On the Mathematical Reconstruction of Two Dimensional Plants

2006 ◽  
Vol 26 (2) ◽  
pp. 113-129 ◽  
Author(s):  
Zbigniew J. Grzywna ◽  
Przemysław Borys ◽  
Gabriela Dudek
Keyword(s):  
Pattern Recognition ◽  
Quantitative Analysis ◽  
Medicinal Plants ◽  
Surface Density ◽  
Iterated Function Systems ◽  
Linear Ordering ◽  
Mathematical Representation ◽  
Computer Memory ◽  
Two Dimensional ◽  
Iterated Function

A set of 10, chosen medicinal plants (some of them with a reputation as remedies for tuberculosis) has been investigated through Partitioned Iterated Function Systems-Semi Fractals with Angle (PIFS-SFA) coding, Lempel, Ziv, Welch with quantization and noise (LZW-QN) compression, and surface density statistics (f(α)-SDS) discrimination techniques. The final outcomes of this quantitative analysis were, firstly: the linear ordering of the plants in question accompanied by the hope that it reflects their medical significance, secondly: the mathematical representation of each of the plants, and thirdly: the impressive compression achieved, leading to remarkable computer memory saving, and still permitting successful pattern recognition i.e., proper identification of the plant from the compressed image.

Quantitative analysis and pattern recognition of two-dimensional electrophoresis gels.

1984 ◽  
Vol 30 (12) ◽  
pp. 1919-1924 ◽  
Author(s):  
G Ridder ◽  
E VonBargen ◽  
D Burgard ◽  
H Pickrum ◽  
E Williams
Keyword(s):  
Pattern Recognition ◽  
Image Analysis ◽  
Quantitative Analysis ◽  
Data Reduction ◽  
Two Dimensional ◽  
Two Dimensional Electrophoresis ◽  
Analysis Techniques ◽  
Bacterial Cultures ◽  
Dimensional Electrophoresis ◽  
Image Analysis Techniques

Abstract We describe a system, both hardware and software, that provides quantitative analysis and data reduction of two-dimensional electrophoresis gels. Image-analysis techniques are used to determine spot intensities and to match spot patterns among many gels. A pattern-recognition program is used to extract the useful information contained in the spot lists. The application of this technology to a study of supernates from bacterial cultures is described.

scholarly journals C1 ROBUSTLY MINIMAL ITERATED FUNCTION SYSTEMS

2010 ◽  
Vol 10 (01) ◽  
pp. 155-160 ◽  
Author(s):  
F. H. GHANE ◽  
A. J. HOMBURG ◽  
A. SARIZADEH
Keyword(s):  
Iterated Function Systems ◽  
Compact Manifolds ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Iterated Function

We construct iterated function systems on compact manifolds that are C1 robustly minimal. On the m-dimensional torus and on two-dimensional compact manifolds, examples are provided of C1 robustly minimal iterated function systems that are generated by just two diffeomorphisms.

scholarly journals Partitioned iterated function systems with division and a fractal dependence graph in recognition of 2D shapes

2011 ◽  
Vol 21 (4) ◽  
pp. 757-767 ◽  
Author(s):  
Krzysztof Gdawiec ◽  
Diana Domańska
Keyword(s):  
Pattern Recognition ◽  
Iterated Function System ◽  
Global Analysis ◽  
Recognition Rate ◽  
Iterated Function Systems ◽  
Dependence Graph ◽  
Local Analysis ◽  
Self Similarity ◽  
Pattern Recognition Methods ◽  
Iterated Function

Partitioned iterated function systems with division and a fractal dependence graph in recognition of 2D shapesOne of the approaches in pattern recognition is the use of fractal geometry. The property of self-similarity of fractals has been used as a feature in several pattern recognition methods. All fractal recognition methods use global analysis of the shape. In this paper we present some drawbacks of these methods and propose fractal local analysis using partitioned iterated function systems with division. Moreover, we introduce a new fractal recognition method based on a dependence graph obtained from the partitioned iterated function system. The proposed method uses local analysis of the shape, which improves the recognition rate. The effectiveness of our method is shown on two test databases. The first one was created by the authors and the second one is the MPEG7 CE-Shape-1 PartB database. The obtained results show that the proposed methodology has led to a significant improvement in the recognition rate.

ON A CLASS OF FRACTAL MATRICES III: LIMIT STRUCTURES AND HIERARCHICAL ITERATED FUNCTION SYSTEMS

1995 ◽  
Vol 05 (04) ◽  
pp. 1119-1156 ◽  
Author(s):  
ANDRÉ M. BARBÉ
Keyword(s):  
Fractal Dimension ◽  
Quantitative Analysis ◽  
Iterated Function System ◽  
Iterated Function Systems ◽  
Point Of View ◽  
Dimension Function ◽  
Space Filling ◽  
Iterated Function ◽  
Present Part ◽  
Standard Limit

Fractrices (fractal matrices, excess-matrices) were defined in an earlier paper, Part I, as a special class of integer matrices with multifractal features. In contrast with Part II where a quantitative analysis of these objects was performed from a finitist constructivist point of view, the present Part III discusses the corresponding genuine limit fractal version. First this is done by a standard limit analysis which eventually leads to a (nonstandard) hyperreal-number view on this limit. Then a related hierarchical iterated function system is constructed whose attractor is the very same limit. This limit is either a hierarchical Zeno or Cantor set, or a space filling set. Its fractal dimension function is investigated.

scholarly journals THE AESTHETICS AND FRACTAL DIMENSION OF ELECTRIC SHEEP

2008 ◽  
Vol 18 (04) ◽  
pp. 1243-1248 ◽  
Author(s):  
SCOTT DRAVES ◽  
RALPH ABRAHAM ◽  
PABLO VIOTTI ◽  
FREDERICK DAVID ABRAHAM ◽  
JULIAN CLINTON SPROTT
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Iterated Function Systems ◽  
Two Dimensional ◽  
Computer Scientist ◽  
Large Community ◽  
Iterated Function ◽  
Fractal Images ◽  
The Relationship ◽  
Aesthetic Judgments

Physicist Clint Sprott demonstrated a relationship between aesthetic judgments of fractal images and their fractal dimensions [1993]. Scott Draves, aka Spot, a computer scientist and artist, has created a space of images called fractal flames, based on attractors of two-dimensional iterated function systems. A large community of users run software that automatically downloads animated fractal flames, known as "sheep", and displays them as their screen-saver. The users may vote electronically for the sheep they like while the screen-saver is running. In this report we proceed from Sprott to Spot. The data show an inverted U-shaped curve in the relationship between aesthetic judgments of flames and their fractal dimension, confirming and clarifying earlier reports.

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