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Speed Calculation: the Details

Module by: Heather Johnston, Siddharth Gupta, Veena Padmanabhan, Grant Lee. E-mail the authors

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

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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 = 1 N ∑n=1N | C n,t | I t 1 N n 1 N | C n,t | (1)

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:

AAC= 1 I t 1 N ∑n=1N | C n,t − C n,t-1 | AAC 1 I t 1 N n 1 N | C n,t C n,t-1 | (2)

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.

ASC= 1 I t 1 N ∑n=1N C n,t − C n,t-1 2 ASC 1 I t 1 N n 1 N C n,t C n,t-1 2 (3)

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.

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Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

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