scholarly journals An investigation of machine learning method based on fractal compression

2019 ◽  
pp. 204-208
Author(s):  
E Y Minaev
Keyword(s):  
Machine Learning ◽  
Autonomous Robots ◽  
Main Idea ◽  
Iterated Function Systems ◽  
Mobile Platforms ◽  
Fractal Coding ◽  
Fractal Compression ◽  
Iterated Function ◽  
Fractal Images ◽  
Domain Block

In this article the method of machine learning with cyclic fractal coding and the use of domain block dictionary, adapted for use on mobile platforms, with optimization of performance and volume of stored fractal images is investigated. The main idea of the method is to use the fractal compression method based on iterated function systems to reduce the dimension of the original images, and to use cyclic fractal coding to represent the class of images. As a result of research of the method it was found that the share of correctly recognized objects on MSTAR averages 0.892, the recognition time averages 254 ms. The achieved results are acceptable for use in mobile platforms, including UAVs and ground autonomous robots.

SHRINKING TARGET PROBLEM FOR RANDOM IFS

Fractals ◽  
2018 ◽  
Vol 26 (06) ◽  
pp. 1850085
Author(s):  
ZHIHUI YUAN
Keyword(s):  
Lower Bound ◽  
Hausdorff Dimension ◽  
Main Idea ◽  
Iterated Function Systems ◽  
Target Problem ◽  
Iterated Function ◽  
Poincare Recurrence ◽  
Poincaré Recurrence

We describe the shrinking target problem for random iterated function systems which are semi-conjugate to random subshifts. We get the Hausdorff dimension of the set based on shrinking target problems with given targets. The main idea is an extension of ubiquity theorem which plays an important role to get the lower bound of the dimension. Our method can be used to deal with the sets with respect to more general targets and the sets based on the quantitative Poincaré recurrence properties.

scholarly journals BASED ON RANGE AND DOMAIN FRACTAL IMAGE COMPRESSION OF SATELLITE IMAGERIES IMPROVED ALGORITHM FOR RESEARCH

2014 ◽  
pp. 71-74
Author(s):  
SAEMA ENJELA ◽  
A.G. ANANTH
Keyword(s):  
Image Compression ◽  
Image Coding ◽  
Fractal Image Compression ◽  
Compression Technique ◽  
Fractal Coding ◽  
Fractal Compression ◽  
Urban Image ◽  
Fractal Image ◽  
Domain Block ◽  
Improved Algorithm

Fractal coding is a novel method to compress images, which was proposed by Barnsley, and implemented by Jacquin. It offers many advantages. Fractal image coding has the advantage of higher compression ratio, but is a lossy compression scheme. The encoding procedure consists of dividing the image into range blocks and domain blocks and then it takes a range block and matches it with the domain block. The image is encoded by partitioning the domain block and using affine transformation to achieve fractal compression. The image is reconstructed using iterative functions and inverse transforms. However, the encoding time of traditional fractal compression technique is too long to achieve real-time image compression, so it cannot be widely used. Based on the theory of fractal image compression; this paper raised an improved algorithm form the aspect of image segmentation. In the present work the fractal coding techniques are applied for the compression of satellite imageries. The Peak Signal to Noise Ratio (PSNR) values are determined for images namely Satellite Rural image and Satellite Urban image. The Matlab simulation results for the reconstructed image shows that PSNR values achievable for Satellite Rural image ~33 and for Satellite urban image ~42.

FAMILY OF SHAPE PRESERVING FRACTAL-LIKE BÉZIER CURVES

Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050105
Author(s):  
K. M. REDDY ◽  
G. SARAVANA KUMAR ◽  
A. K. B. CHAND
Keyword(s):  
Convex Hull ◽  
Iterated Function Systems ◽  
Shape Preserving ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Curves And Surfaces ◽  
Iterated Function ◽  
Curvature Continuity ◽  
Fractal Images ◽  
Self Similar

Subdivision schemes generate self-similar curves and surfaces for which it has a familiar connection between fractal curves and surfaces generated by iterated function systems (IFS). Overveld [Comput.-Aided Des. 22(9) (1990) 591–597] proved that the subdivision matrices can be perturbated in such a way that it is possible to get fractal-like curves that are perturbated Bézier cubic curves. In this work, we extend the Overveld scheme to [Formula: see text]th degree curves, and deduce the condition for curvature continuity and convex hull property. We find the conditions for positive preserving fractal-like Bézier curves in the proposed subdivision matrices. The resulting 2D/3D curves from these binary subdivision matrices resemble with fractal images. Finally, the dependence of the shape of these fractal-like curves on the elements of subdivision matrices is demonstrated with suitably chosen examples.

Face Detection Based on the Theory of Fractal Compression

2014 ◽  
Vol 945-949 ◽  
pp. 1825-1829
Author(s):  
Qing Sen An ◽  
Yue Bin Chen ◽  
Jing Fan ◽  
Jin Long Wang
Keyword(s):  
Image Compression ◽  
Face Detection ◽  
Iterated Function Systems ◽  
Fractal Image Compression ◽  
Fractal Compression ◽  
Fractal Image ◽  
Iterated Function ◽  
The Face ◽  
Face Similarity

The face detection has been a very important issue, the use of local and global face similarity between faces can be detected. In this paper, based on fractal image compression theory, we construct a local iterated function systems as a description of the face to detect the face.

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.

scholarly journals Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line

2020 ◽  
pp. 1-31
Author(s):  
Balázs Bárány ◽  
Károly Simon ◽  
István Kolossváry ◽  
Michał Rams
Keyword(s):  
Hausdorff Measure ◽  
Similar Case ◽  
Iterated Function Systems ◽  
The Self ◽  
Dimensional Hausdorff Measure ◽  
Assouad Dimension ◽  
Iterated Function ◽  
Self Similar ◽  
Weak Separation ◽  
Topological Sense

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Hausdorff dimension less than 1 then it has zero appropriate dimensional Hausdorff measure and its Assouad dimension is equal to 1. Our main contribution is in showing that if the cylinders intersect then the IFS generically does not satisfy the weak separation property and hence, we may apply a recent result of Angelevska, Käenmäki and Troscheit. This phenomenon holds for transversal families (in particular for the translation family) typically, in the self-similar case, in both topological and in measure theoretical sense, and in the more general self-conformal case in the topological sense.

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