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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 - PowerPoint PPT Presentation
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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 methodLatent printsLivescan images – fingerprint sensors
FTIR optical scannerCapacitive scannerPiezoelectric scannerThermal scanner
Figure 6-6 from The Fingerprint Sourcebook
Image Enhancement
Many acquisition types leads to many noise characteristicsEnhancement algorithms help correct unwanted noise
Latent Print EnhancementAutomated EnhancementFigure 6-10 from The Fingerprint Sourcebook
Feature Extraction
Binarization algorithm – Black is ridges, white is valleysThinning algorithm leads to the thinned image or skeletal imageMinutiae detection algorithm locates the x, y, and theta coordinates of the minutiae pointsMinutiae 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 fingerprintsCould use Hough transform
Then match minutiae
Fingerprint is then given a matching scoreHigh = high probability fingerprint are a matchLow = 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 individualBefore digital fingerprints, forensic experts used filing cabinets to organize prints using a classification systemPrints are explicitly classified by overall shape: right loop, left loop, whorl, arch, tented arch, and double loopCan 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 CharacteristicsRidge 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 MethodComparison
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 paths
Examination MethodEvaluation
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 MethodRecurring, 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 MethodVerification
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 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
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 decreaseFor 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 libsUniversal 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 lineTen 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 apartIntersection of lines with first continuous ridgeline were landmarksAfter 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 minutiaeBifurcation 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)
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