With regards to how ridge formation values or weights are determined, Pat Wertheim states:  “In a truly scientific comparison, however, one accepts the idea that not all features in a fingerprint are exactly equal in the weight they contribute to the identification.  Some features contribute more to the conclusion, others less.  Some features may weigh as a grain of sand when tested on the scale, others may weigh as a cobblestone.  In Ridgeology, it is up to the expert doing the comparison to determine the relative weight of each feature.  The expert makes the determination based on training and experience.” [71] 

Based on surveys of groups of fingerprint examiners, by Christophe Champod, Cedric Neumann and others, to investigate their perceptions of certain types of ridge formations, the results showed a lack of consensus with regards to the value or weight given to each ridge formation type.  Fingerprint examiners were given images of ridge formations displaying pores, ridge edges, scars, warts, creases, ridge widths, incipient ridges, and a dot.  The results from the surveys showed “No agreement has been demonstrated with respect to the value to be accorded to the characteristics in question.  The answers from the participants were evenly distributed between the possible answers for most of the characteristics.” [72] 

Based on these surveys, examiner "training and experience" is not an accurate, reliable weighing scale to use to define the relative weight for ridge formations.  As a result, a more accurate, reliable weighing scale is needed.  Based on Meehl's work, it has been demonstrated that in general statistical models are more accurate than non-statistical models [53].  Subsequently, a weighing scale based on statistics, as opposed to fingerprint examiner professional judgement, should be considered superior to define relative weights for ridge formations.

The T-Model may be considered a statistical weighing scale that has demonstrated to be a more accurate and reliable tool to identify the largest and best look-alikes, as well as the most notable erroneous identifications ever made, as insufficient to infer identification with (so far) a zero error rate (see Error Rate in Terms of Look-alikes and Error Rate in Terms of Duplication Likelihood).  

Based on the above survey and results from validation studies performed by the author (see Validation Study), examiner “training and experience” is the less accurate and less reliable weighing scale compared to the statistical weighing scale of the T-Model to define relative weights for ridge features.      

Ridge Formation Weights and Their Subsequent Match Probabilities are Defined Based on Frequency of Occurrence

Quantitative weights for the following most common ridge formation types used in fingerprint identification are based on frequency of occurrence with reduced weights for directional ridge formations (ending and bifurcating ridge units) found in diminishing areas and expanded weights for these same ridge formation types found in non-diminishing areas: 

Continuous Ridge Units

Approximately 19,984 .45mm x .45mm mini cells containing continuous ridge units were established from the extrapolation of the Osterburg study.  The percentage distribution of continuous ridge units is defined as 86.37, which establishes the quantitative weight as 1.1577.   For purposes of conservativeness, this value is rounded down to the nearest hundredth place and defined as 1.15.

The probability for the continuous ridge unit is subsequently defined as 1/1.15.

The Ending Ridge Unit

Based on extrapolation of results from the Osterburg study, the quantitative weight for an ending ridge unit is defined as 13.34.  The Quantitative weight for a unit ending ridge is refined based on its location in a fingerprint and whether or not it’s orientation is deemed to be influence by pattern force (see Pattern Force).   Subsequently the quantitative weight for an ending ridge unit is subjected to reduction or expansion based on the presence or absence of pattern force and defined as follows:

Pattern Force Ending Ridge Unit:            10.00
Non-Pattern Force Ending Ridge Unit:     14.25

The probabilities for these ridge formation types are subsequently defined as 1/10 and 1/14.25 respectively. 

The Bifurcating Ridge Unit

Based on extrapolation of results from the Osterburg study, the quantitative weight for a bifurcating ridge unit is defined as 25.01.  The Quantitative weight for a unit bifurcation is refined based on its location in a fingerprint and whether or not it’s orientation is deemed to be influence by pattern force (see Pattern Force).   Subsequently the quantitative weight for a bifurcating ridge unit is subjected to reduction or expansion based on the presence or absence of pattern force and defined as follows:

Pattern Force Bifurcating Ridge Unit:                18.75
Non-Pattern Force Bifurcating Ridge Unit:         26.75

The probabilities for these ridge formation types are subsequently defined as 1/18.75 and 1/26.75 respectively. 

Ending/Bifurcating Ridge Unit

With the exception of continuous ridge units and pores, based on frequency of occurrence the ending ridge and bifurcating ridge units are the most frequently occurring ridge formations in fingerprints and subsequently most often used by latent print examiners to individualize. On occasion there are connective ambiguities that prevent clear classification of either of these ridge unit types.  For purposes of refinement, a separate ending/bifurcating ridge formation type is included to represent the ending/bifurcating ridge unit type with connective ambiguity.  The quantitative weight for this ridge unit type is defined as the average between the quantitative weights for an ending ridge unit and bifurcating ridge unit.  This value is consistent with the following suggestion made by Dr. David Stoney: 

"Connective ambiguities and deformation of the fingerprint might affect the calculation of information content to some degree, but the problem is not serious.  For example, a typical connective ambiguity would create uncertainty about whether a minutia was a fork or an ending ridge.  We might assume the minutiae to be one or the other, or perhaps take an average the two frequencies of occurrence." [9]

For purposes of conservativeness, the quantitative weight for an ending/bifurcating ridge formation is rounded down to the nearest quarter and defined based on the presence or absence of pattern force as follows:

Pattern Force Ending/Bifurcating Ridge Unit:            (10 + 18.75) / 2        =     14.375
Non-Pattern Force Ending/bifurcating Ridge Unit:    (14.25 + 26.75) / 2    =     20.500

The probabilities for these ridge formation types are subsequently defined as 1/14.375 and 1/20.50 respectively. 

The Single Ridge Unit (Dot)

Extensive fingerprint "close match" experiments for different arrangements of dots were performed to better understand how they occur in fingerprints and to estimate their relative values, e.g., probabilities.  Sets of 500 and 1000 flat fingerprint samples, e.g., 50 and 100 ten-print records from different individuals, were used for the experiments.  The different types of dots tested were defined as follows:

Single Dots

The single dot was defined as a single ridge unit in size not greater than .5mm wide and .5mm long, and with no Level II neighbor within 1mm in the same furrow.  There was no distinction made between incipient dots and mature dots.  For purposes of simplicity, any clear, apparently reliable dot, regardless of size, was defined as a “single dot” as long as its nearest neighbor in the same furrow was measured to be more than 1mm distant.*

*Note:  The measure “1mm” was selected based on the sum of the rough size of the average ridge unit, e.g., 0.5mm, and the distance for the average ridge break unit, e.g., 0.5mm.  It was theorized that if the position of a dot is greater than 1mm from it’s nearest Level II neighbor, then it is not connected to or influenced by another ridge feature, e.g., a continuous ridge, ridge break, or any other level II ridge feature, and therefore it is more independent, more rare and as a result bears greater weight, than a dot located within 1mm of a Level II neighbor within the same furrow, e.g., a “clustered dot”.

Clustered Dots

The clustered dot was defined as a single ridge unit, e.g., not greater than .5mm width and .5mm long, and with a Level II neighbor 1mm away in the same furrow.  Again, there was no distinction made between incipient dots and mature dots.  Any clear, apparently reliable dot, regardless of size, was defined as a “clustered dot” as long as its nearest neighbor in the same furrow was measured to be less than 1mm distant.

Dot Experiments

Eight (8) "close match" experiments were performed using various arrangements of dots.  The number of close matches found in 500 and 1000 sets of flat fingerprints was counted.  Based on the number of close matches found in these population groups, the number of close matches predicted by the T-Model was compared to the number of close matches observed.  As a result of the data gathered by these experiments, the previous weighting accorded to a dot was significantly refined (see below chart for "Values for Dots").

In summary, experimental results showed that close matches for same numbers of "Cluster Dots", e.g., dots less than 1mm to it’s nearest Level II neighbor in the same furrow, were found to occur much more frequently than single dots, e.g., dots separated by a distance greater than 1mm to its nearest Level II neighbor in the same furrow.  As a result, arrangements of single dots were determined to be more rare and therefore have more value, than arrangements of cluster dots.  Subsequently, the value for individual single dots was greater than the value for individual cluster dots.

Based on numbers of close matches observed by experiment for the different arrangements of single and cluster dots, values and probabilities for individual single and cluster dots were refined and applied to the T-Model. 

For purposes of conservatism, the weights or values accorded to single and cluster dots were rounded down to the nearest half.  See the below chart "Values for Single and Cluster Dots".

Note:  Information regarding the dot experiments are also listed under Validation Study.

Values for Single and Cluster Dots

The Trifurcating Ridge Unit

Frequency of occurrence for trifurcating ridge units reported by Osterburg seemed inconsistent with empirical data gathered as a result of two decades of operational experience performed by the author.  It was not clear if Osterburg defined a trifurcating ridge unit as a rod attached to an innermost re-curving ridge or some other type of ridge configuration.  As a result, a separate study was performed to validate or invalidate these particular findings.  Based on a study of 39 flat fingerprints taken at random from ten-print files, and based on a trifurcating ridge unit defined as a single continuous ridge unit that divides into 3 separate ridge units (or 3 ridge units that merge into 1) so that the ridge unit resembles a mini pitchfork, there was not one trifurcating ridge unit observed in the 39 fingerprints examined.  As a result of this study and absent a frequency of occurrence study involving a larger fingerprint sample, the quantitative weight assigned to a trifurcating ridge unit was reconfigured based on formulae for the miscellaneous ridge formation type and defined as 23,136.

The probability for a trifurcating ridge unit is subsequently defined as 1/23,136.

The Core Region

For purposes of the model, a core region is defined as a 1mm x 1mm area of equal amount of .45mm x.45mm ridge and furrow units centered at the innermost re-curve of a fingerprint.  A frequency of occurrence study was performed using 39 randomly selected flat fingerprints to determine the quantitative weight for a core region. A total of 37 1mm x 1mm core regions containing a total of 111 ridge units were found.  The cell distribution for a unit core region was established as .47 with a quantitative weight of 209.40.  For purposes of conservativeness, this value is rounded down to the nearest whole number.  As a result, the quantitative weight for a core region is defined as 209.

The probability for a 1mm x 1mm core region is subsequently defined as 1/209. 

The Delta Region

For purposes of the model, a delta region is defined as a 1mm x 1mm area of equal amount of .45mm x.45mm ridge and furrow units centered on a ridge at or nearest to the point of divergence of two type lines and located at or directly in front of the point of divergence.  A frequency of occurrence study was performed using 39 randomly selected flat fingerprints to determine the quantitative weight for a unit delta region.  As a result of the study, a total of 17 1mm x 1mm delta regions containing a total of 51 ridge units were found.  The cell distribution for a unit delta region was subsequently established as .22 with a quantitative weight of 453.64.  For purposes of conservativeness this value is rounded down to the nearest whole number and defined as 453.

The probability for a 1mm x 1mm delta region is subsequently defined as 1/453. 

Scars

For purposes of the model, a scar is defined as a white line or curve characteristic of a cut left on the skin after an injury that traverses at least 2 ridges and 2 furrows, i.e. is approximately equal to or longer than 2mm, which does not display the characteristics of a crease.

Scars were treated as independent events in which the quantitative weight for any length of scar equals that of any different length of scar.  A scar is considered an independent event, which regardless of length bears a quantitative weight that is based on frequency of occurrence.  The following frequency of occurrence study was performed to define the quantitative weight for a scar:  A sample of 1000 randomly selected flat fingerprints from ten-print files was examined for the presence of scars.  A total of 42 scars were found.  A scar traverses both ridge and furrow units and therefore its cell distribution was calculated in terms of percentage to the total number of cells, or 46,272.  Based on 46,272 ridge and furrow units, there are a total of approximately 1,101,410 independent ridge/furrow units in 1000 flat fingerprints.   A frequency of 42 scars out of a possible 1,101,410 independent ridge/furrow unit events equates to a frequency of .00003813 and a quantitative weight of 26,224. 

The probability for a scar is subsequently defined as 1/26,224. 

Note:  The value for a scar is based on a larger fingerprint sample and deemed more accurate that the conserrvative value for ridge formations not found in a given fingerprint sample, i.e. 23,136. 

Creases

For purposes of the model, a crease is defined as a white line or linear void area located above the distal phalange flexion crease that traverses at least 2 ridges and 2 furrows, i.e. is approximately equal to or longer than 2mm, which does not display the characteristics of a cut or scar.   A crease is considered an independent event, which regardless of length bears a quantitative weight that is based on frequency of occurrence.  The following frequency of occurrence study was performed to define the quantitative weight for a crease:  2000 randomly selected flat fingerprints from ten-print files were examined for the presence of creases.  A total of 1737 creases were found.  A crease traverses both ridge and furrow units and therefore its cell distribution was calculated in terms of percentage to the total number of cells, or 46,272.  Again, based on 46,272 ridge and furrow units, there are a total of approximately 1,101,410 independent ridge/furrow units in 1000 flat fingerprints.   As a result, a frequency of 1737 independent 2mm± crease events out of a possible 1,101,410 independent ridge/furrow unit events equates to a frequency of .001577 and a quantitative weight of 634.

The probability for a crease is subsequently defined as 1/634.

Pores

Pores are biologically inherent to all ridge units and therefore it may be stated that they possess a biological frequency of occurrence equal to 100%.  However, due to their minuteness, not all pores consistently reproduce in latent impressions nor do they consistently reproduce in deliberate or intentionally recorded impressions.  The actual frequency of occurrence for a unit sweat pore significantly differs from biological frequency of occurrence and therefore a frequency of occurrence study based on observable pore distribution was used in order to establish the quantitative weight for an individual pore. 

A random sample of 39 flat fingerprint impressions from ten-print cards was examined for the presence of pores.  The total number of pores found was 4,286.  Based on a total cell distribution of 23,136, the cell percentage distribution for pores is 18.52, which defines the quantitative weight of a single pore as 5.3980.  For purposes of simplicity and conservativeness, the quantitative weight for a unit pore is rounded down to 5. 

The probability for a pore is subsequently defined as 1/5. 

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For purposes of conservativeness, quantitative weights for ridge formation types were rounded down to the nearest whole number or simpilest fraction.

The quantitative weight of 5 for a pore is agreeable since it is the same weight established by David Ashbaugh, although in a different manner [18].

Friction skin magnified 50x showing pores (Click image to enlarge)