**Statistical Analysis of Widths and Heights of Fingerprint Images in
Terms of Ages from Segmentation Data**

October 15, 2008

**Jin Chu Wu**

In the July Report, the statistical analysis of widths and heights of
fingerprint images from segmentation data was presented. In this October
Report, the statistical analysis in terms of ages is carried out. All
these results will provide references for designing targets for the
evaluation of the fast tenprint capture (FTC) devices. As stated in the
draft of "Specifications for Fast Tenprint Capture Devices", Version
1.0, one of the three aspects in the evaluation of FTC devices is the
absolute measurement, i.e., stipulating the specifications and designing
targets to implement specifications. One of many aspects in the absolute
measurement is the geometric accuracy. And the geometric accuracy is
related to the finger sizes.

As pointed out in the July Report, in order to obtain the finger sizes,
one way is to collect samples. For instance, the human finger sizes can
be collected in any public areas. Then, an inferential statistical
analysis follows. The alternative is to analyze the segmentation data.

Here we need to emphasize again that while analyzing the segmentation
data, 1) the sizes of two thumbs cannot be obtained, 2) only the widths
and heights but not the thicknesses of the fingers can be estimated, 3)
the widths and heights shown in the segmentation data are the widths and
heights of fingerprint images, respectively, that are smaller than the
widths and heights of real fingers, which is because only the front part
of a finger touches the platen of a live scanner to form a flat
fingerprint image during a capture process. This third point is the most
important issue. Nonetheless, the analysis of the segmentation data can
provide some information, for example, the proportion between two finger
sizes, etc., for designing the simulated fingers to be the targets in
the absolute measurement.

The segmentation data were provided by Craig Watson's subgroup and they
included data from dos3s and lacnty (LA County). Some data contained the
age information, but some data didn't. In addition, some data were
corrupted, in which the sizes of width and/or height were
inappropriately recorded, or the birth date and the capture date did not
match properly, or the age of the subject was less than 10. The
corrupted data were deleted.

The set of the segmentation data is the direct product of the set of
gender (male and female), the set of eight fingers (R2, R3, R4, R5, L7,
L8, L9, and L10), and the set of the dimension (width and height). They
can be mathematically expressed as,

{segmentation data} = {male, female} $\otimes$ {R2, R3, R4, R5, L7, L8,
L9, L10} $\otimes$ {width, height}

As a result, the segmentation data can be subdivided into 32 subsets in
terms of gender, finger, and the dimension, such as M_R2_w, M_R2_h, etc.

Further, as far as the age is concerned, the age is divided into three
groups: age 10 to 30, age 31 to 60, and age 61 and up. Therefore, the
total is 96 subsets. All these 96 subsets are denoted, respectively, as
M_R2_w_30, M_R2_w_60, M_R2_w_90, and so on.

In each subset of the 96 subsets, the statistical analysis was carried
out. And the results, such as the number of data (i.e., the sample
size), the median, the mean, the standard error (SE) of the sample mean,
and the 95% confidence interval (CI) of the sample mean, are provided.
The unit of the sizes in the segmentation data was in pixel, as
requested, which is more accurate than other units. However, only the
results in terms of the unit millimeter, which were converted from the
results using the unit of pixel, are provided. Otherwise, too many
tables would be listed. The results in the unit of pixel are available
on request.

The results of the statistical analysis are listed from Table 1 to Table
6. It is shown in these six tables that the median and the mean are
quite close in each subset. This indicates that the distribution in each
subset is quite symmetric. Therefore, the standard errors and the 95%
confidence intervals of the sample mean instead of the median were
computed. The standard error for female is generally greater than the
one for male. This is because the sample size for female is smaller than
the sample size for male in the segmentation data, especially for the
age group of "10 to 30", and "31 to 60".

Generally speaking, it follows from these six tables that the
fingerprint image sizes extracted from the segmentation data do not vary
too much with respect to the age. Moreover, by comparing these six
tables with the two tables in the unit of millimeter as shown in the
July Report, it seems that while designing the targets of fingers, the
age may not be a factor for the majority of cases.

  -------------- ------------ ------------ ---------- --------- ------------------
  **Fingers**    **Number**   **Median**   **Mean**   **SE**    **95% CI**

  M_R2_w_30      11922        14.63        14.66      0.0127    (14.63, 14.68)

  M_R3_w_30      11922        15.29        15.17      0.0132    (15.15, 15.20)

  M_R4_w_30      11922        14.63        14.70      0.0122    (14.68, 14.73)

  M_R5_w_30      11922        13.82        13.65      0.0137    (13.62, 13.68)

  M_L7_w_30      11275        14.53        14.40      0.0127    (14.37, 14.42)

  M_L8_w_30      11275        15.04        14.97      0.0137    (14.94, 15.00)

  M_L9_w_30      11275        14.43        14.36      0.0127    (14.33, 14.38)

  M_L10_w_30     11275        13.41        13.37      0.0142    (13.34, 13.39)

  F_R2_w_30      5829         13.31        13.31      0.0163    (13.28, 13.34)

  F_R3_w_30      5829         13.72        13.64      0.0183    (13.60, 13.68)

  F_R4_w_30      5829         13.41        13.40      0.0168    (13.36, 13.43)

  F_R5_w_30      5829         12.19        12.17      0.0188    (12.13, 12.21)

  F_L7_w_30      5799         13.00        13.00      0.0163    (12.97, 13.03)

  F_L8_w_30      5799         13.31        13.28      0.0183    (13.24, 13.31)

  F_L9_w_30      5799         13.00        12.89      0.0173    (12.85, 12.92)

  F_L10_w_30     5799         11.58        11.66      0.0188    (11.62, 11.70)
  -------------- ------------ ------------ ---------- --------- ------------------

Table 1 The statistical results for the widths in millimeter of the
2^nd^, 3^rd^, 4^th^, and 5^th^ finger of the right hand and the 7^th^,
8^th^, 9^th^, and 10^th^ finger of the left hand for both male and
female, in the age group of 10 to 30, where the number stands for the
sample size.

  -------------- ------------ ------------ ---------- --------- ------------------
  **Fingers**    **Number**   **Median**   **Mean**   **SE**    **95% CI**

  M_R2_h_30      11922        23.98        23.86      0.0203    (23.82, 23.90)

  M_R3_h_30      11922        24.38        24.34      0.0244    (24.29, 24.39)

  M_R4_h_30      11922        24.79        24.80      0.0229    (24.76, 24.85)

  M_R5_h_30      11922        21.54        21.47      0.0224    (21.43, 21.51)

  M_L7_h_30      11275        23.57        23.67      0.0198    (23.63, 23.71)

  M_L8_h_30      11275        24.38        24.14      0.0264    (24.08, 24.19)

  M_L9_h_30      11275        24.79        24.87      0.0229    (24.83, 24.91)

  M_L10_h_30     11275        21.13        20.94      0.0254    (20.88, 20.98)

  F_R2_h_30      5829         21.95        21.76      0.0279    (21.71, 21.82)

  F_R3_h_30      5829         22.45        22.43      0.0325    (22.37, 22.50)

  F_R4_h_30      5829         22.35        22.34      0.0325    (22.28, 22.41)

  F_R5_h_30      5829         19.51        19.24      0.0305    (19.18, 19.30)

  F_L7_h_30      5799         21.64        21.56      0.0274    (21.50, 21.61)

  F_L8_h_30      5799         22.35        22.33      0.0315    (22.27, 22.39)

  F_L9_h_30      5799         22.25        22.25      0.0305    (22.19, 22.31)

  F_L10_h_30     5799         19.10        19.06      0.0310    (19.00, 19.12)
  -------------- ------------ ------------ ---------- --------- ------------------

Table 2 The statistical results for the heights in millimeter of the
2^nd^, 3^rd^, 4^th^, and 5^th^ finger of the right hand and the 7^th^,
8^th^, 9^th^, and 10^th^ finger of the left hand for both male and
female, in the age group of 10 to 30, where the number stands for the
sample size.

  -------------- ------------ ------------ ---------- --------- ------------------
  **Fingers**    **Number**   **Median**   **Mean**   **SE**    **95% CI**

  M_R2_w_60      12383        15\. 44      15.22      0.0127    (15.20, 15.25)

  M_R3_w_60      12383        15\. 44      15.60      0.0132    (15.57, 15.62)

  M_R4_w_60      12383        15.14        15.13      0.0127    (15.11, 15.16)

  M_R5_w_60      12383        13.82        13.92      0.0142    (13.89, 13.95)

  M_L7_w_60      11818        15.04        15.02      0.0127    (15.00, 15.05)

  M_L8_w_60      11818        15.44        15.48      0.0132    (15.45, 15.50)

  M_L9_w_60      11818        14.94        14.86      0.0127    (14.83, 14.88)

  M_L10_w_60     11818        13.82        13.71      0.0142    (13.68, 13.74)

  F_R2_w_60      5891         13.82        13.95      0.0178    (13.91, 13.98)

  F_R3_w_60      5891         14.22        14.16      0.0188    (14.12, 14.19)

  F_R4_w_60      5891         13.82        13.75      0.0173    (13.71, 13.78)

  F_R5_w_60      5891         12.29        12.38      0.0193    (12.34, 12.42)

  F_L7_w_60      5884         13.61        13.58      0.0173    (13.55, 13.62)

  F_L8_w_60      5884         13.82        13.79      0.0183    (13.76, 13.83)

  F_L9_w_60      5884         13.21        13.26      0.0178    (13.23, 13.30)

  F_L10_w_60     5884         11.99        11.91      0.0193    (11.87, 11.95)
  -------------- ------------ ------------ ---------- --------- ------------------

Table 3 The statistical results for the widths in millimeter of the
2^nd^, 3^rd^, 4^th^, and 5^th^ finger of the right hand and the 7^th^,
8^th^, 9^th^, and 10^th^ finger of the left hand for both male and
female, in the age group of 31 to 60, where the number stands for the
sample size.

  -------------- ------------ ------------ ---------- --------- ------------------
  **Fingers**    **Number**   **Median**   **Mean**   **SE**    **95% CI**

  M_R2_h_60      12383        23.98        23.91      0.0198    (23.87, 23.95)

  M_R3_h_60      12383        24.38        24.24      0.0234    (24.19, 24.29)

  M_R4_h_60      12383        24.38        24.48      0.0224    (24.44, 24.52)

  M_R5_h_60      12383        21.54        21.27      0.0218    (21.23, 21.32)

  M_L7_h_60      11818        23.77        23.78      0.0198    (23.74, 23.82)

  M_L8_h_60      11818        24.38        24.20      0.0249    (24.15, 24.25)

  M_L9_h_60      11818        24.79        24.71      0.0218    (24.67, 24.76)

  M_L10_h_60     11818        21.13        21.07      0.0234    (21.02, 21.11)

  F_R2_h_60      5891         21.95        21.77      0.0284    (21.72, 21.83)

  F_R3_h_60      5891         22.35        22.31      0.0325    (22.25, 22.38)

  F_R4_h_60      5891         21.95        22.05      0.0320    (21.99, 22.11)

  F_R5_h_60      5891         19.00        18.99      0.0300    (18.93, 19.05)

  F_L7_h_60      5884         21.64        21.58      0.0284    (21.53, 21.64)

  F_L8_h_60      5884         22.25        22.23      0.0320    (22.17, 22.30)

  F_L9_h_60      5884         21.95        21.98      0.0305    (21.92, 22.04)

  F_L10_h_60     5884         18.90        18.87      0.0305    (18.81, 18.93)
  -------------- ------------ ------------ ---------- --------- ------------------

Table 4 The statistical results for the heights in millimeter of the
2^nd^, 3^rd^, 4^th^, and 5^th^ finger of the right hand and the 7^th^,
8^th^, 9^th^, and 10^th^ finger of the left hand for both male and
female, in the age group of 31 to 60, where the number stands for the
sample size.

  -------------- ------------ ------------ ---------- --------- ------------------
  **Fingers**    **Number**   **Median**   **Mean**   **SE**    **95% CI**

  M_R2_w_90      1004         15.85        15.89      0.0503    (15.80, 15.99)

  M_R3_w_90      1004         16.26        16.08      0.0488    (15.98, 16.18)

  M_R4_w_90      1004         15.65        15.68      0.0472    (15.59, 15.78)

  M_R5_w_90      1004         13.87        13.99      0.0544    (13.89, 14.10)

  M_L7_w_90      1013         15.95        15.87      0.0523    (15.77, 15.98)

  M_L8_w_90      1013         16.15        15.98      0.0478    (15.89, 16.08)

  M_L9_w_90      1013         15.44        15.33      0.0488    (15.24, 15.43)

  M_L10_w_90     1013         13.82        13.84      0.0549    (13.74, 13.95)

  F_R2_w_90      1003         15.04        14.95      0.0457    (14.86, 15.04)

  F_R3_w_90      1003         15.14        14.99      0.0472    (14.90, 15.08)

  F_R4_w_90      1003         14.63        14.48      0.0452    (14.39, 14.56)

  F_R5_w_90      1003         13.00        12.93      0.0503    (12.83, 13.03)

  F_L7_w_90      1004         14.53        14.40      0.0472    (14.31, 14.50)

  F_L8_w_90      1004         14.63        14.53      0.0462    (14.44, 14.62)

  F_L9_w_90      1004         13.82        13.91      0.0457    (13.82, 14.00)

  F_L10_w_90     1004         12.19        12.22      0.0508    (12.12, 12.32)
  -------------- ------------ ------------ ---------- --------- ------------------

Table 5 The statistical results for the widths in millimeter of the
2^nd^, 3^rd^, 4^th^, and 5^th^ finger of the right hand and the 7^th^,
8^th^, 9^th^, and 10^th^ finger of the left hand for both male and
female, in the age group of 61 and up, where the number stands for the
sample size.

  -------------- ------------ ------------ ---------- --------- ------------------
  **Fingers**    **Number**   **Median**   **Mean**   **SE**    **95% CI**

  M_R2_h_90      1004         24.28        24.11      0.0762    (23.96, 24.26)

  M_R3_h_90      1004         24.38        24.37      0.0813    (24.21, 24.53)

  M_R4_h_90      1004         23.88        23.87      0.0828    (23.71, 24.04)

  M_R5_h_90      1004         21.03        20.88      0.0823    (20.72, 21.04)

  M_L7_h_90      1013         24.28        24.10      0.0747    (23.95, 24.24)

  M_L8_h_90      1013         24.38        24.43      0.0823    (24.27, 24.59)

  M_L9_h_90      1013         24.28        24.21      0.0798    (24.06, 24.37)

  M_L10_h_90     1013         21.13        20.90      0.0823    (20.74, 21.06)

  F_R2_h_90      1003         21.95        22.04      0.0737    (21.89, 22.18)

  F_R3_h_90      1003         22.35        22.39      0.0798    (22.24, 22.55)

  F_R4_h_90      1003         21.74        21.67      0.0716    (21.53, 21.81)

  F_R5_h_90      1003         18.69        18.62      0.0721    (18.48, 18.76)

  F_L7_h_90      1004         21.64        21.58      0.0716    (21.44, 21.72)

  F_L8_h_90      1004         22.15        22.21      0.0767    (22.06, 22.36)

  F_L9_h_90      1004         21.44        21.51      0.0732    (21.36, 21.65)

  F_L10_h_90     1004         18.69        18.50      0.0777    (18.35, 18.65)
  -------------- ------------ ------------ ---------- --------- ------------------

Table 6 The statistical results for the heights in millimeter of the
2^nd^, 3^rd^, 4^th^, and 5^th^ finger of the right hand and the 7^th^,
8^th^, 9^th^, and 10^th^ finger of the left hand for both male and
female, in the age group of 61 and up, where the number stands for the
sample size.