A Subpixel-Based Fingerprint Reconstruction

Algorithm

Andreas Habegger, Lorenz Mueller, Josef Goette, and Marcel Jacomet

Bern University of Applied Sciences, HUCE-microLab

CH-2501 Biel-Bienne, Switzerland

Abstract—The reconstruction of fingerprints from the outputof sweep sensors is a crucial part of algorithms for fingerprintfeature extraction. We present an efficient and accurate techniquefor fingerprint reconstruction from two-line sensors requiringsub-pixel methods. We propose a dedicated computation of theshift between two consecutive slices, yielding not only efficiencybut also accuracy as we demonstrate by test data-sets.

Keywords: Fingerprint reconstruction, sweep sensors, syn-

thetic fingerprint re-sampling model, sub-pixel reconstruction,

slice correlation, shift estimation.

I. INTRODUCTION

Fingerprints are the favorite biometrics for user authenti-

cation.1 Automatic fingerprint recognition systems represent

more than 66% of the worldwide biometrics market [1]. With

the principle goal to reduce cost and energy consumption

[2], the sweep fingerprint sensor technique has been adopted

by various sensor-manufacturers [3], [4], [5].2 An additional

benefit of sweep sensors is their self-cleaning feature avoiding

theft from latent fingerprints. The output of sweep sensors is

a sequence of consecutive slices (consecutive frames, CFs).

The fingerprint reconstruction problem then is building the

complete fingerprint out of the CFs. Sliding a finger over a

sweep sensor generally shows not uniform speed, pressure,

and adhesion during the capturing phase, which complicates

the problem. Reconstruction algorithms for sweep sensors with

eight and more pixel lines have been developed and published

in the past [8], [9], [10]. We consider two-line sweep sensors

for which the reconstruction algorithms are proprietary and

not published, [4], [5]. These algorithms run in dedicated

high performance, power hungry companion chips, which

are not suitable for our target low-cost, low-power, portable

applications that we realize with hardware algorithms. Recon-

structing a fingerprint from two-line CFs suffer from stretching

or shortening of the reconstructed fingerprint. These artifacts

finally result in lower authentication qualities, like higher

false matching rates (FMR) and higher false non-matching

rates (FNMR). Direct feature extraction algorithms [11], [12]

or sub-pixel reconstruction techniques help to improve the

authentication quality.

1We use authentication synonymously for identification and verification.2Sensing principles are capacitive, capacitive combined with RF transmis-

sion [6], [7], temperature sensing, and the like.

The paper presents our sub-pixel shift estimation technique

in Section III, followed by a reconstruction method in Sec-

tion IV. To simplify testing, we have developed a slicing

model for two-line sweep sensors in Section II. We show the

robustness and stability of our algorithm using the model and

true data in Section V.

II. SYNTHETIC SLICE MODEL

Performance analyses of fingerprint reconstruction algo-

rithms vary depending on the quality of the input data. Fur-

thermore, captured data suffer from sensor dependent artifacts,

and they do not explicitly give accurately measurable and re-

producible sweep-speed profiles. Therefore, a synthetic model

of the sensor output CFs is useful for the algorithm design and

its calibration. The synthetic sensor model represents a two-

line sensor with parametrizable resolution (typically, we use

144- or 192 pixel columns). Because fingerprints are smooth

signals, we have used an up-sampling approach to first obtain

”almost analog” fingerprints, from which we next generate our

synthetic slices.

To build the model we start from a complete capture of

a true fingerprint, taken as our mother fingerprint. We know

that the initial template was sampled by a sensor with pixels

of 50 by 50µm2 area. Therefore, a re-sampled version of

the template by a factor of, say for example 10, results in

”almost analog” sub-pixels of 5 by 5µm2 area. To generate

sensor output CFs for various sweep-speed distributions,3 we

specify the geometry of the sensor pixels and integrate over the

sub-pixels of the ”almost analog” fingerprint. Additionally, the

model allows to specify the number of bits per pixel as well

as the sampling rate. Most often we use the generation of CFs

with either a constant velocity, or with a constant acceleration

and a certain initial velocity.

III. SUB-PIXEL SHIFT ESTIMATOR

Sweep fingerprint sensors capture with constant sample-rate

CFs from a sweeping finger. The sweep speed varies in time,

and, therefore, the displacements ∆s between each two CFs

vary as well. Our algorithm estimates the sequence of ∆s

based on an ad-hoc formula involving correlation coefficients

that indicate the similarity (CC) of two sensor-pixel columns.

3Our model allows to specify any acceleration time-evolution for anexperimental finger sweep.

978-1-4673-0859-5/12/$31.00 ©2012 IEEE

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We denote by F1[n] the left pixel column of the nth frame and

by F2[n] its right pixel column.4 We compute

F1[n] ⋆ F2[n] = CCs[n] , (1)

F1[n] ⋆ F1[n+ 1] = CCl[n] , (2)

F2[n] ⋆ F1[n+ 1] = CCr[n] . (3)

Here CCs[n] is the correlation between the left and right

pixel column of frame number n; CCl[n] gives the correlationbetween the left pixel column of frame n and its follower

frame n + 1; finally, CCr[n] is the correlation between the

right pixel column in frame n and the left pixel column in

frame n+ 1.

We have developed our displacement estimation Formula (4)

by a careful analysis of the sub-pixel image reconstruction

problem. We compute5

∆s[n] ≈CCr[n]− CCs[n]

CCl[n] + CCr[n]− 2 · CCs[n]. (4)

Figure 1 shows simulation results obtained by numerous

fingerprint capturing- and reconstruction experiments, where

each experiment uses a different but constant sweep speed.

We have increased the sweep speed in steps of 0.02 pixels

per frame from one experiment to the next, starting with 0.02

and ending with 1 pixel per frame. Consider for example the

constant sweep speed of 0.3 pixel per frame: We see by the

vertical blue ”bar” together with the remaining single points

how the calculated ∆s[n] values for all n scatter around the

true value 0.3, represented by the corresponding point on the

linear black slope. The magenta curve represents for all sweep

speeds the mean values of the calculated ∆s[n] values.

Fig. 1. Performance analysis of our estimation algorithm over the full speedrange for constant sweep speeds.

4We assume, that we sweep from left to right and generate, in succession,the frames 1, 2, . . . , n, n+ 1, . . ..

5In the case where two CFs result in CCx[n] = 1, we set the ∆s[n] to itsprevious value. At the border where no previous value has been estimated,we initialize ∆s[1] = 0, implying no shift.

Figure 1 reveals that our algorithm (4) is a biased estimation

with a speed-dependent variance. We see the bias as difference

between the black curve and the magenta curve in the figure.

We reduce the bias of the algorithm in a two step process:

First, we attenuate the variance (vertical extent of blue ”bar”)

with a linear moving average FIR filter; thereby, our algorithm

adapts the filter length based on the estimated sweep speed.

Second, our algorithm reduces the bias, by either passing

the filtered sequence through a look-up table (LUT), or by

applying a polynomial correction.

Figure 2 shows the results obtained by the two described

optimization steps. For the situation of a constant sweep speed

of 0.06 pixels per frame, the scattered blue dots give the

bare ∆s[n] estimations, the red curve is the filtered output,

and the magenta curve is the resulting output of the look-up

table correction.6 We see that the final (magenta) curve well

approximates the ideal line of constant reference speed of 0.06

pixels per frame.

Fig. 2. Our estimation algorithm with described post processing applied toa constant sweep speed experiment. The involved sweep speed is 0.06 pixelsper frame, corresponding to 3µm/sample.

Figure 3 shows our overal estimation algorithm in an

experiment with a variable sweep speed but constant ac-

celeration. Additionally we compare the performance of the

LUT correction with a 5th-order polynomial correction. As

already stated, the difference between the two approaches is

minor. The experiment also shows, that our algorithm also well

performs for non-constant sweep speeds.

IV. FINGERPRINT RECONSTRUCTION

The reconstruction of the entire fingerprint first rearranges

the pairwise incoming pixel columns in the correct physical or-

6The LUT processing might not be the best hardware implementation of theneeded correction. We find, however, that using a polynomial-based correctionresults in a very similar performance for polynomials of order at least 3. Wefind the polynomials by a least square fit, using our experimental data fromFigure 1, to map the magenta curve to the black curve.

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Fig. 3. Experiment with a variable sweep speed: constant acceleration of−0.05µm/sample and an initial speed of 10 µm/sample. The solid line isthe true sweep speed, the circles show the LUT optimization, and the x-marksshow the polynomial optimization.

der. The obtained stream of pixel columns appears as an over-

sampled, non-equidistant version of the true pixel columns.

Therefore, we apply standard signal processing techniques:

Low-pass filtering followed by down-sampling perform the re-

construction, even for the mentioned non-equidistant samples.

In the cases where the sweep speeds are low,7 we obtain

many sub-pixel columns per physical grid. In the cases of

higher sweep speeds, we get lesser sub-pixel columns per

physical grid; the maximal sweep speed we consider is 1

pixel per physical grid. Our low-pass reconstruction filter

adapts its length according to the number of sub-pixel columns

per grid when it computes the reconstructed pixel columns.

Note that although the sub-pixel columns generally are non-

equidistant, we implicitly treat them as equidistant by our

low-pass filter approach. We find that the distortions resulting

from this simplification are negligible as their impact is only

local. The more important feature for fingerprint reconstruction

algorithms targeting authentication is to be length-preserving

on a true pixel, but not sub-pixel, level.

V. ACCURACY AND ROBUSTNESS ANALYSIS

We have analyzed the accuracy and the robustness of our

sub-pixel fingerprint reconstruction algorithm using various

synthetic CFs. These synthetic CFs all base on a real finger-

prints8 serving as the mother templates of our synthetic slice

model. We generate different CFs for various sweep speeds.

The goal of the experiments is to demonstrate the robustness of

our approach by analyzing the following two variables: Global

stretching and worst-case local stretching.

7We consider sweep speeds as low if the displacement from frame to frameis low, that is, much smaller than 1 pixel/frame.

8The previously described LUT as well as the correction polynomial baseon a different mother fingerprint, the ”calibration fingerprint template.”

Figure 4 shows the estimated sweep speeds in pixels per

frame as a function of reconstructed physical pixels for various

test sweep speeds for one single finger. We see, first, that

our estimation algorithm has intervals of under- and intervals

of over estimated sweep speeds; second, that the general

estimation pattern remains the same for all tested speeds. We

note, that the same finding is valid for all other analyzed

fingers; however, the patterns differ for different fingers, see

Figure 5. The observed relatively large pattern variations from

finger to finger are not harmful for authentication applica-

tion, because authentication always verifies a finger against

its enrolled finger template. Speed estimation errors lead

to stretching/shrinking errors. Because the speed estimation

patterns for each given finger are very robust, we expect that

potential distortions are similar for the enrolled finger and the

finger to be verified.

Fig. 4. Estimated sweep speeds as function of position along the fingerprintfor various test sweep speeds (0.06, 0.12, 0.18, . . . , 0.48 pixels per frame)for one selected finger. The plot shows the worst case out of 8 different finger.

With results as those shown in Figure 4 we calculate as

robustness measures the global stretching as well as the worst-

case local stretching: We find the global stretching (which

depends on the used test sweep speed) by comparing the

various image lengths to some reference length. We also find

the worst case local stretching by integrating intervals of too

fast or too slow estimated local speed values and reading out

the extremum.

We have experimented with 7 different fingers and an

additional 8th finger used for calibration. For the 7 fingers

we have done simulations with 8 sweep speeds in the realm

of Figure 4. For each of the 7 fingers we have determined the

total length of the reconstructed finger, and calculated the error

with respect to the mean length over all used sweep speeds for

that finger.9 In total we end up with 56 absolute errors εL. The

9We do not compare the extracted lengths to the length of the motherfingerprint, as a realistic scenario does not know a ”mother” fingerprint, butneeds to do enrollment with algorithms featuring the same distortion patterns.

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Fig. 5. Estimated sweep speeds as function of position along the fingerprintfor the test sweep speed 0.06 pixels per frame for 8 different fingers.

standard deviation of these εL is 5.8 pixels. We might compare

this value with to the approximate extend of fingerprint ridge

which is somewhere between 5 and 15 pixels.

Figure 6 illustrates the global as well as the local stretching.

We have selected the worst case situation for the local stretch-

ing, which happens to be the situations already been shown by

Figure 4. We have used the sweep speeds 0.06 and 0.3 pixels

per frame, respectively. We show the reconstructed fingers for

both sweep speeds. The global stretching for this situation is

easily seen in the figure. The local stretching effect is indicated

by the vertical green lines showing corresponding areas on

both reconstructed fingers and their reconstructed widths.

Fingerprint minutiae extraction usually used in authentication

bases on distances between landmarks; therefore, local and

global reconstruction qualities influence the FMR and FNMR

values of the complete authentication system.

For additional verification of the algorithm’s functionality,

we have replaced the synthetic data generated by our slice

model by data captured by a real, state-of-the-art, capacitive

two-line sweep sensor. Preliminary results indicate findings

comparable to the reported findings, which are based on the

synthetic data. Of course, with true data in the experiments

we cannot compare to a well-defined reference as we can do

when using the synthetic data of our model.

VI. CONCLUSIONS

We have presented an accurate method for sub-pixel finger-

print reconstruction, which is well suited for sweep sensors

featuring two pixel columns only. We presently implement this

algorithm in dedicated hardware, and thereby, we will prove its

efficiency and fast execution. The goal is to realize an overall

system for low-power mobile applications. We have shown that

in our approach the sweep speed estimation plays a central role

and is most important for high-quality fingerprint reconstruc-

tion. We have introduced a synthetic sub-pixel sweep sensor

model, which is the basis for a quantitative and reproducible

Fig. 6. Influence of inaccurate ∆s estimations: The global stretching forthe sweep speeds 0.06 and 0.3 pixels per frame, respectively, is 11 pixels,corresponding to 550µm. The green lines help to see local stretching effects.

performance analysis of our sweep-speed estimation algorithm

as well as the overall fingerprint reconstruction algorithm.

Preliminary experiments with data from true state-of-the-art

sensors indicate that our findings are well reproduced in reality.

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