Delta Areas

For purposes of simplicity, both delta and core ridge formations were defined as any ridge arrangement found within a 1mm x 1mm area located at the center point of any triradiae ridge formation (delta) and at and below any innermost re-curving ridge (core).  It was observed that directional minutiae located around delta formations were impacted by pattern force based on predictable ridge orientation.   A study was performed using 234 flat fingerprints from ten-print files.  A total of 139 ending ridges and 94 bifurcations were found between the delta and diverging type lines all with tails oriented towards the diverging types lines.  These minutiae were deemed less random and therefore subject to reduction.  The reduction factor that was applied to directional ridge formations with non-random orientation was defined as follows:  The total value for a ridge formation is fundamentally based on its shape and position.  The value for ridge formation shape was assigned a 50% weight and position was assigned the other 50%.   The 50% value for shape was then reduced by another 50% based on predictable ridge orientation in one direction as opposed to two directions, i.e. one way or the opposite way.  As a result the reduction factor applied to an ending ridge impacted by pattern force such that its orientation is predictable was defined as its quantitative weight (based on frequency of occurrence) multiplied by these two factors, or 13.33 x .5 x .5 = 3.33.  This value was then subtracted from the quantitative weight assigned to the average ending ridge. 

The quantitative weight for an ending ridge impacted by pattern force was subsequently defined as follows:

13.33 – 3.33 = 10

The match probability for an ending ridge impacted by pattern force is the reciprocal of its quantitative weight and was subsequently defined as 1/10. 

Similarly the reduction factor applied to a unit bifurcation was defined as 25.01 x .5 x .5, or 6.25.  The quantitative weight for a diminishing area bifurcation was subsequently defined as follows:

25.01 – 6.25 = 18.75

The match probability for a diminishing area bifurcation impacted by pattern force is the reciprocal of its quantitative weight and was subsequently defined as 1/18.75. 

Ridge formation types and their orientations outside the 1mm x 1mm core area were not found to be reliably predictable. 

Core Areas

Although minutiae orientation about core areas may tend to be influenced in various degrees, the degree of influence and boundaries for each, were unclear and difficult to define.  For purposes of simplicity, minutiae in these areas were not subject to reduction unless they were part of a diminishing area (see Pattern Force 2/2).

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Directional ridge formations, e.g. ending ridge and bifurcating ridge units, found between diverging types lines and delta regions that orient towards diverging type lines are assigned reduced quantitative weights of 10 and 18.75 respectively. The corresponding match probabilities for these ridge formation types are defined as 1/10 and 1/18.75 respectively, the reciprocal of each.

These ridge formations may be single and not located in a diminishing area funnel (see Pattern Force 2/2) but are nevertheless significantly impacted by pattern force to reliably predict orientation and therefore warrant reduction in quantitative weight.

 Figure 1

The single ending ridge (marked in red) is located between two diverging type lines and a delta region.  It is oriented towards the diverging type lines.  As a result the quantitative weight assigned  to this type of ending ridge unit is 10.  The corresponding match probability is defined as 1/10, the reciprocal of 10.