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Fractal Image Coding as Projections Onto Convex Sets [chapter]

Mehran Ebrahimi, Edward R. Vrscay
2006 Lecture Notes in Computer Science  
We show how fractal image coding can be viewed and generalized in terms of the method of projections onto convex sets (POCS).  ...  In this approach, the fractal code defines a set of spatial domain similarity constraints.  ...  Introduction In this paper we show how fractal image coding can be formulated in terms of a powerful method known as projections onto convex sets (POCS) [15] .  ... 
doi:10.1007/11867586_46 fatcat:ojnp7p7zunbtdflzzg4opemds4

Regularized Fractal Image Decoding

Mehran Ebrahimi, Edward Vrscay
2006 2006 Canadian Conference on Electrical and Computer Engineering  
We apply our technique to the under-determined missing fractal code problem as verification to the theory presented.  ...  The goal of this paper is to present a new recipe for the fractal image decoding process.  ...  image coding using projections onto convex sets [5] .  ... 
doi:10.1109/ccece.2006.277593 dblp:conf/ccece/EbrahimiV06 fatcat:xipettl7mzd7xh2bqodql4k3aq

Continuous Evolution of Fractal Transforms and Nonlocal PDE Imaging [chapter]

Edward R. Vrscay
2006 Lecture Notes in Computer Science  
Traditional fractal image coding seeks to approximate an image function u as a union of spatially-contracted and greyscale-modified copies of itself, i.e., u ≈ T u, where T is a contractive fractal transform  ...  As a result, the asymptotic limiting function y∞ is a modification of the fixed pointū of the original fractal transform.  ...  Indeed, this formulation is quite analogous to the method of projections onto convex sets (POCS) [18] .  ... 
doi:10.1007/11867586_42 fatcat:o5y54jk7xvdr5anwx6he6czdvq

Set theoretic compression with an application to image coding

N.T. Thao, M. Vetterli
1998 IEEE Transactions on Image Processing  
As an initial validation, we show the results of an experiment where these tools are used to modify the encoding process of block discrete cosine transform (DCT) coding in order to yield less blocking  ...  From this starting point, we develop a set of tools to design a new class of encoders for image compression, based on a set decomposition and recombination of image features.  ...  In the cross-product As a consequence of this definition, the projections onto typical convex sets can be easily derived and their expressions are given in Table I .  ... 
doi:10.1109/83.701165 pmid:18276320 fatcat:25jf24b4dzeyjekplqws7qon5e

Collective sensing: a fixed-point approach in the metric space

Xin Li, Pascal Frossard, Houqiang Li, Feng Wu, Bernd Girod, Shipeng Li, Guo Wei
2010 Visual Communications and Image Processing 2010  
Inspired by the works on fractal image decoding and nonlocal image processing, we propose to view an image as the fixed-point of some nonexpansive mapping in the metric space in this paper.  ...  The potential of this new paradigm, which we call "collective sensing", is demonstrated on the lossy compression application where significant gain over current state-of-the-art (SPIHT) coding scheme has  ...  of contractive transformations in fractal coding).  ... 
doi:10.1117/12.862516 dblp:conf/vcip/Li10 fatcat:xx2hx3snwbbejp6nvfm5q2cir4

Fractal Properties of Magic State Distillation [article]

Patrick Rall
2017 arXiv   pre-print
By studying these fractals we demonstrate that some protocols are more effective when not restricted.  ...  We show that if we lift this one-parameter restriction and embrace the complexity, distillation exhibits fractal properties.  ...  The input magic states are then projected onto the |0 state and the possibly faulty | Ā ⊗k state is projected onto the code space and decoded to yield a k qubit output state ρ . See [9].  ... 
arXiv:1708.09256v1 fatcat:7tvllr4zubeajdpkujt457hrem

The visible part of plane self-similar sets

Kenneth J. Falconer, Jonathan M. Fraser
2010 arXiv   pre-print
We confirm this when F is a self-similar set satisfying the convex open set condition and such that the orthogonal projection of F onto every line is an interval.  ...  Given a compact subset F of R^2, the visible part V_θ F of F from direction θ is the set of x in F such that the half-line from x in direction θ intersects F only at x.  ...  Examples A large range of self-similar sets satisfy the convex open set condition and project onto intervals in all directions and so satisfy the conditions of Theorem 2.1.  ... 
arXiv:1004.5067v1 fatcat:b26i7nizlfcm7p6uhgz6uf2cna

Adaptive post-processing for fractal image compression

Nguyen Ky Giang, D. Saupe
2000 Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101)  
Like all block based techniques, fractal coding suffers from blocking artifacts, in particular at high compression ratios.  ...  Fractal image compression is a block based technique. The blocks of the underlying image partition are called range blocks.  ...  ., projection onto convex sets (POCS) [10] , constrained least squares (CLS) [11] , require a prior distortion model and thus cannot be straightforwardly adapted to fractal compression.  ... 
doi:10.1109/icip.2000.899258 dblp:conf/icip/NguyenS00 fatcat:lda2wlxalzbrrlp34rh3zwzzra

Page 8428 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
Shaw, Restoration of 3D real images using projection onto convex sets (127-144); M. Razaz and R. A. Lee [Richard .  ...  Barnsley, Fractal image compression (183-210); Dietmar Saupe and Raouf Hamzaoui, Complexity reduction methods for fractal image com- pression (211-229); S. G. Hoggar and L.  ... 

The visible part of plane self-similar sets

Kenneth J. Falconer, Jonathan M. Fraser
2012 Proceedings of the American Mathematical Society  
We confirm this when F is a self-similar set satisfying the convex open set condition and such that the orthogonal projection of F onto every line is an interval.  ...  Examples A large range of self-similar sets satisfy the convex open set condition and project onto intervals in all directions and so satisfy the conditions of Theorem 2.1.  ...  Thus the generator codes a family of similarity transformations {S i } that map the ends of K onto its component line segments.  ... 
doi:10.1090/s0002-9939-2012-11312-7 fatcat:kktxxtfsxnfixp5occdu5guifa

VISUALIZATION OF HYPERFRACTALS

JAN ANDRES, MIROSLAV RYPKA
2013 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
More precisely, address sets of hyperfractals, i.e. fractals living in hyperspaces, will be visualized in this way.  ...  The projections of the related attractor onto X and Σ are the attractor A * of the original IMS {(X, d), F 1 , F 2 , . . . , F n } and Σ, respectively. Example 4.  ...  Now, let us realize how support functions of images of convex sets for similitudes look like.  ... 
doi:10.1142/s0218127413501678 fatcat:gguv3ppav5drzhrg3qjlkzfnoi

Application of the POCS inversion method to cross‐borehole imaging

Ingi Th. Bjarnason, William Menke
1993 Geophysics  
The projection onto convex sets (POCS) algorithm can impose physically plausible constraints that allow high quality tomographic images to be produced.  ...  Each constraint is viewed as defining a set (in function space) of images that satisfy that particular constraint.  ...  The image is projected onto this set simply by setting the prescribed pixels to zero.  ... 
doi:10.1190/1.1443485 fatcat:krp4p24wgjawtial5fzxnfgara

Application of the POCS inversion method to cross-borehole imaging

1994 International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts  
The projection onto convex sets (POCS) algorithm can impose physically plausible constraints that allow high quality tomographic images to be produced.  ...  Each constraint is viewed as defining a set (in function space) of images that satisfy that particular constraint.  ...  The image is projected onto this set simply by setting the prescribed pixels to zero.  ... 
doi:10.1016/0148-9062(94)93035-x fatcat:eyr5vtlbivgntc5r7v7ew4vui4

Entropy-Functional-Based Online Adaptive Decision Fusion Framework With Application to Wildfire Detection in Video

O. Gunay, B. U. Toreyin, K. Kose, A. E. Cetin
2012 IEEE Transactions on Image Processing  
Index Terms-Projections onto convex sets, active learning, decision fusion, online learning, entropy maximization, wildfire detection using video.  ...  Decision values are linearly combined with weights which are updated online according to an active fusion method based on performing entropic projections onto convex sets describing sub-algorithms.  ...  According to the projection onto convex sets (POCS) theory, when there are a finite number of convex sets, repeated cyclical projections onto these sets converge to a vector in the intersection set [14  ... 
doi:10.1109/tip.2012.2183141 pmid:22249709 fatcat:2apizyvqbjeahkzchxivoxml24

Image analysis for digital media applications

Hong Yan
2001 IEEE Computer Graphics and Applications  
Many research staff and postgraduate students of the Image Processing Lab at the University of Sydney and the Signal Processing Lab at the City University of Hong Kong have worked on these projects and  ...  provided the images presented in this article.  ...  Maximum entropy 2 and projection onto convex sets (POCS) 3,15 are two effective algorithms for solving restoration problems.  ... 
doi:10.1109/38.895126 fatcat:pfhnkx3zyrhtpmpwchb7dhg4ym
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