Presentation on theme: "Statistics of Fingerprints"— Presentation transcript:
1 Statistics of Fingerprints Dakota Boyd, Dustin Short, Elizabeth Lee, John Huppenthal, Shelby Proft, Wacey Teller
2 History of Fingerprinting Originally used paper and ink fingerprintsFingerprints were matched using trained individualsInitially, each country has its own standardsDigital fingerprinting lead to international standardsFingerprints can now be matched or partially matched using algorithmsSection from The Fingerprint Sourcebook
3 Problems with Automated Fingerprint Processing Systems Digital Fingerprint acquisitionImage enhancementFeature/Minutiae extractionMatchingIndexing/retrievalSection from The Fingerprint Sourcebook
4 Fingerprint Acquisition Ink and paper methodLatent printsLivescan images – fingerprint sensorsFTIR optical scannerCapacitive scannerPiezoelectric scannerThermal scannerFigure 6-6 from The Fingerprint Sourcebook
5 Image EnhancementMany acquisition types leads to many noise characteristicsEnhancement algorithms help correct unwanted noiseLatent Print EnhancementAutomated EnhancementFigure 6-10 from The Fingerprint Sourcebook
6 Feature ExtractionBinarization 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 minutiaeSection from The Fingerprint Sourcebook
7 MatchingFactors that influence matching from fingerprint acquisition: displacement, rotation, partial overlap, nonlinear distortion, pressure, skin conditions, noise from imaging, errors from feature extractionFirst need to establish alignmentPrograms may use core and delta points to align fingerprintsCould use Hough transformThen match minutiaeFingerprint is then given a matching scoreHigh = high probability fingerprint are a matchLow = low probability the fingerprints are a matchSection from The Fingerprint Sourcebook
8 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 vectorsSection from The Fingerprint Sourcebook
9 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.
10 The Osterburg ModelDivide 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 = x and are Osterburg’s observed frequencies of an empty cell and a ridge ending.Problem: This model assumes each cell/section event is independent.If a cell contains minutiae, it is rare that the eight surrounding cells will contain minutiae.
11 The Stoney and Thornton Model 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.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.
12 The Pankanti, Prabhakar, and Jain Model 2001Model 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.
14 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.
15 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).
16 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.
18 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.
19 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.
20 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.
21 Examination MethodAnalysis, 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.
22 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 distortion
23 Examination Method Comparison Determine whether the details in two prints are in agreement based upon similarity, sequence, and spatial relationship occurs in the comparison phaseBecause no print is ever perfectly replicated, mental comparative assessment consider tolerance for variations in appearance caused by distortionMakes comparative measurements of first, second, and third level details are made along with comparisons of the sequences and configuration of ridge paths
24 Examination Method Evaluation The formulation of a conclusion base upon analysis and comparison of friction ridge skinThe examiner makes the final determination as to whether a finding of individuation or same source of origin can be madeMakes comparative measurements of first, second, and third level details are made along with comparisons of the sequences and configuration of ridge paths
25 Examination MethodRecurring, Reversing, and Blending Application of ACEThe 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.
26 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 EThe actual examination is represented in the model by threee smaller circles with capital A, C, and E.
27 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 madeMany evaluation take place. Eventually the final analysis and comparison lead to the final evaluation
28 Examination Method Verification The independent examination by another qualified examiner resulting in the same conclusionIt is another person going through the ACE process of verifying if the two prints conclusion are the sameThe verifier must not know the decision of the previous conclusion to get decisions that is nonbiased
29 Decision ThresholdsDecisions must be made within each phase of ACE whether to go foreword, backwards, or to stop in the examination process must be decidedHistory 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 pointsThe 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
30 Decision ThresholdsThe prevailing threshold of sufficiency is the examiners determination that sufficient quantity and quality of detail exists in the prints being comparedQuantitative-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
31 QQ Threshold CurveOne unit of uniqueness in agreement is the theoretical minimum needed to determine the prints had been made by the same unique and persistent source
32 QQ Threshold CurveAgreement (white area): sufficient detail agree and support a determination that the prints came from the same sourceDisagreement (white area) sufficient details disagree and warrant a determination that the prints came from different sourcesInconclusive (gray and black areas): the examiner cannot determine whether the details actually agree or disagree or cannot determine sufficiency of sequences and configurations
33 APPLICATION OF SPATIAL STATISTICS TO LATENT PRINT IDENTIFICATIONS
34 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 modelingScanning ten-print cards using TWAIN compliant softwareImage processing (image rotation, fingerprint cropping, image enhancements)Export to Universal Latent Workstation software package for minutia detectionGeoregistration of vector minutia point files and print images into a standardized coordinate reference systemExport of vector and raster data layers to GIS-compliant data formats for use in the ESRI ArcGIS software suite.
45 Geometric Morphometric Analysis Research on fingerprints traditionally done using biometrics, which analyze linear geometric properties but ignore underlying biological propertiesIgnoring these may exclude important bio patternsBiomathematics include inherent biological properties of featuresGM is a biomathematical model that includes biometrics, along with other fields for a comprehensive analysis
46 GM AnalysisUsed for mandibular morphology, craniofacial features, identification using sinus cavities, pediatric skeletal ageFor this project, GM used to study shape variation of four pattern types: left and right loops, whorls, and double loop whorlsGIS used for efficiencyTasks: Establish Methodology. Begin Analysis.
47 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 ridgelineFor 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 degreesFor whorls and double loop whorls, core defined as ridge ending in the middle
48 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 required
49 Method: Landmark and Semi-landmark Designation and Acquisition Core and vertices of triangles defined as landmarksFor loops:Radial line template of seven lines, eighteen degrees apart. Intersections of lines and first continuous ridgeline are semi-landmarks
50 Method: Landmark and Semi-landmark Designation and Acquisition 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 lineWhere top six lines intersect with ridgeline that the core is on are more landmarks
51 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
52 Method: Generalized Procrusted Analysis Landmark and semi-landmark coordinates superimposed into a coordinate system in order to conduct statistical analysisCalculated Procrustes mean shape values
53 Method: Generalized Procrusted Analysis RSL and LSL, W and DLW superimposed onto each other with geometric transformations to determine variance
54 Method: Thin-Plate Spline Procrustes mean shape values analyzed using R statistical software to produce TPS deformation grids
55 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
56 Method: Principle Component Analysis Captured a percentage of total variation based on distribution to summarize original larger data setDirection of relative displacement for each landmark determined
57 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 landmarkWhorls: Continuous ridgeline showed little shape variation. Delta and crease landmarks showed significant variationLSL-RSL: greater dispersion due to size variation and rotational effectsW-DLW: same as LSL-RSL
58 Results: Thin-Plate Spline The greater the deformation in the grid, the more shape variation between the twoRSL-LSL: high degree of shape consistency with greatest variation in the delta regionW-DLW: same as RSL-LSL
59 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 typeDirection of variation represented by vector lineDegree of variation indicated by amount of deformation in gridRSL-LSL: different directions of variation, greatest variation in delta regionsW-DLW: greatest variation in delta regions
61 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 methodsGoal 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
62 False-Match Probabilites and Monte Carlo Analyses Used for village placement to avoid natural disasters, species diversity, evolution, air traffic controlFor 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 duplicates
63 False-Match Probabilites and Monte Carlo Analyses Methods and background are numerically and theoretically intensive, so will paper to those more interestedNo assumptions – works well for small sample sizes, but assumptions must be used for larger numbersCompared different sample sets to determine probability of a false-match1200 fingerprints
64 False-Match Probabilites and Monte Carlo Analyses GISStandardize coordinate space and analyze print by sectionEight simulations to determine how each attribute affects false-match probabilitiesNine overlapping grid cells and total minutiae in each cell countedSets of three, five, seven, or nine minutiae selected
67 False-Match Probabilites and Monte Carlo Analyses Minutiae selected without replacement50 prints selected for LSL, RSL, W, DLW20 prints selected for arches, 25 for tented archesSimulations iterated 1000 timesComparisons across and within pattern typesNeeded to account for variance of each minutiaeBifurcation angles, ridge ending roundness, etc.
68 MC Results Similar probability results for all pattern types As robustness of simulation expanded, probability of false match decreased greatlyUsing 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 inOnly one false match found when considering position of 9 minutiae
70 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 examinedSimilar patterns of minutiae, but not type were foundSmall sample size limits conclusions100,000 fingerprints considered desirable for strong results (6-7 weeks of computer time)