Minutiae Structures in Nature
First issue: 2008-02-06 - Last update: 2008-03-08
| In
biometric systems the individuality of fingerprint patterns is used to
distinguish humans with surprising reliability. The reason for the uniqueness
of the ridge structure of fingerprints is the random arrangement of bifurcations
and line endings which deliver very characteristic image details. Aim of
this standing document is to compile every known occurrence of minutiae
patterns [Wikipedia]
in nature to demonstrate the universality of it. For a more detailed consideration
of minutiae patterns in flower and animal structures see [1]
and [2]. |
Human fingerprints
| Human fingerprint structure |
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| Author: unknown |
License: GFDL
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| Fingerprint-like patterns
are bound to a surface. Additionally, fingerprint-like patterns comprise
a stripe component such that the inverse structure also belongs the same
pattern family. This enables additional structure elements when compared
to vein-like structures [2].
While in vein-like patterns all lines are connected to something like a
root line and thus have a common begin, fingerprint lines (which express
as ridges and valleys in 3D), may begin anywhere and end anywhere. This
is illustrated in the following binarized human fingerprint image: |
| Binarized fingerprint image |
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| Author: Manfred Bromba |
License: limited to
this article
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| It is well known that the
very basic structures which define minutiae are the line endings and the
line bifurcations (ramifications). This is shown in the following two images
from the Optel homepage [4]: |
Line ending (white lines) |
Bifurcations (white lines) |
| If the black lines are considered,
the situation is inverted: line endings transform to bifurcations, and
vice versa. All other line structures can be attributed to these two cases.
For animal fingerprints, see the fingerprint pages of Jean-François
Mainguet [8] and Hans van den Nieuwendijk [9]. |
Artificial Fingerprints
| There are at least two different
ways to try understand the creation of minutiae structures. The most obvious
method is to analyze the underlying physical and chemical micro phenomena
and then to build a (mathematical) model and compare the (numerical) solutions
with the reality. This often is the most cumbersome way. Another possibility
is to look for known solutions of (simple) models which accidently coincide
with the natural phenomenon. Such a model can also be used to synthesize
minutiae patterns. An example of fingerprint synthesis is given in the
article of Wieslaw Bicz [4] where also a link to a sample
software from Optel is given. |
| Artificial fingerprints
with different coarse characteristics |
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| Author: Wieslaw Bicz |
License: personal permission
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The Zebra
| Zebra stripes are already
binarized as they only comprise two colors with sharp borders. In comparison
to human fingerprints, the line distance and width strongly depends on
the location on the fur. Also the minutiae are unequally but nevertheless
randomly distributed. |
| Zebra |
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Stapelia gigantea
| Fingerprint patterns in
plants is a rare phenomenon, but it exists as the following case shows!
The photograph has been taken in the Botanical Garden of Munich [3]. |
| Stapelia gigantea |
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| Author: Manfred Bromba |
License: cc-by-sa
3.0
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Origin: this
article
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| Stapelia gigantea
zoomed |
 |
| Author: Manfred Bromba |
License: cc-by-sa
3.0
|
Origin: this
article
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Ripple Marks
| The explanation of ripple
marks at a beach, best viewed at low tide, have engaged scientists since
more than 100 years [5]. Hertha Ayrton was one of the
first researches able to build a (mechanical) model to successfully simulate
the formation of ripple marks with its characteristic minutiae. Physical-mathematical
models have been considered, e.g., by Ingo Rehberg [6].
It is shown that the main mechanism for creating ripples is the interaction
of flowing fluids over sand in the presence of a disturbance. |
| Low tide at a beach
of Borkum (Germany) |
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| Author: Amanda77 |
License: GFDL
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| As the next two images show,
ripple marks have even been conserved as fossils. |
| Fossil ripple marks
from the Hassberge mountains (Germany) |
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| Author: R. Kirchner |
License: GFDL
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| Fossil ripple marks
found in Capitol Reef National Park (USA) |
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Dunes
| The next two examples of
minutiae structures I found thanks to a book of Robert Laughlin [7]
about emergence [Wikipedia].
To learn more about the term emergence I found in the German Wikipedia
two images which clearly show fingerprint structures: dunes and cow trails
[Wikipedia]. |
| Dune in Morocco |
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| The formation of dune structures
can be explained in the same way as in the case of water ripple marks.
Here, the wind takes over the role of the flowing water. |
Cow Trails
| Top view on cow trails on a steep mountain
meadow |
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| On impassable grounds such
as on steep meadows, cows - just like humans - prefer to use caved paths.
This leads to a number of parallel paths which occasionally bifurcate.
In contrast to fingerprints, there will be no endings. This restricts minutiae
to one type only. |
Clouds
| Altocumulus clouds |
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| This example of a ridge
structure in clouds suggest that as soon as nature shows a stripe pattern,
the pattern will be broken by minutiae. |
Cactus Ripples
| Echinopsis huascha
(?) |
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| Author: Manfred Bromba |
License: cc-by-sa
3.0
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Origin: this
article
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| This cactus shows two bifurcations
in its ripples, see right hand side. The photograph has been taken in a
garden in Mallorca. |
Humpback Whale
| Megaptera novaeangliae |
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| When viewing the documentary
film "Earth" (2007) in our cinema, I saw that the dark and white stripe
contours in the skin of humpback whales show beautiful minutiae structures.
As shown in the image of a dead whale above, these 3d structures seem to
be the largest ones for animals which are directly comparable with human
fingerprints. |
Acknowledgment
| The author would like to
thank all photographers for their personal or general permission to publish
their photos in this article. All rights remain with the contributors. |
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Literature and Links
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Manfred Bromba, Biometric
Animals (http://www.bromba.com/knowhow/BiometricAnimals.htm) |
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Manfred Bromba, Individuality
of Plants (http://www.bromba.com/knowhow/BiometricPlants.htm) |
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Botanical Garden of Munich
(http://www.botmuc.de/) |
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Wieslaw Bicz, New numerical
methods of fingerprints' recognition based on mathematical description
of arrangement of dermatoglyphics and creation of minutiae (http://www.optel.pl/software/english/method.htm) |
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Hertha Ayrton, The Origin
and Growth of Ripple-mark. Proceedings of the Royal Society of London A84:
285 (1910) (http://cwp.library.ucla.edu/articles/ayrton/Ayrton_ripple/ripple.html) |
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Research papers of Ingo
Rehberg (http://www.staff.uni-bayreuth.de/~btp915/research.html) |
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Laughlin, Robert (2005),
A Different Universe: Reinventing Physics from the Bottom Down, Basic Books,
ISBN 0-465-03828-X |
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Mainguet, Jean-François;
"Fingerprint", (http://perso.wanadoo.fr/fingerchip/biometrics/types/fingerprint.htm) |
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van den Nieuwendijk, Hans;
"FINGERPRINTS.TK" (http://www.fingerprints.tk/) |
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