# 0.5 Speed calculation: the details

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Specifics on our algorithm to calculate the speed of a known object.

## Extensibility

To make our speed algorithm as extensible to as many different situations as possible, we normalize the results with respect to the overall intensity in the image. This gives a measure of change whose magnitude is scaled by the size of the image. The overall intensity is calculated as where Cn,t is the compressed sensing measurement along basis element n and time t. The CS resolution, or number of data points taken per frame, is N.

${I}_{t}=\frac{1}{N}\phantom{\rule{+0em}{0ex}}\sum_{n=1}^{N} |{C}_{\mathrm{n,t}}|$

## Average absolute change to measure speed

As described earlier, increased velocity yields greater change between subsequent measurements in time of a particular projection. Our calculation to measure velocity is:

$\mathrm{AAC}=\frac{1}{{I}_{t}}\phantom{\rule{+0em}{0ex}}\frac{1}{N}\phantom{\rule{+0em}{0ex}}\sum_{n=1}^{N} |{C}_{\mathrm{n,t}}-{C}_{\mathrm{n,t-1}}|$

Since we are interested only in the amount of change that occurs, the absolute value is taken. Because the projections themselves are random, any one measurement is not a good indication of the change and it is only by averaging a number of calculations that a meaningful value can be computed.

## Average squared change to measure speed

As another way to measure the change between frames, the squared difference between frames is taken. This measure was suggested by Ilan Goodman to explore the Parseval equivalencies often observed between domains.

$\mathrm{ASC}=\frac{1}{{I}_{t}}\phantom{\rule{+0em}{0ex}}\frac{1}{N}\phantom{\rule{+0em}{0ex}}\sum_{n=1}^{N} {\left({C}_{\mathrm{n,t}}-{C}_{\mathrm{n,t-1}}\right)}^{2}$

Since this metric computes the square of the two norm of , it is linearly proportional to the intensity changes of the difference image in the pixel domain.

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
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Renato
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Kyle
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what school?
Kyle
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Joe
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research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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absolutely yes
Daniel
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it is a goid question and i want to know the answer as well
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Anassong
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NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
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s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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