HU = 40.000\,\mathrm{HU}

WL = 40.000\,\mathrm{HU}

WW = 400.000\,\mathrm{HU}

, the governing relation

g=\mathrm{clip}\left(\dfrac{\mathrm{HU}-WL}{WW}+\tfrac12\right)

yields

g = 0.500\,\mathrm{—}

. A HU number mapped onto a 0–1 grey. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Pixel HU HU40 HUWindow level WL40 HUWindow width WW400 HU

Outputs

Display grey g0.500 —

Reading speed

Watch on YouTube

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Narration of this film

A HU number mapped onto a 0–1 grey.

Lung WW/WL ~ 1500/−600, bone 2000/+300, soft tissue 400/+40. Windowing is not a dose change.

Reading speed

Watch on YouTube