Patterns of dermatoglyphics have been an object of interest to people for long time now, and thanks to that they have been examined and described quite extensively. Unfortunately, the approach to this subject developed by dactylography mainly for needs of criminology does not lend itself to easy mathematical formalisation. In practice this means that classic methods of fingerprints' recognition are not suitable for direct implementation in form of computer algorithms. In spite of this obvious fact, authors of many existing solutions - known and described in the literature dealing with ways of numerical processing of fingerprints, have attempted, usually in a direct way, eventually with small departures from that, to apply classic dactylographics formulas. Such approach has led to creation of very complicated programmes, which can analyse an image of a finger with employment of sophisticated methods, primarily so-called mathematical morphology. So complicated a solution of the problem precludes creation of simple programmes, unsusceptible to input errors (see [1]).

It seems that one of the basic problems hindering construction of algorithms for analysis of fingerprint images was lack of good mathematical model of the structure of dermatoglyphics. To create such a model one should understand first the essence of the phenomenon, and also to develop methods of its reliable and easy algorithmisation. As a starting point in our attempts of creation of such a model we selected the problem of synthesis of pattern of dermatoglyphics - chiefly minutiea. Everything indicated that resolving of this problem would be the key to solving of other problems.

Over the period of several years we have carried out many numerical experiments, which at the end bore fruits in form of creation of suitable model of a finger. On this basis there was created an original algorithm of synthesis of images of dermatoglyphics, and in particular all the possible arrangements of so called minutiea. The model allows to looks at digital coding of a fingerprint from a new point of view: not only as a set of pixels but some (quite simple) two-dimensional function of very interesting qualities. It also enables mathematical cataloguing of minutiea and types of patters, and this means revolution in methods of analysing, processing and compression of fingerprint images. The below presents synthetic images of minutiea, which are met most often (according to [2]), along with the table showing our conventional numerical classification (number and type of bifurcations):

Drg. 1		Drg. 2		Drg. 3		Drg. 4

Drg. 5		Drg. 6		Drg. 7		Drg. 8

Drg. 9		Drg. 10		Drg. 11		Drg. 12
Drg. 13		Drg. 14		Drg. 15		Drg. 16

Drg.1	Beginning or ending	L	Drg.9	Double whorl	RLRL
Drg.2	Singel bifurcation	L	Drg.10	Singel bridge	RL
Drg.3	Double bifurcation	LL	Drg.11	Twin bridge	RLLR
Drg.4	Triple bifurcation type 1	LLL	Drg.12	Interval	RL
Drg.5	Triple bifurcation type 2	LLL	Drg.13	Point	RL
Drg.6	Triple bifurcation type 3	LLL	Drg.14	Through line	LR
Drg.7	Hook	RL	Drg.15	Crossing	LR
Drg.8	Single whorl	RL	Drg.16	Side contact	RL

Due to commercial potential of the method, we cannot yet describe the methods of synthesis in detail, but to present its capabilities we can provide a demonstration programme Fingerprint Creator generating an extensive range of dermatoglyphic patterns. User of the programme can set by himself, among others, such parameters of synthesis as:

• type of pattern (concentric, curved, looped)
• number of munitions
• density of dermatoglyphics
• width of dermatoglyphics
• shift and rotation of centre of the pattern

Programme in DOS version enables recording of the generated pattern in one of three format (and two for Windows version):

Form of data	Size of data (bytes)	Extension of data file
One-bit bitmap	8222	*.bmp
Matrix of "pure" bytes	65536	*.fin
Set of synthesis parameters	6	*.par (*.fpp for Windows)

Attention should be given to the last form, and concretely the size of the set, which is created with that. The synthesis method created by us needs only 6 bytes to generate one from several million images of dermatoglyphics! Although this version of the programme cannot generate all the possible patters, but we think we will be able to achieve that soon. Assuming (with overestimation) that the number of possible human fingerprints can reach 100 milliard, it can be easily calculated that the minimum number of bytes needed for numbering all the patterns will not exceed 6, because 100 milliard = 10¹⁴ < 256⁶ = 6 bytes. As it can be easily noticed creation of a catalogue with all the possible patterns and referring to such classification is in practice impossible to be carried out. It is possible, however, to use a finger's number if it will be a univocal parameter of the synthesis' parameter. Below are presented examples of synthetic images of fingers generated with Fingerprint Creator:

The basic goal of creation of a finger's model was however the necessity of development of new, better algorithms of analysis. And indeed - knowing the mathematical description of artificial patters - it was possible to create a method of processing and analysis of images of real fingerprints. It contains algorithms of recognition of minutins (including their directions and types) directly onto the non-filtering, fully dynamic (full grey level) image of a finger. Because we do not use binarisation, skeletonisation or other similar methods, we do not have any problems with loosing of information present in those processes, and the minutiea, which are recognised, are really the very ones in almost 100% (classic algorithms often detect a great number of false minutiea, it sometimes occurs that even largely above 50%). An additional trump in the analysis method employed by us is possibility of their implementation in the form of very quick algorithms. On their basis we managed to create very effective methods of filtration, allowing cleaning dermatoglyphics from any "defects." Their employment decreases natural redundancy of an image resulting in the image of the real finger looking somewhat "synthetic," although it still possesses all the properties of the original essential for its recognition.

Our method also allows a broadly understood "finger engineering," for unrestrained ingeration in the image's structure. For example with its assistance additional minutiea or lines can be positioned in any given place in the real picture of the finger without altering the rest of the structure. Also it is possible, conversely, to deprive the finger's image of several or all the real minutiea. Below please find an example of an effect of our algorithm's application - searching for minutiea on an ultrasonic image of dermatoglyphics. The shown image comes from our ultrasonic holographic camera.

It should be emphasised that the processing methods created by us perform very well also on other types of images and are of relatively low sensitivity to the character of input data. So far we have successfully tested them on:

• ultrasonic images from our own ultrasonic hollographic camera;
• ultrasonic images obtained with a microscopic method (scanning with a focused beam);
• optical images from many different devices employing an effect of full internal reflection or light diffusion on the contact surface with the finger;
• optical images from devices of "touchless" type that see directly the finger's surface;
• scanned ink generated images;
• images from a piroelectric reader by Thomson-CSF;
• synthetic patterns of "Fingerprint Creator" programme.

Due to particularly effective way of analysis of dermatoglyphics and, primarily, a systematic approach to this issue, we are in the position to propose much more from manufacturers of classic programmes of fingers' recognition. We are also ready to adapt our algorithms in the case of other finger's readers of a especial character of data. Should you express your interest in our offer, please contact us.

 

[1] R.H. Andersen, P. Jürgensen, Fingerprint verification - For Use in Identity Verification Systems, Aalborg University, (1993)
[2] Cz.Grzeszyk, Daktyloskopia, PWN Warszawa (1992)