Statistics of Fingerprints

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

Initially, each country has its own standards

Digital fingerprinting lead to international standards

Fingerprints can now be matched or partially matched using algorithms Section 6.1-6.3 from The Fingerprint Sourcebook

Problems with Automated Fingerprint

Processing SystemsDigital Fingerprint acquisition

Image enhancement

Feature/Minutiae extraction

Matching

Indexing/retrieval

Section 6.4.1 from The Fingerprint Sourcebook

Fingerprint Acquisition

Ink and paper method

Latent prints

Livescan images – fingerprint sensors

FTIR optical scanner

Capacitive scanner

Piezoelectric scanner

Thermal scanner

Figure 6-6 from The Fingerprint Sourcebook

Image Enhancement

Many acquisition types leads to many noise characteristics

Enhancement algorithms help correct unwanted noise

Latent Print Enhancement

Automated EnhancementFigure 6-10 from The Fingerprint Sourcebook

Feature Extraction

Binarization algorithm – Black is ridges, white is valleys

Thinning algorithm leads to the thinned image or skeletal image

Minutiae 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 Sourcebook

MatchingFactors 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 alignmentPrograms may use core and delta points to align fingerprints

Could use Hough transform

Then match minutiae

Fingerprint is then given a matching scoreHigh = high probability fingerprint are a match

Low = low probability the fingerprints are a match

Section 6.4.5 from The Fingerprint Sourcebook

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 Sourcebook

The Galton ModelFirst 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.

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.

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.

The Pankanti, Prabhakar, and Jain

Model2001

Model 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.

First Level DetailDirection of ridge flow in the print.

Not necessarily defined to a specified fingerprint pattern.

General direction of ridge flow is not unique.

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).

Third Level DetailShapes 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.

PersistenceComparing 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.

PersistencePores 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.

PersistenceBasal 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.

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.

Examination Method

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

Makes the decision of whether the print is sufficient for comparison with another print

Looks at the substrate, matrix, development medium, deposition pressure, pressure and motion distortion, and development medium for appearance and distortion

Examination Method

ComparisonDetermine 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 paths

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 paths

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.

Examination MethodBecause 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.

Examination MethodThe black dot in the center represents

the subconscious processing of detail in which perception can occurThe 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

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 nonbiased

Decision ThresholdsDecisions 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 points

The 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

Decision ThresholdsThe 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 needed

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 source

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

APPLICATION OF SPATIAL STATISTICS TO LATENT PRINT IDENTIFICATIONS

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

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.

Distribution of Minutiae

Geometric Morphometric

AnalysisResearch 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 features

GM is a biomathematical model that includes biometrics, along with other fields for a comprehensive analysis

GM AnalysisUsed 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 efficiency

Tasks: Establish Methodology. Begin Analysis.

Method: Landmark and Semi-landmark Designation

and Acquisition30 images each referenced with arcGIS to find core and align in coordinate space

Landmarks – Core, aspects of the delta

Semi-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 middle

Method: Landmark and Semi-landmark Designation

and AcquisitionDelta defined as a triradius consisting of 3 ridge systems converging with each other at an angle ~ 120 degrees

A equilateral triangle, sized as small as possible, placed manually to define the delta. 100% consensus among team required

Method: Landmark and Semi-landmark Designation and

AcquisitionCore 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-landmarks

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

Acquisition

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 Acquisition

Method: Generalized Procrusted Analysis

Landmark and semi-landmark coordinates superimposed into a coordinate system in order to conduct statistical analysis

Calculated Procrustes mean shape values

Method: Generalized Procrusted Analysis

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

Method: Thin-Plate Spline

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

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 another

Method: Principle Component

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

Direction of relative displacement for each landmark determined

Results: Generalized Procrustes AnalysisLSL: 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-RSL

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-LSL

Results: Principle component

analysisCalculations 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 grid

RSL-LSL: different directions of variation, greatest variation in delta regions

W-DLW: greatest variation in delta regions

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 result

False-Match Probabilites and

Monte Carlo AnalysesUsed 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 duplicates

Uniqueness not in question, but partial uniqueness is possible. Since examined prints are rarely full, need to see chances of partial duplicates

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 fingerprints

False-Match Probabilites and

Monte Carlo Analyses

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 selected

False-Match Probabilites and

Monte Carlo Analyses

Minutiae selected without replacement

50 prints selected for LSL, RSL, W, DLW

20 prints selected for arches, 25 for tented arches

Simulations iterated 1000 times

Comparisons across and within pattern types

Needed to account for variance of each minutiae

Bifurcation angles, ridge ending roundness, etc.

False-Match Probabilites and

Monte Carlo Analyses

MC ResultsSimilar 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 million

Using only location, chance is 1 in 1600

Using only location with 5 minutiae, chance is 1 in 125000

Only one false match found when considering position of 9 minutiae

MC ResultsHighest 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 examined

Similar patterns of minutiae, but not type were found

Small sample size limits conclusions

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