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Statistics of Fingerprints Statistics of Fingerprints

Statistics of Fingerprints - PowerPoint Presentation

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Statistics of Fingerprints - PPT Presentation

Dakota Boyd Dustin Short Elizabeth Lee John Huppenthal Shelby Proft Wacey Teller History of Fingerprinting Originally used paper and ink fingerprints Fingerprints were matched using trained individuals ID: 683534

fingerprint minutiae method ridge minutiae fingerprint ridge method prints match variation analysis landmark landmarks fingerprints core level detail probability

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Slide1

Statistics of Fingerprints

Dakota Boyd, Dustin Short, Elizabeth Lee, John

Huppenthal

, Shelby

Proft

,

Wacey

TellerSlide2

History of Fingerprinting

Originally used paper and ink fingerprints

Fingerprints were matched using trained individuals

Initially, each country has its own standardsDigital fingerprinting lead to international standardsFingerprints can now be matched or partially matched using algorithms

Section 6.1-6.3 from

The Fingerprint SourcebookSlide3

Problems with Automated Fingerprint Processing Systems

Digital Fingerprint acquisition

Image enhancement

Feature/Minutiae extractionMatchingIndexing/retrieval

Section 6.4.1 from

The Fingerprint SourcebookSlide4

Fingerprint Acquisition

Ink and paper method

Latent prints

Livescan images – fingerprint sensorsFTIR optical scanner

Capacitive scanner

Piezoelectric scanner

Thermal scanner

Figure 6-6 from

The Fingerprint SourcebookSlide5

Image Enhancement

Many acquisition types leads to many noise characteristics

Enhancement algorithms help correct unwanted noise

Latent Print Enhancement

Automated Enhancement

Figure 6-10 from

The Fingerprint SourcebookSlide6

Feature Extraction

Binarization

algorithm – Black is ridges, white is valleys

Thinning algorithm leads to the thinned image or skeletal imageMinutiae detection algorithm locates the x

,

y

, and theta coordinates of the minutiae points

Minutiae post processing algorithm to detect false minutiae

Section 6.4.4 from

The Fingerprint SourcebookSlide7

Matching

Factors that influence matching from fingerprint acquisition: displacement, rotation, partial overlap, nonlinear distortion, pressure, skin conditions, noise from imaging, errors from feature extraction

First need to establish alignment

Programs may use core and delta points to align fingerprints

Could use Hough transform

Then match minutiae

Fingerprint is then given a matching score

High = high probability fingerprint are a match

Low = low probability the fingerprints are a match

Section 6.4.5 from

The Fingerprint SourcebookSlide8

Indexing Fingerprints

Need to be able to index and retrieve fingerprints of a given individual

Before digital fingerprints, forensic experts used filing cabinets to organize prints using a classification system

Prints are explicitly classified by overall shape: right loop, left loop, whorl, arch, tented arch, and double loop

Can be continuously classified using vectors

Section 6.4.6 from

The Fingerprint SourcebookSlide9

The Galton Model

First probability model for fingerprint individuality (1892).

Variously sized square papers dropped over sections of a fingerprint, and a prediction of whether or not the paper cover minutiae.

Model not based on actual distribution or frequency of minutiae.Estimated probability of different pattern types present and the number of ridges in the selected region of the print.

Probability of finding any given minutiae in a fingerprint given as 1 in 68 billion.Slide10

The Osterburg

Model

1977-1980

Divide fingerprint into 1 sq. mm sections and count the occurrence of 13 different minutiae appearances in each section.Rarity of a fingerprint arrangement = product of all individual minutiae frequencies and empty cells.

Example: 72 sq mm fingerprint, 12 ridge endings, each in one cell, 60 empty cells, probability = (0.766)

60

(0.0832)

12

= 1.25

x

10-20. 0.766 and 0.0832 are

Osterburg’s

observed frequencies of an empty cell and a ridge ending.

Problem: This model assumes each cell/section event is independent.Slide11

The Stoney

and Thornton Model

Classifying Characteristics

Ridge structure and description of minutiae locations.Descriptions of minutia distribution.

Orientation of minutiae.

Variation in minutiae types.

Variation among prints from the same source.

Number of orientations and comparisons.

1985-1989

Determined criteria for an ideal model to calculate individuality of a fingerprint and the probabilistic strength of a match.

Each minutiae pair is described by the six characteristics and the spatial position of the pair within the entire fingerprint.Slide12

The

Pankanti

,

Prabhakar, and Jain Model2001Model assesses probabilities of false matches, not individuality of fingerprints.

Calculates the number of possible arrangements of ridge endings and bifurcations.

Calculated spatial differences of minutiae in pairs, and accept similar spatial calculations as matches. (

x

,

y

,

θ).

Each fingerprint had four captures, separated in two databases, to determine an acceptable tolerance of error based on natural variations.Slide13
Slide14

First Level Detail

Direction of ridge flow in the print.

Not necessarily defined to a specified fingerprint pattern.

General direction of ridge flow is not unique.Slide15

Second Level Detail

Pathway of specific ridges.

Includes starting position, path of the ridge, length, and where the ridge path stops.

Includes configurations with other ridge paths.Uniqueness is found with the ridge path, length, and terminations.A general direction must exist (first level detail).Slide16

Third Level Detail

Shapes of the ridge structures.

Morphology of the ridge: edges, textures, and pore positions on the ridge.

Shapes, sequences, and configurations of third level detail are unique.General direction (first level) and a specific ridge path (second level) must exist for third level detail.Slide17
Slide18

Persistence

Comparing the visibility of minutiae in fingerprints over a time span.

Galton found one discrepancy, where a single bifurcation was not present 13 years later.

Other studies with age spans ranging up to 57 years found no discrepancies of minutiae.All in first and second level detail.Slide19

Persistence

Pores on the ridges of friction ridge skin remain unchanged throughout life. Their location remains the same.

Palm creases (third level detail of the palm) have seen changes over long time periods.

Due to age of the skin, skin flexibility, and other factors. All in third level detail.Slide20

Persistence

Basal layer (regenerative layer between dermis and epidermis).

Friction ridge skin persistency is maintained by the regenerative cells in the stratum

basale, and the connective relationship of these cells.Slide21

Examination Method

Analysis, comparison, evaluation (ACE) and verification (V)

This is one description of a method of comparing details, forming a hypothesis about the source, experimenting to determine whether there is agreement or disagreement, analyzing the sufficiency of agreement or disagreement, rendering an evaluation, and retesting to determine whether the conclusion can be repeated.Slide22

Examination Method

Analysis

The assessment of a print as it appears on the substrate.

Makes the decision of whether the print is sufficient for comparison with another printLooks at the substrate, matrix, development medium, deposition pressure, pressure and motion distortion, and development medium for appearance and distortionSlide23

Examination Method

Comparison

Determine whether the details in two prints are in agreement based upon similarity, sequence, and spatial relationship occurs in the comparison phase

Because no print is ever perfectly replicated, mental comparative assessment consider tolerance for variations in appearance caused by distortion

Makes comparative measurements of first, second, and third level details are made along with comparisons of the sequences and configuration of ridge pathsSlide24

Examination Method

Evaluation

The formulation of a conclusion base upon analysis and comparison of friction ridge skin

The examiner makes the final determination as to whether a finding of individuation or same source of origin can be made Makes comparative measurements of first, second, and third level details are made along with comparisons of the sequences and configuration of ridge pathsSlide25

Examination Method

Recurring, Reversing, and Blending Application of ACE

The examiner can change the phase of the examination often re-analysis, re-compares, and re-evaluates.

There is no clear linear path to this ACE process because the decision of choosing whether the two fingerprints are the same complicates things.Slide26

Examination Method

Because of the ambiguity of the process the colored diagram is used to illustrate the process.

The critical application of ACE is represented in the model by red area A, green area C and blue area E

The actual examination is represented in the model by

threee

smaller circles with capital A, C, and E. Slide27

Examination Method

The black dot in the center represents the subconscious processing of detail in which perception can occur

The gray represents other expert knowledge, beliefs, biases, influences and abilities.

The white that encircles the grey represents the decision has be made

Many evaluation take place. Eventually the final analysis and comparison lead to the final evaluation Slide28

Examination Method

Verification

The independent examination by another qualified examiner resulting in the same conclusion

It is another person going through the ACE process of verifying if the two prints conclusion are the same The verifier must not know the decision of the previous conclusion to get decisions that is nonbiasedSlide29

Decision Thresholds

Decisions must be made within each phase of ACE whether to go foreword, backwards, or to stop in the examination process must be decided

History of threshold:

New Scotland Yard adopted a policy (with some exceptions) of requiring 16 pointsThe FBI abandoned the practice of requiring a set number of points

The IAI (International Association for Identification) formed a committee to determine the minimum number of friction ridge characteristics which must be present in two impressions in order to establish positive identification Slide30

Decision Thresholds

The prevailing threshold of sufficiency is the examiners determination that sufficient quantity and quality of detail exists in the prints being compared

Quantitative-qualitative threshold (QQ)

For impressions from volar skin, as the quality of details in the prints in creases, the requirement for quantity of detail in the prints decreases, as the quantity of details decrease

For clearer prints, fewer details are needed and for less clear prints, more details are neededSlide31

QQ Threshold Curve

One unit of uniqueness in agreement is the theoretical minimum needed to determine the prints had been made by the same unique and persistent sourceSlide32

QQ Threshold Curve

Agreement (white area): sufficient detail agree and support a determination that the prints came from the same source

Disagreement (white area) sufficient details disagree and warrant a determination that the prints came from different sources

Inconclusive (gray and black areas): the examiner cannot determine whether the details actually agree or disagree or cannot determine sufficiency of sequences and configurations Slide33

APPLICATION OF SPATIAL STATISTICS TO LATENT PRINT IDENTIFICATIONS Slide34

Methodology

Ten

-print cards

- Qualitative image

assessment

•Scan, segregate and image enhancement

•Orientation, ULW minutiae detection, mark core and delta

•Geo-referencing and image QC

•GIS data conversion

•Spatial analysis of ridge lines and minutiae

•Statistical analyses and probability modeling Slide35
Slide36

Extraction Software

Free Fingerprint Imaging Software

 -- fingerprint pattern classification, minutiae detection, Wavelet Scalar Quantization(

wsq) compression, ANSI/NIST-ITL 1-2000 reference implementation, baseline and lossless jpeg, image utilities, math and neural net libs

Universal Latent Workstation (

ULW

)

-- interoperable and interactive software for latent print examiners. The software improves the exchange and search of latent friction ridge images involving various Automated Fingerprint Identification Systems.Slide37
Slide38
Slide39

Distribution of MinutiaeSlide40
Slide41
Slide42
Slide43
Slide44
Slide45

Geometric Morphometric Analysis

Research on fingerprints traditionally done using biometrics, which analyze linear geometric properties but ignore underlying biological properties

Ignoring these may exclude important bio patterns

Biomathematics include inherent biological properties of featuresGM is a biomathematical

model that includes biometrics, along with other fields for a comprehensive analysisSlide46

GM Analysis

Used for mandibular morphology, craniofacial features, identification using sinus cavities, pediatric skeletal age

For this project, GM used to study shape variation of four pattern types: left and right loops, whorls, and double loop whorls

GIS used for efficiencyTasks: Establish Methodology. Begin Analysis.Slide47

Method: Landmark and Semi-landmark Designation and Acquisition

30 images each referenced with

arcGIS

to find core and align in coordinate spaceLandmarks – Core, aspects of the deltaSemi-landmarks – Points along a ridgeline

For loops the core was defined as the point along the innermost ridgeline that forms the first full loop where the tangential angle is closest to 0 degrees

For whorls and double loop whorls, core defined as ridge ending in the middleSlide48

Method: Landmark and Semi-landmark Designation and Acquisition

Delta defined as a

triradius

consisting of 3 ridge systems converging with each other at an angle ~ 120 degreesA equilateral triangle, sized as small as possible, placed manually to define the delta. 100% consensus among team requiredSlide49

Method: Landmark and Semi-landmark Designation and Acquisition

Core and vertices of triangles defined as landmarks

For loops:

Radial line template of seven lines, eighteen degrees apart. Intersections of lines and first continuous ridgeline are semi-landmarksSlide50

For loops:

Two reference lines, one vertical, going through core; one horizontal from lowermost vertex to vertical line

Ten equidistant lines drawn from core to horizontal line

Where top six lines intersect with ridgeline that the core is on are more landmarks

Method: Landmark and Semi-landmark Designation and AcquisitionSlide51

For whorls:

Line template constructed with thirteen lines, nine degrees apart

Intersection of lines with first continuous ridgeline were landmarks

After defining landmarks and semi-landmarks, GIS used to record the features for all 120 prints

Method: Landmark and Semi-landmark Designation and AcquisitionSlide52

Method: Generalized

Procrusted

Analysis

Landmark and semi-landmark coordinates superimposed into a coordinate system in order to conduct statistical analysisCalculated Procrustes mean shape valuesSlide53

Method: Generalized Procrusted

Analysis

RSL and LSL, W and DLW superimposed onto each other with geometric transformations to determine varianceSlide54

Method: Thin-Plate Spline

Procrustes

mean shape values analyzed using R statistical software to produce TPS deformation gridsSlide55

Method: Thin-Plate Spline

TPS grids provide a smooth interpolation of inter-landmark space and provide exact mapping for landmarks and semi-landmarks from one pattern type onto anotherSlide56

Method: Principle Component Analysis

Captured a percentage of total variation based on distribution to summarize original larger data set

Direction of relative displacement for each landmark determinedSlide57

Results: Generalized Procrustes

Analysis

LSL: semi-landmarks were tightly clustered around mean shape showing little shape variation for both core ridgeline and continuous ridgeline. Large dispersion of delta landmarks and crease landmark

Whorls: Continuous ridgeline showed little shape variation. Delta and crease landmarks showed significant variation

LSL-RSL: greater dispersion due to size variation and rotational effects

W-DLW: same as LSL-RSLSlide58

Results: Thin-Plate Spline

The greater the deformation in the grid, the more shape variation between the two

RSL-LSL: high degree of shape consistency with greatest variation in the delta region

W-DLW: same as RSL-LSLSlide59

Results: Principle component analysis

Calculations used to reduce total of landmarks and semi-landmarks to one set to summarize degree of shape variation in each pattern type

Direction of variation represented by vector line

Degree of variation indicated by amount of deformation in gridRSL-LSL: different directions of variation, greatest variation in delta regions

W-DLW: greatest variation in delta regionsSlide60
Slide61

False-Match Probabilites

and Monte Carlo Analyses

“A computer algorithm used to repeatedly

resmaple data from a given population to make inferences about stochastic processes”Ideal for rare events, hard to analyze rare events with other methods

Goal is to produce an expected result, E(X) where X is a random variable. MC

sim

creates n independent samples of X, and as n increases, the average of the samples converges to the expected resultSlide62

False-Match Probabilites

and Monte Carlo Analyses

Used for village placement to avoid natural disasters, species diversity, evolution, air traffic control

For this project: There is biological ground to believe that fingerprints are unique, but statistics allows for duplicatesUniqueness not in question, but partial uniqueness is possible. Since examined prints are rarely full, need to see chances of partial duplicatesSlide63

Methods and background are numerically and theoretically intensive, so will email paper to those more interested

No assumptions – works well for small sample sizes, but assumptions must be used for larger numbers

Compared different sample sets to determine probability of a false-match

1200 fingerprintsFalse-Match Probabilites

and Monte Carlo AnalysesSlide64

GISStandardize coordinate space and analyze print by section

Eight simulations to determine how each attribute affects false-match probabilities

Nine overlapping grid cells and total minutiae in each cell counted

Sets of three, five, seven, or nine minutiae selectedFalse-Match Probabilites

and Monte Carlo AnalysesSlide65
Slide66
Slide67

Minutiae selected without replacement

50 prints selected for LSL, RSL, W, DLW

20 prints selected for arches, 25 for tented arches

Simulations iterated 1000 timesComparisons across and within pattern typesNeeded to account for variance of each minutiaeBifurcation angles, ridge ending roundness, etc.

False-Match

Probabilites

and Monte Carlo AnalysesSlide68

MC Results

Similar probability results for all pattern types

As robustness of simulation expanded, probability of false match decreased greatly

Using all criteria with location, three minutiae has a false-match chance of 1 in 5 millionUsing only location, chance is 1 in 1600Using only location with 5 minutiae, chance is 1 in 125000

Only one false match found when considering position of 9 minutiaeSlide69
Slide70

MC Results

Highest false match probability in regions below core and near delta (more minutiae)

Regions above core have very low false match probability (less minutiae)

Most matches found using Monte Carlo are obviously not matches when examinedSimilar patterns of minutiae, but not type were foundSmall sample size limits conclusions

100,000 fingerprints considered desirable for strong results (6-7 weeks of computer time)Slide71