Entracer - Entropy sensitive ﬁngerprint feature extraction. · Entracer - Entropy sensitive...

Entracer - Entropy sensitive fingerprint feature

extraction.

Preda Mihailescu, Krzysztof Mieloch and Axel Munk

Abstract

We give a top - down description of a system of algorithms for fingerprint data extraction, to

be denoted as theentracer. The purpose of these algorithms is to optimally take advantage of the

inner structure of the ridge flow of a fingerprint. Aiming to develop new methods for matching and

classification, we train theentracer to extract a maximal amount of information present in a finger

image.

This is done in an adaptive way, which leads to good information and even performance gains with

respect to classical image processing strategies used in fingerprint recognition. The time gained can be

used for the improvement of the accuracy of the recognition,using feedback. Tracing is not sensitive

to warping and, in general, to connectivity preserving deformations due to pressure, torsion, etc.

As a practical example, we will report about extended tests on identification of minutiae using the

entraceron the FVC database.

Index Terms

Fingerprint recognition, minutiae extraction, feature extraction, ridge tracing, minutiae duality.

P. Mihailescu is with the Mathematical Institute, University of Gottingen.

K. Mieloch and A. Munk are with the Institute for Mathematical Stochastics, University of Gottingen.

November 2, 2007 DRAFT

IEEE TRANSACTIONS ON 1

Entracer - Entropy sensitive fingerprint feature

extraction.

I. INTRODUCTION

Fingerprints have been used since more than one century for human identification. Prior

to computers, this was done exclusively for forensic use andthe matching of fingerprints was

performed by trained experts, following quite elaborate guidelines forvisual fingerprint matching

[1]. Experience lead to the choice ofminutiaeas the main identification items. Roughly, minutiae

arebifurcations and endings of fingerprint ridge lines. Specialized guidelines feature more than

a dozen additional types of minutiae, but in general a sufficient amount (between12 and18, in

various national legislations) of well identified endings and bifurcations are accepted as evidence

of identity. Although the minutiae are the primary criterion for identification, human experts take

all features of a fingerprint into account. Achieving such a performance with the aid of computers

is an open target and we attempt through this research to makea step in this direction.

In the last two decades, automated fingerprint recognition grew to a young discipline, reaching

maturity. A large amount of papers have been published and the state of the art is covered by

surveys and books ( [2], [3], [4], [?], among others). The reader interested in reviews of the state

of the art in fingerprint recognition may consult these publications and the secondary literature

of these sources.

The applications of fingerprinting go way beyond traditional forensics and a whole line of

products using fingerprints for various authentication requirements are already on the market. A

common limitation of the current methods is related to the fact that theAutomated Fingerprint

Identification Systems(AFIS) are strongly focusing upon the minutiae location, and as a con-

sequence hardly any of the additional information contained in a finger image is actively used

(see e.g. [2]). As already mentioned, this information is actively taken into consideration by

the human expert in the visual process of matching. The limitation is correlated with a lack of

image processing techniques designed specifically for the task of extracting complex information

features from fingerprint images. On the one hand, AFIS allows quick searches in large databases

resulting in small lists of matching proposal. On the other hand, the algorithms currently used



in AFIS cannot reach the accuracy of human experts and that iswhy the final decisions are still

taken by experts. Extending the set of informations actively used by AFIS may improve this

situation, even if human experts cannot be replaced.

Some of the reasons leading to the above - mentioned limitations of AFIS are:

A. The use of pattern recognition techniques unspecific to the problem. Reinventing and adapt-

ing these techniques for the particular application of fingerprinting may result in several

improvements.

B. The focus on minutiae recognition. With image processing it is possible to identify most

of the passive information is used by human expert. This may be a lengthy process and

there is little experience concerning means by which this passive information may be used

for improving the performance of AFIS. In fact, recently, the necessity to take additional

informations, as for instance thelevel 3 fingerprint data– curvature, length, connectivity

and other topological properties – has become a concern in the biometrics community [5].

C. The fact that main partial problems of fingerprint recognition, like image enhancement,

orientation field extraction, skeletonizing, minutiae identification, etc.are mostly solved

independently of each other. These operations however have a deep correlation and treating

them as a sequence of independent processing steps may not beoptimal. The increasing of

the interdependency of tools used to address these various problems can lead to algorithmic

improvements and to a reduction of error rates.

The main purpose of our approach is to extract metric and topological information available

in a fingerprint and used by human experts in their identification work. The data is accessible

in simpledata structureswhich can be used for ulterior purposes, like classification, matching,

indexing or biometric security. Starting from the state of the art techniques used in fingerprint

recognition, we develop some new image processing approaches dedicated to the specific area

of application.

In Section II we give a general overview of the method denotedas theentracer; Section

III treats in more detail the concepts of entropy and recursion or feed-back which support our

approach and expand upon the relationship between orientation fields and tracing. Section IV

and V describe in more detail the building blocks – tools and primitives – of the tracing system.

In Section VI we give an overview of related work and Section VII presents results for the FVC

database on the accuracy of minutiae extraction, in comparison with other algorithms. The paper



concludes in Section VIII with an overview of further applications of the tracing algorithm and

the data it extracts.

II. DESCRIPTION OF THE METHOD

The primary aim of our approach is to extract amaximal amount of relevant information

from a fingerprint. The typical data which we extract from a fingerprint includes for instance

currently less features, such as ridge connection information, data ridge curvature, connectivity

and neighboring relations of ridge segments.

Our data extraction approachmay differ from current ones in more than one aspect. Thus, we

attack the problems of orientation flow extraction, ridge and minutiae recognitionsimultaneously,

taking advantage of their interdependence. In doing this, we use a simple adaptive - orentropy

sensitive- approach.

Here the term of entropy is used in the intuitive understanding of density of information: thus

an area of good image quality, situated outside the zone between deltas and core has typically

smooth, clear ridge flow and, in our sense, low entropy. The algorithms are designed to be

particularly fast and efficient in such areas. Conversely, in areas with higher information density,

due either to particularities of the fingerprint or to noise,the algorithms may use iterations and

additional decision resources in order to complete the dataextraction. The mechanism invests

thus more effort in data extraction in zones of high information density: entropy sensitivity can

thus be considered as a form of data adaptive process. The idea of adaptive algorithmshas been

common for decades in pattern recognition, numerical analysis and statistical image analysis.

See for instance [?], where locally adaptive weights are used to improve the quality of noisy

images. It is also used in some other fields of pattern recognition such as OCR; it is, however,

with very few exceptions, not used in fingerprint recognition.

Extraction quality can be improved byrecursivity . In this way a first round of extraction

only treats theeasy(low entropy) areas, and the gathered information can be recursively used

as a guide for extraction indifficult zones. Designing robust image enhancement and extraction

techniques using feed-back is a topic which we shall treat indetail in later publications.

We give next some details about the method, which will allow abetter discussion of our use

of the notions of entropy and recursion.



The information which we currently extract in addition to the relevant minutiae locations are

data such as:

• Complete ridge lines - based upon sufficiently dense interpolation points.

• Ridge curvatures.

• Graph connectivity of ridges.

• Neighboring relations of ridge segments.

• The same information for thenegative image(“valleys”).

The purpose of theredundant informationis obvious when considering the fact that data extrac-

tion as adecision process: the algorithm has to decide whether an encountered artefact is genuine

or generated by noise. Redundancy allows tovalidate features such as minutiae, connections,

etc., on base of several complementary data. Non - validatedfeatures are treated as uncertain,

but may be validated in the process of recursion.

Informations such as line connectivity can help in the latermatching process for deciding about

minutiae which, due to image distortions, cannot be identified by their geometric location data.

This adds to the metric matching process, such as currently used, and which is highly sensitive

to nonlinear distortions of the fingerprint images, the possibility of topological verifications, by

nature independent of metric data.

We envision the performer of the decision process of data extraction as a (software-based)

robot, which we denote byentracer. The data are extracted by the robot by following ridge lines

and using itsdecision toolsand the previously extracted data. As an example of the advantage of

parallel data extraction, one may consider the fact that many fingerprinting algorithmsskeletonize

the ridges (in the binary image) before actually searching for minutiae. Our experience shows

that these operations may be completed simultaneously withgain in timeand accuracy; for our

purpose, the skeleton is a side information of ridge tracingand minutiae localization which have

not been used so far.

The entracer receives a fingerprint image as input. It may write to one or more auxiliary images

in order to keep track of its state and it outputs the relevantextracted data in some linked lists

of labeled graphs. The vertices of these graphs are minutiaeand the lines are ridges connecting

the minutiae. The ridges are labeled with information allowing to recover their geometric shape,

length, curvature and neighboring ridge segments.

The reader should, however, bewarned not to identifythe fingerprint information with a labeled



graph and then to deduce that matching may draw upon the experience of matching algorithms

in graph theory. The reason why this restriction to a labeledgraph is too information destructive

has to do with geometric properties such as adjacency of ridges and connected components or

ridge distanceof two points, that is the number of ridges crossed by the lineconnecting two

points. This information is of great importance for imprintmatching and it is not easily concealed

in a labeled graph.

Ideally, theentracerstarts scanning an image in an arbitrary point on a ridge and can follow a

ridge line while writing data to the auxiliary images and theoutput graph. The process isiterated

until the full image is marked as analyzed. Theentraceruses abag of toolsfor following the

ridge lines, making decisions about minutiae or local imageenhancements, etc. We shall discuss

below in more detail some typical tools which are implemented.

The ridge and thevalley line - images, or simply the white and black lines in a binarized

fingerprint, are naturally dual to each other. Ideally, bifurcations of the first correspond bijectively

to endings of the latter. Natural exceptions are encountered only at deltas; further exceptions are

consequences of noise and thus the location of dual minutiaecan be used as quality measure

for the extraction. This certainly not novel ( [3], p. 86) observation of theduality of ridge and

valley images becomes a fruitful resource for validating minutiae locations.

In image zones with moderate noise usually at least one of theridge or valley line flow

remains quite accurate. When thus a traced, e.g. ridge, lineis distorted by noise, it is possible

to use duality and proceed the tracing locally in the valley image. Tracing is herewith a data

extraction approach which takes advantage of duality. We shall give below several instances of

the current use of duality in early and advanced stages of thetracing process.

In highly blurred image parts, even using duality, a single tracing run is not sufficient for

deciding the correct ridge flow and eventual location of minutiae. More involvederror correcting

methods are called for in such situations.

Tracing relays on connectivity and is thus robust with respect to connectivity preserving

distortions. In particular, deformations arising in contact sensors are of less importance for

tracing.



III. F INGERPRINT ENTROPY AND RECURSION

We shall now relate the intuitive notion of information density or entropy which we use to

the information theoretical one.

It is useful to consider the notion of anideal imprint which is blurred by a series of factors,

leading to the final scanned fingerprint image. The ideal imprint can be envisioned, for instance,

as one of the synthetical fingerprint images produced by programs like Cappelli’s [6]. The

possible blurring factors include scars, either natural oractivity related (mechanical, chemical,

etc.) skin degradation, as well as image capturing effects produced by grease, dirt, sweat, dryness

and further causes. Finally, one considers the image sum

Σ = I + B,

whereΣ is the scanned image,I is the ideal imprint of the finger andB is the sum of all the

distortions.

Accordingly, thefingerprint entropyin a neighborhood of one locationσ ∈ Σ is H(σ) =

H(i)+H(b), wherei ∈ I andb ∈ B are the corresponding locations inI, B, respectively. Since

B is essentially noise, the entropyH(b) is the classical entropy. The local entropy in the ideal

image is aridge entropy: it is a measure of the torsion and continuity of ridges.

The principle of recursion corresponds technically to the fact that conditional entropy is

always less than unconditional one; thus accumulated information is used to improve decisions

on uncertain events. We illustrate this principle with someaspects which have been already

implemented and lead to useful results.

• Recursive binarisation.A very powerful method of binarisation [7] uses a priori knowledge

about the orientation field; this is of course not available at the time of the first binarization.

In poor quality images we may improve binarisation, with very interesting consequences

for the quality of the overall data extraction, as follows: start with a simple binarization

followed by a stripped version of tracing which yields a robust orientation field.

The orientation field can be smoothened in the areas of poor image quality, by extrapolation

of the values in surrounding stable areas. Classical low pass filters can be used for instance

to this purpose, see e.g. [8]. The resulting orientation field can then be fed back into the

advanced binarization and the obtained image is then input to theentracer.



Fig. 1. An example of scars. Left: Original grey level image.Middle: identification of scars by theentracer. Right: after

recursive bridging

• Concentrated use of duality and recursion. Accurate minutiae location and validation may

be difficult. In a first run of the tracer, one locates individually minutiae in valleys and

ridges. In a second analysis (recursion), one matches pairsof corresponding minutiae in

ridges and valleys, thus obtaining also their precise location. Minutiae matched in this way

are calledvalidated. Invalid minutiae are reanalyzed in a third recursion: theycan either be

discarded asspurious minutiaeor yield some useful additional information.

• Recursion and bridging.Bridging is the process by which two close endings with opposed

directions are under certain circumstances joined in the assumption that the line is interrupted

by noise. Note that in our definition, the noise is related to the ideal print, so it may well

be that the endings exits on the actual finger, but they do not correspond to assumptions

we make about the ideal image and are therefore discarded. The bridging is an a posteriori

decision, i.e. it is taken in presence of a full pair of finger graphs for ridges and valleys.

Thus, it is a particular instance of recursion. It also illustrates how invalid minutiae may

carry some additional information, for instance about

• Scars. A posteriori analysis (recursion) allows the identification of clearscars: these appear

as several pairs of opposed endings along the same ridge direction and are aligned in a

transversal direction to the local tangent field. See Fig. 1

While recursion refers here to the repetition of some data extraction process, we use in this

paper the related term ofiteration to describe a far simpler mechanism, occurring in the process

of tracing: the repeated positioning and orientation of theentracer.



A. From orientation fields to the entracer.

We shall review below the relatively few tracing - related methods to be found in literature.

They may have different purposes from ours. Yet they are distinguished from the majority of

algorithms for fingerprinting by the fact that they are not bound to isotropic,window related

operations, but use directly the natural flow pattern of the finger. The visual impression of

fingerprints suggests that the effort for detecting the sametype of data - e.g., ridge orientation

- varies over the image: this is the effect of theridge entropyas introduced in the last section.

This suggest an adaptive, entropy sensitive tracing.

IV. TRACING PRIMITIVES

In our approach theentracer is defined in a top-down functional specification. Thus, at more

than one level of the specification, the tools designed for achieving given functionalities can be

instantiated in various ways. A learning by doing research reveals optimal methods for solving the

tasks of these tools. The description of theentraceris therefore made in some generality, while

following the lines of an existing implementation. The implementation confirms the realizability

and usefulness of the concepts and shall be illustrated below by its capacity to localize minutiae

correctly.

The entracer interacts with one of

1. The input image (Input).

2. The auxiliary files and images (Input/Output).

3. The extracted data structures (Output).

The images are all of the same size, represented by Cartesiancoordinates1 ≤ X ≤ n; 1 ≤

Y ≤ m. The entracer itself keeps track of its own current locationT (X, Y ) and uses thetools

for tracing ridge lines and extracting data. The tools are built upon tracing primitives. We shall

consistently consider the tracing of ridge lines; the operations for valley lines are identical. When

performed in parallel, they may influence each other, providing mutual information; this fact is

omitted in this paper. We sort the tracing primitives according to the files and structures with

which they interact.



Fig. 2. Image from the FVC2002 [9] database (databaseDb2 a, image15 1). On the left the original, in the middle is presented

the image after binarization and border determination, on the right: graph with minutiae as the result of tracing the valleys

A. The finger image and its tracing primitives

The input image I = P (X, Y ) : 1 ≤ X ≤ n; 1 ≤ Y ≤ m represents a fingerprint and we

assume that the border of the actual finger has been previously determined, in such a way that

the pixels outside of the fingerprint are marked by unique values, which are distinct from pixel

values of the fingerprint (see Fig. 2).

Tracing is possible for grey level images using essentiallythe same primitives we shall

describe. This has some relevance in particular for emerging touchless sensors, [10]. We restrict

our attention in this paper to binarized input images and primitive instantiations will be described

based on this assumption1. Our experience shows that grey level tracing poses in general more

problems then binarization followed by binary tracing; thegrey level information can be stored

for additional processing only in the areas which could not be ”solved” in the binary image.

The pointsP (X, Y ) may have one of the valuesR, V, B, U , whereR andV stand for ridge

and valley,B for border and the additional possibilityU - undecided - is reserved for unclearly

binarized points.

1We shall, however, mention a binarization method, which uses theentracer.



The major primitives for reading an input image are thelocation, direction and ending

primitives. The location primitive decides whether a pointP (X, Y ) ∈ I belongs to a ridge

or valley. Ideally, this decision may be taken by solely considering the value of the pixel under

consideration; this is the simplest realization of this primitive. In presence of noise such a

decision is mostly inaccurate; the primitive has to optimally use context information for giving

a good decision with a minimal amount of work.

A first practical specialization distinguishes betweeninitial location - andborder detection -

primitives. The first is used for choosing a starting point for the tracing of a ridge line. In some

cases it may draw back upon some reliable information about already traced adjacent lines. It

must also give reliable decisions in absence of such information and is thus the more delicate

localization primitive: it will decide by analyzing a larger neighborhood of the pointP (X, Y ).

Since it is easiest to perform tracing when following the median line of a ridge, acentering

primitive will be used for positioning a localized ridge point in the center of a ridge for subsequent

tracing. Centering is a tool of initial location and for relocation.

The border detectionis a simpler form of initial ridge point location. It is used in the context

of tracing as follows: starting in a centered ridge point, one follows a line and needs to decide

when this line exits the traced ridge (thus entering a valleyarea). The contextual information is

higher in this case, and thus the primitive simpler - and alsomore often used. We note however,

that a border detection based only on one change of pixel values along a line is often inaccurate

and more environment data have to be taken into consideration.

The direction primitive decides between a fixed set of discrete angles, thedirection in which

the traced ridge proceeds. Thus, starting from theentracerpositionT (X, Y ), the discrete lines

with prescribed discrete angles are followed using the border location primitive for establishing

the point where they leave the traced ridge. The angle corresponding to the maximal line within

the traced ridge will then be chosen as current direction of the tracing. This leads to repositioning

of the entracer followed by its centering. Direction choice can also use contextual information

- either from the current direction of the ridge line in theentracer’s positionT (X, Y ), or, when

starting the tracing of a new ridge, from adjacent tangent field information gathered in auxiliary

files from previously traced ridges.

Finally, theending- primitive decides where a ridge ends. This may be a border point, or a

proper ridge end. In these cases the decision is made by interacting only with the input image.



A scanned ridge line may also end when hitting an already analyzed ridge line; in this case

one finds a ridgebifurcation and the decision results by interacting also with the auxiliary files

in which scanned areas are marked. Note that ridge scanning may start in any point of a ridge

and follows then one initial direction. Theentracerhas to keep track of the starting point and

direction and after hitting an end it will reposition in the starting point and complete the ridge

scanning in the direction opposite to the starting direction until hitting a new end.

B. The auxiliary images and their primitives

Thetrack - image is an auxiliary image, in which the tracer marks the scanned areas. One may

additionally use atangent field - image for storing scanning directions identified by the direction

primitives. Thestarting point grid is a two dimensional array of equally spaced points, with

relative distance approximately equal to the ridge width. This grid is used for testing possible

start points for entracing and marking all used points.

C. Thefinger data structure

The finger data structure is a linked list - a graph - ofridge segments. Conceptually, a ridge

segment is the section of a ridge between two endings, bifurcations or border points. The ridge

segment itself carries additional detail. Such are the intermediate center points located at small

distance - typically a ridge width - from one another, together with their local direction. Segment

length and maximal curvature are additional informations which are stored in a segment. The

nodesor ridge endingsare the dual to segments. Thus segments point to nodes and nodes point

to all segments ending there (more than one segment is ending in a node, exactly when the node

is a bifurcation). The tracer writes data to local segments and inserts the results in the finger

data structure at completion of a segment tracing. In a postprocessing step, the adjancence of

ridge segments is marked in both dual images, in view of ulterior applicaitons to matching and

security.

V. TOOLS AND ERROR CORRECTION

The design of theentraceris illustrated by the metaphor of a flat robot tracing the borders of

a discontinuous track – the ridge lines. The tracks borders may be interrupted by pebbles spread

along the track (noise).



Fig. 3. Aura in a starting point (on the right) and in a following point (on the left)

A human operator (initial location primitive) places the robot on the track. The robot cannot

look much ahead, but the trained one quickly identifies the road direction and proceeds along

the way, keeping close to the middle of the road; it can pass over isolated pebbles but recognizes

when the pebble density is such that he probably crossed the road edge, and then corrects his

direction. The entracer’s way of “looking ahead” consists in stretching out “feelers”; anentracer’s

feeler Φα is a directed line segment with direction

Φα(X, Y ) = (X, Y ) + ⌊m · (cos α, sin α)⌋ : m ∈ N ,

starting at theentracer’s current position. Theangle α of the feeler is the angle between this

segment and the positive axes of the abscissae and in this context, the brackets(X, Y ) denote

the unique anglemod 2π, determined by the vector from the origin to the point of Cartesian

coordinates(X, Y ) and thex - axes. Aborder locationprimitive glides along the segment and

identifies the next border position. The border locator is thus part of the feeler’s mechanism,

the setΦα is its support. The feeler’s action can be described by a function which associates to

a givenentracer - point T (X, Y ) on a ridge the next border crossingBα(X, Y ) in the feeler’s

directionα. This also determines the angular border distance

lα(X, Y ) =| (X, Y ) − Bα(X, Y ) |,

which is of subsequent relevance.

In order to determine the optimal direction for continuing along the track, various directions

must be scattered. The tool for choosing the optimal direction is called anAura :

Ω(X, Y ) = Φα : α ∈ A(Ω) ∪ α0.

Here,α0 is the previous direction of movement by which the point(X, Y ) was reached by the

tracer. It is thus undefined in a starting point and defined otherwise. If α0 is undefined, the

direction setA(Ω) is simply a discrete set of equidistant angles in the circle.Otherwise,A(Ω) is



Fig. 4. Set of angular border distances

a smaller subset of the circle angles, which defines a sufficiently large cone symmetric around the

directionα0: even at narrow cores, ridges do not take abrupt turns, but rather change smoothly

their direction, while the current border distances along the movement direction decrease. An

example of direction restricting is shown on Fig. 3.

In a cynetic view of the tracing process, this would correspond to the fact that theentracer

can drive fast along close-to-straight ridge sections (long maximal border distances), while it

must slow down at turns. The informationλΩ gathered by an aura is a set of distances to the

border along the aura directions (angular border distances, see Fig. 4):

λΩ(X, Y ) = lα(X, Y ) : α ∈ A(Ω).

For the convenience of ulterior decisions, the angles inA(Ω) come reordered according to

decreasing values oflα; thus lαi, i ≥ 1 is the i−th largest border length. Together with this set

of distances, the aura also outputs the related set ofcentered remote points:

ΓΩ(X, Y ) = Cα(X, Y ) : α ∈ A(Ω).

If Bα(X, Y ) is the angular border point found by the feelerΦα(X, Y ), then the corresponding

centered point is determined by a centering primitive whichfinds a close ridge point situated at

the center of the ridge. Centering has multiple advantages:the most immediate is that it makes

it easy to decide whether the target point hits an already traced region. This would indicate a

closebifurcation. The aura output must be processed by theentracer in order to proceed the

tracing. For this it must decide about one from a set of possible events. For each event there

is a dedicatedevent analyzer: a tool which sorts out the odds that the given event occurs. We

describe next the simpler events and their analyzers.



Fig. 5. An example of bridging with use of neighborhood information.

The continuation event is merely the case in which the ridge continues in a direction α1. In

this case the tracer is moved from(X, Y ) to the remote centered pointCα1(X, Y ), the current

directionα0 is set toα1 and the tracing process is iterated. Continuation is clear when the angular

border distancelα(X, Y ) is large enough (typically more than two ridge widths) and a small

environment ofCα1(X, Y ) does not belong to an already traced region. If all angular border

distances are small (of the order of magnitude of one ridge width, say), we have the indication

of a probableending event. Since endings are the most common false artefacts, the analyzer

must perform a series ofconfirmation testsbefore declaring the tracer position as ending. If the

ending is confirmed, the center of the ending line is added to the minutiae list of the finger data

structure. Theentraceris repositioned to the starting location of the current segment, and tracing

is continued in the opposite direction. If this task had already been completed, the segment is

closed. Confirmation/validation tests are performed byerror correctors.

A simple example is thebridge corrector. This tool verifies whether it is possible or not to

continue the ridge across a small interruption due to noise.It says whether building abridge

beyond the supposed ending is consistent with the larger environment data. Given duality, a good

indication for the possibility of bridging is the absence ofa bifurcation of the valley around the

supposed ending. Another necessary condition is the presence of a ridge of equal direction

beyond the bridged interruption (See Fig. 5). Bridging can be decided on line (i.e. at tracing

time) and a posteriori, in recursion: the first case occurs inevident situations, for instance at

very short interruptions of a clear ridge. Recursion allowsusing more information in the case

of larger gaps to bridge.

If the possibility of bridging is confirmed, then the bridgedposition is stored to a separate data

structure which shall be used for a posteriori identification of scars. Then tracing is continued

across the bridge.



Fig. 6. Traced line and the bifurcation event

Fig. 7. Bifurcation before and after validation

If the border locator reports meeting of another trace line,this indicates abifurcation (Fig.

6). The context is passed on to a bifurcation confirmation tool. By duality, error correctors for

valley endings can be used in this case. However, when closing confirmed bifurcations, some

extra points have to be considered. First, the multiplicityof the bifurcation has to be determined

separately. Further, in the case of an a priori bifurcation,(at least) two new segments start at the

bifurcation. They must be marked open for ulterior tracing.In the a posteriori case, an existing

segment – which is encountered by the currently traced one, yielding the bifurcation – is split

in two by the minutia found. This fact has to be reflected in thefinger structure, too. With the

exception of singular points, to each bifurcation corresponds an ending in the dual area. That

fact is used forvalidation of minutiae. A minutia is said to be validated if its dual counterpart

is found, see Fig. 7.

The iteration works based upon theStart point grid Γ, as follows: a first starting point

S1(X, Y ) ∈ Γ is searched, for instance on the medial line of the finger image, possibly far

away from the core zone of the finger. The initial location primitive decides whether this is a

valid starting point2. Subsequently, the ridge to whichS1 belongs is traced in both directions

until endings or border points are reached. After that, the image is scanned in the orthogonal

direction to the ridge throughS1 for a new valid starting pointS2. Invalid starting points are

2In the first iteration, invalid starting points may occur outside of the finger area. In later iterations, one also checks that the

start point is not in a traced area



marked inΓ; valid starting points are also marked, after completion ofthe tracing cycle starting

in those points. The process is iterated in both directions until the image border is hit. Normally,

when this process is closed, the whole image may have been scanned. However, the termination

decision is made on the base of the marked points in the starting point grid. Termination is

confirmed by the fact that the number of marked points inΓ grows at each iteration.

VI. RELATED RESEARCH

We shall give a brief review of the papers which use tracing orrelated ideas. These do not

exploit the full potential of the approach and have mostly the target of extracting minutiae and

the reported results may be related to images which are not inthe public domain. The next

section will reflect our results in the particular application of the entracer to minutiae extraction

and provide some partial base of comparison.

In the seminal paper of Maio and Maltoni [11] and several follow up papers [12], [13], ridge

tracing in grey value images is proposed. The tracing is performed by investigating data along

segments normal to the ridge flow. The papers of Maio and Maltoni are a reference in the domain

of tracing and no later attempt to use this method for incorporating additional fingerprint features

in the matching process is known to us.

There are fine differences between various approaches to tracing. The tangential ridge tracing

which we perform in binary images allows adaptivity. Thus, few decisions are necessary in

areas with stable ridge flow. In the normal approach of Maio et. al., the ridge lines are scanned

equidistantly, without using preexisting information. Chang and Fan [13] have considered a

variant of normal tracing, in which a some adaptivity is usedin the sense that the ridge is

scanned only every few pixels rather than every pixel like inthe original method. Interestingly,

in [13] the quality of extracted minutiae is referred to a setof data extracted by using the same

method with scanning step1, thus essentially the results of Maio and Maltoni – and not bya

human expert, as common in the context. The authors use then the same method, dropping the

scanning distance gradually from 2 to 10 pixel, with sensible loss of accuracy. In comparison,

the entracer has a scanning step which may vary between1 − 2 ridge widths (10 − 20 pixels)

in the core zone to4− 6 ridge widths in external zone of smooth ridge flow. The quality is not

decreased by the large scanning step, which is determined interactively at every position from

the quality of the data. Jiang, Ser and Yau [14] use an improved adaptive gray level tracing



10 1 47 1 11 8

Fig. 8. Sample fingerprint impressions from the database [18], with good quality on the left and bad on the right.

method and show that its matching performance is comparableto the results of single step gray

level tracing. They do not consider the quality of minutiae extraction. Liu, Huang and Chang

[15] make also use of the surrounding furrows in their gray level tracing algorithm.

We believe that these concrete figures suggest the fact that the simple word “adaptivity” or

“entropy sensitive” cannot sufficiently describe a method or process. A further decision concerns

the use of grey level or binary images for tracing. Grey levelwas traditionally chosen for the

reason it contains more information. This may make tangential tracing and thus high scale

adaptivity difficult, while the normal scanning involves some operations which are common also

for binarization. There appears to be evidence that binary level tracing together with the storage

of grey level data is an efficient compromise.

An idea related to tracing and which followsbordersof ridge lines has been proposed recently

in the literature [16], [17]), as an alternative to skeletonizing. The authors use chain codes and

run length codes. The performance for minutiae extraction is given explicitely in [17], yet it lays

below the methods based on grey-level tracing discussed above.

VII. PRACTICAL EXAMPLES

The entracer algorithm has been tested on fingerprint images from FVC 2002[18]. The

segmentation of the images was done as in [19] and smoothing and binarization are based on

ideas from [19].

In order to examine the quality of the algorithm, the qualityof the extracted minutiae is being

tested. The tracer was run on a database containing 123 fingerprint images. The true minutiae



10 1 47 1 11 8

Fig. 9. Minutiae extracted by theentracer, for fingerprint images from Fig. 8.

positions, directions and types were manually marked. Fromthe FVC2002 Db2a database we

took three first impressions from fingers with indexes from 10upto 50. Three examples with

different quality are shown in Fig. 8. The quality of the images is variable and for images in the

lower quarter of quality, the placing of minutiae is not an obvious decision, even for a human

expert. Image 118 is a ponderate example from this range.

The Fig. 9 presents results of minutiae extraction and the Fig. 10 and 11 display samples of

ridge extraction by theentracer.

In order to evaluate the quality of extracted minutiae features, the following concepts are

defined [20] [21]:

Matched minutia A true (marked) minutia that was matched within the given tolerance by

one detected by the algorithm.

Missed minutia A true minutia that was not identified within the given tolerance. The

tolerance is set to|Mp − Np| < tp and cos ∠(Md, Nd) > td, whereMp

is the position of the minutia andMd is a vector pointing along the minutia

direction. The constants were set totp = 10, td = 0.96 (corresponding to

an angle of15 degrees).

Spurious minutia A minutia detected by the algorithm which lays in a region containing no

true minutia.

Flipped minutia Detected minutia type is different from thetrue minutia type.

Given a minutiae setE extracted by our algorithm and a setG of true (expert marked)

minutiae, we consider the following sets:



TABLE I

DETAILED RESULTS FOR THE FINGERPRINT IMPRESSIONS FROMFIG. 8

Image |G| |E| |M | |S| |CC| |M |/|G| |S|/|E| |CC|/|C|

10 1 33 31 2 0 29 0.061 0 0.935

47 1 42 38 4 3 30 0.095 0.079 0.882

11 8 20 12 5 3 12 0.25 0.25 0.556

• S = E \ G - set of spurious minutiae

• M = G \ E - set of missed minutiae

We split the setC = E ∩ G of correctly extracted minutiae into two sets:

• FC - set of flipped minutia

• CC - minutiae with correctly extracted type

In order to describe the accuracy of minutiae extraction letus define following quantities [22]:

• |M |/|G| - the proportion of missed minutiae

• |S|/|E| - the proportion of spurious minutiae

• |CC|/|C| - the proportion of correctly classified minutiae.

The performance for images from Fig. 8 is illustrated in the Table I. Here are some comments

about the more frequent sources of error. Spurious minutiaeare naturally connected to regions

with high noise and can hardly be avoided, unless one uses involved smoothing techniques which

would falsify the quality of the results. The loss oftype information of the minutia happens in

the preprocessing and the extraction is consistent with thetype in the binary image.

Note that with very few exceptions, at least18 − 20 minutiae were correctly detected, while

the average is close to30. Assuming that12− 18 minutiae pairs are enough to ensure a legally

positive identification, we see that even the higher values of |M |/|G| are still admissible. The

same holds for the value1 − |CC||C|

, since some AFIS do not use the minutiae type information.

However, most matching methods are very sensitive to the existence of spurious minutiae and

consequently the value|S|/|E| should be low.

We attempted to compare our method to the line following method in the grey fingerprint



TABLE II

RESULTS FOR ALL123 FINGERPRINT IMPRESSIONS IN THE DATABASE.

|M |/|G| |S|/|E| |CC|/|C| |CC|

Mean 0.042 0.083 0.815 30.825

Standard deviation 0.058 0.069 0.094 7.38

TABLE III

COMPARISON WITH GREY LEVEL LINE FOLLOWING

missed minutiae spurious minutiae minutiae with swapped type

grey level line tracing 0.07 0.57 0.17

our method 0.042 0.083 0.815

image of Maio and Maltoni, [11]. As mentioned above, this is the leading method up to date.

The set of13 images on which the results of that paper are established is however not public

and a direct comparison was not possible. Hence, we decided to pursue the following strategies:

A. Comparision with an own implementation of the method of Maio and Maltoni on the same

data base we used.

B. Comparing directly to the results of [11], on base of different images.

The results for A. are shown in the Table III. We note a high amount of spurious minutiae,

suggesting that Maio and Maltoni did use some additional filter which is not described in the

paper [11]; the fact that their method is prawn to generatingnumerous spurious minutiae is also

suggested that a follow up [12] uses neural networks for the elimination of such errors. The

tracing in binary has not this problem, and it is conceivablethat the parallel tracing approach we

use (in contrast with the orthogonal one of Maio and Maltoni)might help also in the grey level

images). The comparison B. is also encouraging for our method, since the results are slightly

better, although the data base is larger and the variance relatively big. Certainly the comparison

is not conclusive, since we have no information about the quality of images in the database of

[11].

Finally, we measured the minutiae extraction goodness by evaluating the influence on match-

ing. The fingerprint impressions from a FVC database were matched according to the FVC



TABLE IV

EQUAL ERROR RATES

Neurotechnologija Entracer

FVC2002 db2 1.056% 0.953%

FVC2000 db3 7.692% 7.253%

10 1 47 1 11 8

Fig. 10. Ridge graphs of fingerprint impressions from Fig 8. Traced in white.

protocol [9], which results in 2800 genuine and 4950 false matchings. We used for preprocessing

of fingerprints and matching of extracted minutiae the VeriFinger software [19]. The equal error

rates for minutiae extracted with VeriFinger software and our method are presented in Table IV.

VIII. C ONCLUSION AND FUTURE WORK

Theentracerdistinguishes itself from other methods for fingerprint recognition by its adaptive

strategy of data extraction, the possibility to use recursion and the embedding of minutiae in the

finger graph containing ridge information like connectivity, adjacency, cuvature and length. Apart

from that, several basic ideas implemented in the elementary primitives are certainly common

points in the automated fingerprint recognition. For instance, the tracer direction is identical to

the local tangent vector and the idea of finding such a vector as the direction with the least

colour fluctuations (or the normal to the one with the most fluctuations) along a sufficiently

long segment (say of four to six ridge width) is one of the simplest ideas used in the classical

methods for computing the tangent field. This is essentiallywhat the initial location primitive

also does, by using the aura. The way the idea is then used is, however, different. As presented



10 1 47 1 11 8

Fig. 11. Ridge graphs of fingerprint impressions from Fig 8. Traced in black.

above, by using the entracing approach one tries to adapt thecomputational effort to the image

- inherent variations of information, which is a classical goal of adaptive algorithms.

In this paper we gave accurate functional specifications of purpose and hierarchy of the

entracerand its parts/primitives.

The extraction process performed by an entracer serves varoious purposes. Comparing to state

of the art is possible for a variety of targets, of course. We have treated in this paper the quality of

minutiae extraction. Subsequent papers shall consider theapplications of theentracerto the key

problems of fingerprinting: matching, indexing, classification and security; the primitives used

are the same. We recently pointed out [23] that the use of fingerprints in connection with the

fuzzy vault scheme of Juels and Sudan [24] is insecure. Additional information such as extracted

by entracing can be used for raising the security of the vaultto cryptographical standards [23].

Some authors consider that new sophisticated models are called for in order to cope with

the problems posed by poor image quality [2]. Furthermore, we believe that fingerprints are an

empirical knowledge item and models need field confirmation.Any field research is dependent

on the interface by which it processes its data, and in the case of field tests on fingerprints such

an interface needs to be automated. Our approach of extracting the maximal possible amount

of significant data from a finger image can be useful also for storing data bases of reusable

information gathered from field tests. In such contexts restricting solely to minutiae data may

be insufficient.



ACKNOWLEDGEMENTS

The authors acknowledge the support of the projectExplicite and algorithmic methods in

number theory, cryptology and pattern recognition, by theVolkswagen foundation, for the first

author, and theDFG, Graduiertenkolleg 1023Identification in mathematical models, for the

second.

REFERENCES

[1] A. K. Jain, L. Hong, S. Pankanti, and R. Bolle, “An identity-authentication system using fingerprints,”Proc. IEEE, vol. 85,

no. 9, pp. 1365–1388, Sept. 1997.

[2] A. K. Jain and S. Pankanti,Automated Fingerprint Identification and Imaging Systems, ser. Crc Series in Forensic and

Police Science. CRC Press, 2001, ch. 8, pp. 275–326.

[3] D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar,Handbook of Fingerprint Recognition. New York: Springer, 2003.

[4] N. Ratha and N. Bolle,Automatic Fingerprint Recognition Systems. Springer Verlag, 2004.

[5] A. Jain, Y. Chen, and M. D. Demirkus, “Pores and ridges: High-resolution fingerprint matching using level 3 features,”

vol. 29, no. 1, 2007, pp. 15–27.

[6] R. Cappelli, A. Erol, D. Maio, and D. Maltoni, “Syntheticfingerprint-image generation,” inProc. of 15th International

Conference on Pattern Recognition (ICPR2000), vol. 3, 2000, pp. 475–478.

[7] Y. He, J. Tian, X. Luo, and T. Zhang, “Image enhancement and minutiae matching in fingerprint verification,”Pattern

Recognition Letters, vol. 24, pp. 1349–1360, 2003.

[8] L. Hong, Y. Wan, and A. Jain, “Fingerprint image enhancement: Algorithms and performance evaluation,”IEEE

Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 8, pp. 777–789, 1998.

[9] D. Maio, D. Maltoni, R. Cappelli, J. L. Wayman, and A. K. Jain, “FVC2000: Fingerprint verification competition,”IEEE

Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 3, pp. 402–412, 2002.

[10] G. Parziale, “Touchless fingerprinting tehcnology,” in Advances in Biometrics: Sensors, Algorithms and Systems, N. K.

Ratha and V. Govindaraju, Eds.

[11] D. Maio and D. Maltion, “Direct gray-scale minutiae detection in fingerprints,”IEEE Transactions on Pattern Analysis

and Machine Intelligence, vol. 19, no. 1, pp. 27–40, 1997.

[12] D. Maio and D. Maltoni, “Direct gray-scale minutiae detection in fingerprints,”IEEE Transactions on Pattern Analysis

and Machine Intelligence, vol. 19, no. 1, pp. 27–40, 1999.

[13] J. Chang and K. Fan, “Fingerprint ridge allocation in direct grey-scale domain,”Pattern Recognition, vol. 34, pp. 1907–

1925, 2001.

[14] J. X., Y. W., and S. W, “Detecting the fingerprint minutiae by adaptive tracing the gray-level ridge,”Pattern Recognition,

vol. 34, pp. 999–1013, 2001.

[15] H. Liu and Chang, “Direct minutiae extraction from gray-level fingerprint image byrelationship examination,” in

International Conference on Image Processing, vol. 2, 2000, pp. 427–430.

[16] Z. Shi and V. Govindaraj, “A chaincode bsaed scheme for fingerprint feature extraction,”Pattern Recognition Letters,

vol. 27, no. 5, pp. 262–268, 2006.



[17] J. Shin, H. Hwang, and S. Chien, “Detecting fingerprint minutiae by run length encoding scheme,” vol. 29, pp. 1140–1154,

2006.

[18] D. Maio, D. Maltoni, R. Cappelli, J. L. Wayman, and A. K. Jain, “FVC2002: Second fingerprint verification competition,”

in Proc. Int. Conf. on Pattern Recognition (16th), vol. 3, 2002, pp. 811–814.

[19] Verifinger, “Neurotechnologija.”

[20] C. Wu, Z. Shi, and V. Govindaraju, “Fingerprint image enhancement method using directional median filter,” inBiometric

Technology for Human Identification, Proceedings of the SPIE, A. K. Jain and N. K. Ratha, Eds., vol. 5404, 2004.

[21] N. Ratha, S. Chen, and A. Jain, “Adaptive flow orientation-based feature extraction in fingerprint images,”Pattern

Recognition, vol. 28, no. 11, pp. 1657–1672, 1995.

[22] J. Cheng and J. Tian, “Fingerprint enhancement with dyadic scale-space,”Pattern Recognition, vol. 25, pp. 1273–1284,

2004.

[23] P. Mihailescu, “The fuzzy vault for fingerprints is vulnerable to brute force attack.” [Online]. Available:

http://arxiv.org/abs/0708.2974v1

[24] A. Juels and M. Sudan, “A fuzzy vault scheme,” inProc. of the IEEE International Symposium on Information Theory,

2002, p. 408.

PLACE

PHOTO

HERE

Preda Mihailescu (Prof. Dr. Math.) is professor for Explicite Methods in Number Theory and Pattern

Recognition financed by the Volkswagen Stiftung at the University of Gottingen. He received his Masters

Degrees in Mathematics and in Computer Science from the polytechnic Institute ETH in Zurich, 1981,

resp. 1986 and his PhD in mathematics in 1997, also in Zurich. He worked from 1985 to 2000 in the

industry in the domains of numerical analysis and IT - security and cryptography. He is a professor since

the year 2003, with interests ranging from diophantine equations and computational number theory to

biometry and applications to IT - security.

PLACE

PHOTO

HERE

Krzysztof Mieloch (M. Sc.) received his degree in computer science from the University of Wroclaw,

Poland in 2002 and the degree in mathematics from the University of Gottingen, Germany in 2003. Since

2003 he is pursuing research towards a PhD at the Institute for Mathematical Stochastics, University

of Gottingen, Germany. He is a member of the Graduiertenkolleg 1023. His research interests comprise

mathematical methods in image analysis, particularly in the analysis of fingerprints.



PLACE

PHOTO

HERE

Axel Munk (Prof. Dr. rer. nat.) is director of the Institute for Mathematical Stochastics, University of

Gottingen, Germany. He received his degree in mathematicsand his PhD from the University in Gottingen

in 1992 and 1994, respectively. His current research interests include non-parametric statistics and statis-

tical inverse problems. In 1992 Axel Munk received the Gustav Adolf Lienert Award of the International

Biometric Society, German Section. From 1992 to 1994 he was supported by the ”Studienstiftung des

Deutschen Volkes”, and afterwards by the German Research Foundation (DFG) until 1995. He recently

(2005/06) was awarded a research semester on ”Inverse Statistical Problems under Qualitative Prior Information” by the German

Research Foundation (DFG). Axel Munk is guest editor of Statistica Neerlandica, Drug Information Journal, and Biometrical

Journal.


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