Forensic Fractal Analysis

[C. Coppock]

Forensic Fractal Analysis?
Can the future of forensic impression evidence be a mathematical (computational) replacement of the manual comparison processes with us simple old school LPEs regulated to some obscure neglected quality assessment corner? An example is that we can easily do manual Iris comparisons, yet a programmed computer can do it much faster and more accurately, so says the data. While this is not a fractal analysis, it it a great example of computational idealism.

I understand there are current efforts to patent fractal conversions of fingerprint impression data for subsequent computational processes to include search and threshold matching. If this works to an agreeable level of accuracy I would expect an explosion of fractal research and development processes that may only need occasional LPEs to check the test data and hang out on the machine capability thresholds for support. The rest of the crew is mathematicians.

Could this be our film to digital conversion? Somehow I feel like a wayward investor in Kodak. Yes, the same bankrupt Kodak that invented the digital camera... but preferred film.

[Tazman]

According to an online dictionary,

Fractal: noun ▸ a shape that can be repeatedly divided into parts that are smaller copies of the original shape

How would "fractal analysis" apply to a fingerprint comparison?

[sandra wiese]

From Wikipedia:
Fractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset or a pattern or signal extracted from phenomena including natural geometric objects, sound, market fluctuations,[1] heart rates,[2] digital images,[3] molecular motion, networks, etc. Fractal analysis is now widely used in all areas of science.[4] An important limitation of fractal analysis is that arriving at an empirically determined fractal dimension does not necessarily prove that a pattern is fractal; rather, other essential characteristics have to be considered.[5]

Frankly, I'm not sure how helpful this is, but that is what is says!

[Tazman]

From Wikipedia:
Fractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset or a pattern or signal extracted from phenomena including natural geometric objects, sound, market fluctuations,[1] heart rates,[2] digital images,[3] molecular motion, networks, etc. Fractal analysis is now widely used in all areas of science.[4] An important limitation of fractal analysis is that arriving at an empirically determined fractal dimension does not necessarily prove that a pattern is fractal; rather, other essential characteristics have to be considered.[5]

Frankly, I'm not sure how helpful this is, but that is what is says!

Heck, I don't have a clue what that means. Can anybody translate that Wikipedia gibberish about "fractal" into high school level American dialect?

Craig, you started this. Help us out here.

[ER]

So this is mostly a guess, but if I had to guess...

Look at the fractal dimension on this page http://en.wikipedia.org/wiki/Fractal_dimension
Essentially, they are measuring the distance around Britain using yardsticks of different lengths. This pattern of smaller lengths produces a fractal. Granted, it's not what you would picture when you think of a fractal, but mathematically, it's comparable. (apparently)

Now, imagine that they did the same thing with a latent using different tiny measuring lengths to transform the print into a series of tiny straight lines. Combining all of these different measurements, each using a different length to trace out the ridges, they can, theoretically, get a decent approximation of what the latent looks like and where the minutiae are. Then they can search it in AFIS, find the match, and use a LR to tell if it's him.

Will it work?

Maybe. For the good ones.

Maybe not for the really nasty ones.

[Pat]

Forty years ago, a high school diploma or GED and a clean rap sheet would get you a job anywhere as a latent print examiner.

Twenty years ago, any bachelor's degree would get you a job as a latent print examiner

Ten years ago, a BS degree in a natural science would get you a job as a latent print examiner.

Pretty soon, it will take a PhD in mathematics. (No offense, g.)

[NRivera]

You say that jokingly Pat, but I'm afraid it's closer than we'd all like to admit.

[C. Coppock]

Yes, much of the research venue is changing from the crime lab to the mathematician and their computer. The research in biometric search algorithms has been growing very fast. When you take biometrics to a large scale it is necessary to "design out" as much manual comparison as possible as volume simply overwhelms the manual process. This is why there is such a focus on improving the process with research into all areas of mathematics. I have notice the field of fractals has been expanding very quickly since Benoit Mandelbrot gave us the Fractal Geometry of Nature bombshell. It is amazing to see the where fractal aspects are being found and applications are being applied. When I see like efforts applied to biometrics, it makes me wonder if this is the breakout approach they have been looking for? Time will tell. The big picture is that there is a lot of research energy being spent on trying to figure how to drive the “biometric search algorithm bus” around the process of manual latent comparison (us). Automated biometrics is all about acceptable error rates in relationship to effort, not lack of error or minimum error. However, in the mean time we still have our pride and our role in quality control as once research leaves the confines of the test bed, the concept of error and error rate becomes more ambiguous. Ironically, computers don't make matches; they score, rank, and do what they are told. This is our competition, EXTREMELY fast, but not very smart.
Currently, it seems the best way forward to understand the gaps in both the manual and automated search processes to enable us to leverage these machines for all they're worth.

[C. Coppock]

Afterthought: I suppose that any new algorithm(s) need only approach or equal our current error rate to be considered ideal, financially successful and subsequently efficient.

Here is one paper I came across:
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2010 Research Article
Combining Biometric Fractal Pattern and Particle Swarm Optimization-Based Classifier for Fingerprint Recognition

Chia-Hung Lin, Jian-Liung Chen, and Zwe-Lee Gaing
Department of Electrical Engineering, Kao-Yuan University, No. 1821, Jhongshan Rd., Lujhu Township, Kaohsiung County 82151, Taiwan
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I would guess the main challenge would be due to the inherent variability in all biometric collections.

[Neville]

C. Coppock
"Afterthought: I suppose that any new algorithm(s) need only approach or equal our current error rate to be considered ideal, financially successful and subsequently efficient."

Yes That is about it.

So is Fractal like overlaying

[C. Coppock]

I'm seeing two approaches to tackling the difficult latent search issue. One is from our human brain perspective, such as the extended feature set for latent mark-up. The other is from a mathematical approach in finding ways to "encode" mathematically so computers can improve latent searches prior to our verification stage. This is where a fractal approach may find its day in sun. The reason for some of this energetic research effort is due to the relatively low lights out accuracy with current algorithmic models and fractals are rearing their head in more and more research results and efforts. So I don't see the examiner looking at or using fractals, but rather the underlying encoding algorithms being fractal based. We would still see the regular markup for our verification stage. Yet, I'm not a mathematician. I don't know a fractal dimension of a latent from the Euler characteristic of a polyhedron.