Medical Biophysics 3503G Lecture Notes - Lecture 3: Dynamic Range, Standard Deviation

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Is high contrast desirable?
suffiencient contrast is necessary to ensure features stand out from background and
from each other,
but physics of many imaging system present a trade-off b/w spatial resolution, contrast,
and/or signal to noise ratio
make contrasat really high, going to have to pay for it somewhere
and excessive contrast carries a more direct cost (higher contrast then you need it to
be)
consider image depicting an object with 4 circular features:
2 lower contrast objects (bottom left and top right), and we’re dissatisfied
we can rescale image, and make the 2 lower contrast image higher, that also rescales
the gray lvls of the original high contrast images so is there anything misleading about
how the 2 circles are now displayed this is misleading b/c we hit both the top/bottoms
ends of the scale so we’re not showing true values, of these 2 circles, one way to
appreciate it
Dynamic range and window
X axis have object property measureing ex. xray attentuation
Have imaging chain, and zero is minimun value xray attentuation that transducer can
physically measure and 1.0 is the max value
Y axis is the gray levels, that are output form display block at the beginning of the chain,
the first image was constructed was by maping w.e the smallest attenutation was, we
mapped it to gray lvl 0, w.e largest lvl of attentuation mapped to lvl 25 and in b/w we
translated x ray attnetuation to gray lvl by straight line fxn
When image was rescaled, leave background gray lvl the same (96 in both cases)à by
rescaling image, increased slope of straight line, so it went from blue dashed line, to red
solid lineà so we got up to 255 quicker in rescaled imageà and we got back to zero
quixker
The 2 circles that were high contrast in original image were gray lvl 16 and 240à gray lvl
240 (90% of x ray attneutaiton could measure), when we rescaled the image, it got
pumped up to 255, in new image we no longer know that xray attnetuaiton of brightest
circle is 0.9 arbituatry units, but all we know is it’s b/w 0.6 and 1.0 units b/c all those are
getting mapped to 255---à therefore we have less info about high contrast features, b/c
tried to make low contrast features better
0 to 1 arbituary units, is range that tranducer block could physically measure, called
tranducer dynamic range
point at which display map, goes down to gray lvl until the point it goes, first reaches
gray lvl 255, called display window range of attneutaiton values, over which, the gray
lvl gives useful inof about what the actuall xray attenuation was  in this case the
window was form 0.2-0.6
when were maxed out at 255 or floored at 0, those features in image, are said to be
saturated
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we can have wide display window, then images have lower contrast (original image,
with blue curve)
the image made with red curve, display window shorter, so have narrowier display
window, image contrast is higher
therefore increase contrast means reducing display window
↑ Contrast ↔ ↓ Display Window: Easier to distinguish small changes in object
properties, but narrower range of values displayed properly.
Signla to noise ratio (SNR)
nosie: random variation in gray lvl, which occur inregion where youd expect gray lvls to
be the same
high SNR image, the gray lvl within circle is fairly consistent
in low snr image, with losts of noise
if you have to little signal (contrast) or to much noise low SNR it’s harder see
features in the image
local SNR = mean gray lvl in specific region/standard deviation of gray levels in same
region
within circular feature in images on preceding slide,
High-SNR image: alpha = 128 (mean gray lvl in specific region), σ = 16 (standard
deviationof gray lvls) → SNR = 8
Low-SNR image: alpha = 128, σ = 64 → SNR = 2
using circular feature to calculate signal to nosie ratio, for images on previous slide, the
high snr image, the mean gray lvl is 128 insde circle, and standard deviation of all pixels
inside circle is 16
in low SNR mean gray lvl is still 128, but the pixels inside are 64
means gray lvl of the background is the same in the images
if you calculate contrast of image= 128-64/64 = contrast is 1 both circles are contrast 1
but the one is harder to see
contrast isn’t the only thing that tells you how easy it is to see the circle
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