**Specifications for Fast Tenprint Capture Devices**

(Draft, Version 1.0, February 28, 2008)

**1. Scope and Purpose**

The objective of fast tenprint capture (FTC) devices is to obtain 2-d
rolled-equivalent fingerprint images from the 3-d finger objects for ten
fingers at the faster speed than live scanners do. It is mandatory that
the 2-d rolled-equivalent fingerprint images be matchable with those
captured using certified live scanners, which exist numerously in the
current fingerprint systems. The specifications are applied to evaluate
such FTC devices.

Since the fingerprint images captured from 3-d finger objects must be
converted to 2-d rolled-equivalent fingerprint images, this technology
involves not only optical system (hardware) but also conversion
algorithms (software). Hence, the specifications stipulated in this
document are used to evaluate the resultant effect of these two factors
rather than just the effect of the optical system as live scanners do.

The evaluation of FTC devices is threefold. The first is the absolute
measurement, i.e., stipulating the specifications and designing targets
to implement specifications. The second is the relative measurement for
interoperability, namely, matching 2-d rolled-equivalent fingerprint
images produced using FTC devices against those collected from certified
live scanners. The third is the evaluation of the real time of
completing one transaction carried out by an FTC device.

The specifications set in the absolute measurement shall be supported by
the results from the relative measurement. The interactions between the
absolute measurement and the relative measurement shall take several
iterations. Once it is done, only the absolute measurement shall be
invoked to evaluate FTC devices.

**2. The Absolute Measurement**

**2.1 3-D Targets**

The shape and size of the 3-d targets for 10 fingers are determined by
statistically analyzing the existing databases. The unknown geometric
parameters of 3-d targets are the shape of the cross section, the
curvature of the surface, and the length, etc. 3-d targets may start
with regular shaped targets such as cylinder, truncated cone, etc, and
then be evolved to complicated shaped targets with an artificial
ridge-valley structure.

The reflectance intensities on the 3-d targets shall be designed in such
a way that for instance the sine waves and the square waves on the
flattened plane of the target surface with least distortion are
equivalent to those on the flat surface. Or, 3-d targets with
developable surface are employed but located in different inclinations
inside the capture space of FTC devices.

These targets will be used in all the absolute-measurement evaluations
as presented below.

**2.2 Test Directions**

  -----------------------------------------------------------------------
  ![](media/image1.png){width="4.509027777777778in"
  height="2.1666666666666665in"}

  -----------------------------------------------------------------------

There are two possibilities. The test directions are four ways as shown
in Figure (A) or six ways as shown in Figure (B).

**2.3 Measurement Accuracy**

It is a nondeterministic process to obtain 2-d rolled-equivalent
fingerprint images from the 3-d finger objects for ten fingers using FTC
devices. Hence, to determine the values of parameters in the following
absolute measurement, a sufficient number of measures could be carried
out. Then, the measurement accuracy, such as 95% confidence intervals,
etc., can be estimated.

**2.4 Geometric Accuracy**

Assume that X is the arc length of two points in a 3-d target and Y is
the distance of two corresponding points in the corresponding 2-d
rolled-equivalent image. X and Y are in inches[^1]. The arc length is
defined as the length along a curve. It can be computed in the 3-d
Cartesian coordinates using the formula,

  ------------------------------------------------------------------------------------------------------- --------------
  $$s \equiv \int_{}^{}{|\text{dl}|} = \int_{}^{}\sqrt{\text{dx}^{2} + \text{dy}^{2} + \text{dz}^{2}}$$   

  ------------------------------------------------------------------------------------------------------- --------------

where *dl* is a differential displacement vector along a curve γ.

The specifications of the geometric accuracy are listed in the following
table.

  -------------------- ------------------------- -------------------------
  Resolution           X                         D = \|Y -- X\|

  500 ppi              0.00 \< X ≤ 0.07          D ≤ 0.0007 (?)

                       0.07 ≤ X ≤ 1.50           D ≤ X \* 1% (?)

  1000 ppi             0.00 \< X ≤ 0.07          D ≤ 0.0005 (?)

                       0.07 ≤ X ≤ 1.50           D ≤ X \* 0.71% (?)
  -------------------- ------------------------- -------------------------

For 500 ppi, 0.07 inches contain 35 pixels, 1.50 inches contain 750
pixels, and 0.0007 inches are about 1/3 pixel. For 1000 ppi, 0.07 inches
contain 70 pixels, 1.50 inches contain 1500 pixels, and 0.0005 inches
are about ½ pixel.

**2.5 Spatial Frequency Response**

In analogy to the definition of Michelson contrast, the modulation of a
target is defined as

  -------------------------------------------------------------------------------------- --------------
  $$M_{t} = \frac{R_{\text{max}} - R_{\text{min}}}{R_{\text{max}} + R_{\text{min}}},$$   

  -------------------------------------------------------------------------------------- --------------

where R~max~ and R~min~ are the maximal and minimal reflectance
intensities on the target, respectively. The modulation of an image is
defined as

  -------------------------------------------------------------------------------------- --------------
  $$M_{i} = \frac{G_{\text{max}} - G_{\text{min}}}{G_{\text{max}} + G_{\text{min}}},$$   

  -------------------------------------------------------------------------------------- --------------

where G~max~ (G~min~) is the maximum (minimum) grayscale value taken
from all average maximum (minimum) grayscales, e.g., corresponding to
all peaks (valleys) of a sine-wave image, where the average is taken
along the direction perpendicular to the sine wave direction.

Then, the modulation transfer function (MTF) of the device with respect
to the spatial frequency ν of the wave on the target is defined as

  -------------------------------------------------------- --------------
  MTF (ν) = M~i~ / M~t~ .                                  

  -------------------------------------------------------- --------------

Generally speaking, as the spatial frequency ν increases, the modulation
transfer function MTF (ν) decreases. Thus, MTF (ν) describes the
characteristics of the spatial frequency response of FTC devices, which
is the resultant effect of the optical system and the conversion
algorithms. It also demonstrates how the contrast is transmitted from
the real object (target) to the 2-d rolled-equivalent image.

In particular, if the target is formed using square wave (i.e., bar
target), MTF turns out to be contrast transfer function (CTF). CTF can
be calculated in terms of frequency ν by

for 500 ppi devices while ν varies from 1.0 to 10.0 cycles/mm,

  --------------------------------------------------------------- -------
  CTF (ν) = 3.04105 \* 10^-4^ \* ν^2^ -- 7.99095 \* 10^-2^ \* ν + 
  1.02774 ,                                                       

  --------------------------------------------------------------- -------

for 1000 ppi devices while ν varies from 1.0 to 20.0 cycles/mm,

  --------------------------------------------------------------- -------
  CTF (ν) = -1.85487 \* 10^-5^ \* ν^3^ + 1.41666 \* 10^-3^ \*     
  ν^2^ -- 5.73701 \* 10^-2^ \* ν + 1.01341 .                      

  --------------------------------------------------------------- -------

The unknown reflectance intensities on a target corresponding to the
maximal and minimal grayscale values, i.e., G~max~ and G~min~, on an
image can be obtained by using a calibration curve. The calibration
straight line is derived using the least squares simple linear
regression between the reflectance intensities of 14 gray patches and 14
average grayscales of the corresponding images produced by the device. A
sample of calibration straight line is shown in the following figure.

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  ![](media/image2.png){width="2.859027777777778in"
  height="2.4972222222222222in"}

  -----------------------------------------------------------------------

While sampling spatial frequency response, the output images of 3-d sine
wave target or 3-d square wave target shall not exhibit any significant
amount of aliasing.

If sine wave target is used, the requirement of minimum MTF (ν) is
listed in the following table. If square wave target is used, the
requirement of minimum CTF (ν) can be obtained using the above two
formulas.

+-----------------------+-----------------------+-----------------------+
| Frequency             | Minimum MTF (ν)       | Minimum MTF (ν)       |
|                       |                       |                       |
| (cy/mm)               | for 500 ppi           | for 1000 ppi          |
+-----------------------+-----------------------+-----------------------+
| 1                     | 0.905 (?)             | 0.925 (?)             |
+-----------------------+-----------------------+-----------------------+
| 2                     | 0.797 (?)             | 0.856 (?)             |
+-----------------------+-----------------------+-----------------------+
| 3                     | 0.694 (?)             | 0.791 (?)             |
+-----------------------+-----------------------+-----------------------+
| 4                     | 0.598 (?)             | 0.732 (?)             |
+-----------------------+-----------------------+-----------------------+
| 5                     | 0.513 (?)             | 0.677 (?)             |
+-----------------------+-----------------------+-----------------------+
| 6                     | 0.437 (?)             | 0.626 (?)             |
+-----------------------+-----------------------+-----------------------+
| 7                     | 0.371 (?)             | 0.579 (?)             |
+-----------------------+-----------------------+-----------------------+
| 8                     | 0.312 (?)             | 0.536 (?)             |
+-----------------------+-----------------------+-----------------------+
| 9                     | 0.255 (?)             | 0.495 (?)             |
+-----------------------+-----------------------+-----------------------+
| 10                    | 0.200 (?)             | 0.458 (?)             |
+-----------------------+-----------------------+-----------------------+
| 12                    |                       | 0.392 (?)             |
+-----------------------+-----------------------+-----------------------+
| 14                    |                       | 0.336 (?)             |
+-----------------------+-----------------------+-----------------------+
| 16                    |                       | 0.287 (?)             |
+-----------------------+-----------------------+-----------------------+
| 18                    |                       | 0.246 (?)             |
+-----------------------+-----------------------+-----------------------+
| 20                    |                       | 0.210 (?)             |
+-----------------------+-----------------------+-----------------------+

**2.6 Signal-to-Noise Ratio**

In image processing, the signal-to-noise ratio (SNR) is usually defined
as the ratio of the mean of grayscales of all pixels in an area on an
image to the standard deviation of those grayscales. The target used to
create the image is a 3-d surface as indicated in Section 2.1. The
target shall be located in anywhere inside the capture space of FTC
devices. The test field within an image is a random 0.25 inch by 0.25
inch (i.e., 6.35 mm by 6.35 mm) area. While testing SNR, at least 1000
random samples of grayscales are selected from the test field.

If a 3-d white reference target with high reflectance and a 3-d black
reference target with low reflectance are used and located alternately
in the same position inside the capture space of FTC devices, the white
SNR and the black SNR are defined, respectively, as

  ------------------------------------------------------------------------------------------------------------------------------------ --------------
  $$\text{SNR}_{\text{white}} = \frac{{\overline{G}}_{\text{white}}\text{ - }{\overline{G}}_{\text{black}}}{\sigma_{\text{white}}}$$   

  ------------------------------------------------------------------------------------------------------------------------------------ --------------

and

  ------------------------------------------------------------------------------------------------------------------------------------ --------------
  $$\text{SNR}_{\text{black}} = \frac{{\overline{G}}_{\text{white}}\text{ - }{\overline{G}}_{\text{black}}}{\sigma_{\text{black}}}$$   

  ------------------------------------------------------------------------------------------------------------------------------------ --------------

where $\overline{G}$ is the mean of grayscales of all pixels inside the
test field on an image and σ is the unbiased standard deviation derived
from the same set of grayscales. In order to obtain a true measure of
the standard deviation, ${\overline{G}}_{\text{white}}$
(${\overline{G}}_{\text{black}}$) shall be several grayscales below
(above) the system's highest (lowest) obtainable grayscale. Both white
SNR and black SNR shall be greater than or equal to 125. At least 97.0%
of test shall satisfy this requirement.

**2.7 Grayscale Linearity**

All residuals of average grayscales from the simple regression straight
line shall be less than or equal to 7.65 grayscales. The estimated
regression straight line is derived using the least square fit criterion
between 14 reflectance intensities of 3-d gray-patch targets and 14
average grayscales of the corresponding images produced by FTC devices.
This is schematically depicted in the following figure.

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  ![](media/image3.png){width="2.8694444444444445in"
  height="2.152083333333333in"}

  -----------------------------------------------------------------------

**2.8 Grayscale Uniformity**

A 3-d white reference target and a 3-d black reference target shall be
used to determine the grayscale uniformity. The FTC device shall be set
up in such a way that the 3-d white reference target is below device
saturation level and the 3-d black reference target is above device dark
current level.

**2.8.1 Uniformity of Adjacent Lines along Test Directions**

The uniformity of adjacent lines along test directions is measured by
the difference between two means of grayscales corresponding to any two
adjacent lines with length of greater than or equal to 9 pixels on an
image, while target shall be randomly located inside the capture space
of FTC devices. The difference shall not be more than 2.0 grayscales
using 3-d white reference target and 1.0 grayscales using 3-d black
reference target.

**2.8.2 Small Area Uniformity**

The small-area uniformity is measured by the maximum difference between
the grayscale of any individual pixel within a random
0.25-inch-by-0.25-inch (i.e., 6.35-mm-by-6.35-mm) test field on an image
and the mean of grayscales of all pixels in the same test field, while
target shall be randomly located inside the capture space of FTC
devices. The maximum difference shall not be more than 22.0 grayscales
using 3-d white reference target and 8.0 grayscales using 3-d black
reference target.

**2.8.3 Small Area to Small Area Uniformity**

The small-area-to-small-area uniformity is measured by the difference
between two average grayscales of all pixels corresponding to any two
non-contiguous 0.25-inch-by-0.25-inch (i.e., 6.35-mm-by-6.35-mm) test
fields on an image, while targets shall be randomly located inside the
capture space of FTC devices. The difference shall not be more than 12.0
grayscales using 3-d white reference target and 3.0 grayscales using 3-d
black reference target.

**2.9 Grayscale Dynamic Range**

The grayscale dynamic range is defined as the total number of grayscales
used to present the signal on an image. The grayscale ranges from 0
(black) to 255 (white) for 8-bit storage on a pixel. Not only shall the
grayscale be considered, but the frequency of the grayscale occurring on
an image shall also be taken into account while dealing with the
distribution of grayscales employed on an image captured by FTC devices.
Thus, some threshold shall be imposed in order to determine the
grayscale dynamic range on an image. In other words, only those
grayscales whose probabilities of appearance are above a threshold shall
be counted. In the meantime, background, card format lines, boxes, and
text shall be excluded.

The test of grayscale dynamic range shall be taken place with sets of
images captured by FTC devices in a stratified way (i.e., dark, medium,
and light images) and/or sets of FTC devices produced by the vendor. At
least 80.0% of the captured individual fingerprint images shall have a
grayscale dynamic range of at least 200 grayscales, and at least 99.0%
shall have a grayscale dynamic range of at least 128 grayscales.

**3. The Relative Measurement**

The procedure of the evaluation of the relative measurement shall be
progressive, since it may involve sample collection. Once the test
passes the low level, then the test progresses to the next level. The
quantitative analyses will be shown, as the relative measurement
develops.

**3.1 A Primitive Test**

The 2-d rolled-equivalent fingerprint image created by FTC devices shall
be reverse-free and mirror image. The distribution of grayscales of all
pixels excluding the background on an image shall be bimodal
distribution rather than unimodal distribution.

**3.2 A Genuine-Match Test**

The same subject's 2-d rolled-equivalent images of fingers (right-index
finger, left-index finger, and then other eight fingers) created using
FTC devices shall be matchable with those captured using certified live
scanners, in terms of the number and location of minutiae, etc.

**3.3 Reality Tests**

The Gallery is formed by fingerprint images of a set of different
subjects captured using a certified live scanner. The Probe I is formed
by different fingerprint images of the same set of subjects captured
using the same certified live scanner. The Probe II is formed by 2-d
rolled-equivalent fingerprint images of the same set of subjects created
using FTC device. ROC curves shall be generated by employing
the-state-of-the-art fingerprint-image extracting and matching
technology. Then, the ROC curve generated from the Probe II and the
Gallery shall be compared to the ROC curve generated from the Probe I
and the same Gallery. The difference shall be within the tolerance.

The Gallery can also be formed by different 2-d rolled-equivalent
fingerprint images of the same set of subjects produced using FTC
device. In such cases, a subject does FTC device twice as well as
certified live scanner twice, respectively. The fingerprint images
created using FTC device can be mixed with those captured using
certified live scanners to form gallery and probe. Thus, more reality
ROC-curve tests can be taken place.

If the sample size is large enough, the operational criterion, i.e., TAR
at a fixed FAR shall be invoked; otherwise, it has no statistical
significance. If the sample size is not large enough, the area under an
ROC curve shall be employed.

**4. The Speed**

The speed of FTC device is defined to be the real time of completing one
transaction. And the real time of completing one transaction is equal to
the sum of the time of positioning ten fingers into the right position
inside the capture space of FTC device plus the processing time executed
by the system (hardware & software) including the time from capturing
fingers to converting to 2-d rolled-equivalent images. The evaluation of
the speed of FTC device is one way to test the usability of devices. FTC
devices shall be user friendly. The speed of FTC device shall not be
higher than 15 seconds per transaction. This evaluation can be done by
sample collection.

**References**

1.  APPENDIX F: IAFIS Image Quality Specifications, IAFIS-DOC-01078-7.1,
    May 2, 2005; available at
    <http://www.mitre.org/tech/mtf/spec_test.zip>.

2.  Norman B. Nill, Test Procedures for Verifying IAFIS Image Quality
    Requirements for Fingerprint Scanners and Printers, MITRE technical
    report, MTR 05B0000016, April 2005; available at
    <http://www.mitre.org/tech/mtf/spec_test.zip>.

3.  Image Quality Specifications for Single Finger Capture Devices, FBI,
    CJIS Division, version 071006, July 10, 2006; available at
    <http://www.mitre.org/tech/mtf/spec_test.zip>.

4.  Norman B. Nill, Test Procedures for Verifying Image Quality
    Requirements for Personal Identity Verification (PIV) Single Finger
    Capture Devices, MITRE technical report, MTR 060170, December 2006;
    available at <http://www.mitre.org/tech/mtf/spec_test.zip>.

5.  Jin Chu Wu, Charles L. Wilson, Nonparametric analysis of fingerprint
    data on large data sets, Pattern Recognition 40 (2007) 2574-2584.

6.  Jin Chu Wu, Studies of operational measurement of ROC curve on large
    fingerprint data sets using two-sample bootstrap, NISTIR 7449,
    September 2007.

[^1]: 1 inch is equal to 25.4 mm.