This document describes a new method for compressing digital images using fractals. The key points are:
1) Traditional image compression methods can achieve ratios of 2-10x but a new method using fractals has achieved ratios over 10,000x.
2) The method works by breaking an image into segments that are then matched to fractal patterns in a library. Only the codes for the fractal patterns need to be stored, not the full image data.
3) An iterated function system (IFS) uses affine transformations to relate parts of an image. The IFS codes in the library can be used to reconstruct the original image segments. This achieves very high compression ratios.
Image Restoration UsingNonlocally Centralized Sparse Representation and histo...IJERA Editor
Due to the degradation of observed image the noisy, blurred, distorted image can be occurred .To restore the image informationby conventional modelsmay not be accurate enough for faithful reconstruction of the original image. I propose the sparse representations to improve the performance of based image restoration. In this method the sparse coding noise is added for image restoration, due to this image restoration the sparse coefficients of original image can be detected. The so-called nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model, fordenoising the image here we use the histogram clipping method by using histogram based sparse representation to effectively reduce the noise and also implement the TMR filter for Quality image. Various types of image restoration problems, including denoising, deblurring and super-resolution, validate the generality and state-of-the-art performance of the proposed algorithm.
The document describes Threp, a lightweight remapping framework for use in Earth system models. Threp aims to provide a flexible, readable, and efficient framework for remapping data between different grid types, including regular, rectilinear, curvilinear, and unstructured grids. It supports operations like interpolation, masking, and extrapolation between source and destination grids. Threp uses a two-stage process of first generating interpolation weights and then applying those weights to remap data values. It is designed for parallel computation and to be easily extensible to support new interpolation methods and grid types.
Image Restoration and Denoising By Using Nonlocally Centralized Sparse Repres...IJERA Editor
Due to the degradation of observed image the noisy, blurred, Distorted image can be occurred .for restoring image information we propose the sparse representations by conventional modelsmay not be accurate enough for a faithful reconstruction of the original image. To improve the performance of sparse representation-based image restoration,In this method the sparse coding noise is added for image restoration, due to this image restoration the sparse coefficients of original image can be detected. The so-called nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model,for denoising the image here we use the Histogram clipping method by using histogram based sparse representation effectively reduce the noise.and also implement the TMR filter for Quality image.various types of image restoration problems, including denoising, deblurring and super-resolution, validate the generality and state-of-the-art performance of the proposed algorithm.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
CS 354 Shadows (cont'd) and Scene GraphsMark Kilgard
This document summarizes the topics to be covered in a CS 354 class on March 22, 2012. It includes an in-class quiz on shadow algorithms, continuing the discussion of shadow generation algorithms and an introduction to scene graphs. It also provides updates on course status including returning mid-term exams and feedback. The professor's office hours are listed. The lecture will finish the discussion of shadow algorithms and cover scene graphs, which are data structures used to organize rendering of 3D scenes.
The document summarizes a study on fractal image compression of satellite images using range and domain techniques. It discusses fractal image compression methods, including partitioning images into range and domain blocks. Affine transformations are applied to domain blocks to match range blocks. Peak signal-to-noise ratio (PSNR) values are calculated for reconstructed rural and urban satellite images after 4 iterations, showing PSNR of around 17.0 for rural images and 22.0 for urban images. The proposed algorithm partitions the original image into non-overlapping range blocks and selects domain blocks twice the size of range blocks.
This document summarizes a class on interaction and computer graphics. It discusses an in-class quiz, the requirements for Project 2 on programmable shaders, and interaction techniques like back projection for picking objects. New interaction paradigms like multi-touch are presented, along with future directions involving visual, tactile, gesture, speech and emotionally aware interfaces. Students are reminded that the first part of Project 2 is due on April 2nd.
Image Restoration UsingNonlocally Centralized Sparse Representation and histo...IJERA Editor
Due to the degradation of observed image the noisy, blurred, distorted image can be occurred .To restore the image informationby conventional modelsmay not be accurate enough for faithful reconstruction of the original image. I propose the sparse representations to improve the performance of based image restoration. In this method the sparse coding noise is added for image restoration, due to this image restoration the sparse coefficients of original image can be detected. The so-called nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model, fordenoising the image here we use the histogram clipping method by using histogram based sparse representation to effectively reduce the noise and also implement the TMR filter for Quality image. Various types of image restoration problems, including denoising, deblurring and super-resolution, validate the generality and state-of-the-art performance of the proposed algorithm.
The document describes Threp, a lightweight remapping framework for use in Earth system models. Threp aims to provide a flexible, readable, and efficient framework for remapping data between different grid types, including regular, rectilinear, curvilinear, and unstructured grids. It supports operations like interpolation, masking, and extrapolation between source and destination grids. Threp uses a two-stage process of first generating interpolation weights and then applying those weights to remap data values. It is designed for parallel computation and to be easily extensible to support new interpolation methods and grid types.
Image Restoration and Denoising By Using Nonlocally Centralized Sparse Repres...IJERA Editor
Due to the degradation of observed image the noisy, blurred, Distorted image can be occurred .for restoring image information we propose the sparse representations by conventional modelsmay not be accurate enough for a faithful reconstruction of the original image. To improve the performance of sparse representation-based image restoration,In this method the sparse coding noise is added for image restoration, due to this image restoration the sparse coefficients of original image can be detected. The so-called nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model,for denoising the image here we use the Histogram clipping method by using histogram based sparse representation effectively reduce the noise.and also implement the TMR filter for Quality image.various types of image restoration problems, including denoising, deblurring and super-resolution, validate the generality and state-of-the-art performance of the proposed algorithm.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
CS 354 Shadows (cont'd) and Scene GraphsMark Kilgard
This document summarizes the topics to be covered in a CS 354 class on March 22, 2012. It includes an in-class quiz on shadow algorithms, continuing the discussion of shadow generation algorithms and an introduction to scene graphs. It also provides updates on course status including returning mid-term exams and feedback. The professor's office hours are listed. The lecture will finish the discussion of shadow algorithms and cover scene graphs, which are data structures used to organize rendering of 3D scenes.
The document summarizes a study on fractal image compression of satellite images using range and domain techniques. It discusses fractal image compression methods, including partitioning images into range and domain blocks. Affine transformations are applied to domain blocks to match range blocks. Peak signal-to-noise ratio (PSNR) values are calculated for reconstructed rural and urban satellite images after 4 iterations, showing PSNR of around 17.0 for rural images and 22.0 for urban images. The proposed algorithm partitions the original image into non-overlapping range blocks and selects domain blocks twice the size of range blocks.
This document summarizes a class on interaction and computer graphics. It discusses an in-class quiz, the requirements for Project 2 on programmable shaders, and interaction techniques like back projection for picking objects. New interaction paradigms like multi-touch are presented, along with future directions involving visual, tactile, gesture, speech and emotionally aware interfaces. Students are reminded that the first part of Project 2 is due on April 2nd.
This document discusses parallelizing object detection in videos for many-core systems. It presents an object detection algorithm that includes frame differencing, background differencing, post-processing, and background updating. The algorithm is parallelized by vertically partitioning video frames across cores, with some pixel overlap between partitions to reduce communication overhead. The parallel implementation achieves a speedup of 37.2x on a 64-core Tilera system processing 18 full-HD frames per second. A performance prediction equation is also developed and shown to accurately model the real performance results.
This document discusses shadow algorithms for real-time 3D graphics. It begins with an introduction to shadow mapping, a commonly used technique for generating shadows. It describes how shadow mapping works by rendering a depth map from the light's perspective and then using that depth map to determine shadowing when rendering from the camera's perspective. The document then covers specific shadow mapping algorithms and techniques used to improve realism and performance for interactive applications.
Image Restitution Using Non-Locally Centralized Sparse Representation ModelIJERA Editor
Sparse representation models uses a linear combination of a few atoms selected from an over-completed
dictionary to code an image patch which have given good results in different image restitution applications. The
reconstruction of the original image is not so accurate using traditional models of sparse representation to solve
degradation problems which are blurring, noisy, and down-sampled. The goal of image restitution is to suppress
the sparse coding noise and to improve the image quality by using the concept of sparse representation. To
obtain a good sparse coding coefficients of the original image we exploit the image non-local self similarity and
then by centralizing the sparse coding coefficients of the observation image to those estimates. This non-locally
centralized sparse representation model outperforms standard sparse representation models in all aspects of
image restitution problems including de-noising, de-blurring, and super-resolution.
Super Resolution in Digital Image processingRamrao Desai
Super-resolution aims to enhance image resolution by exploiting multiple low-resolution images. Key techniques include Bayesian methods using priors, Wiener filtering, Markov random fields, and learned models from example images. Super-resolution involves modeling blurring, sampling, and aliasing effects, and using techniques like deconvolution and example-based learning to recover high-frequency details beyond the Nyquist limit. It requires accurate motion estimation and modeling of the imaging process to combine information from multiple low-resolution images.
The document reports on the results of three image processing projects. The first project implemented Lloyd-Max quantization to reduce image file sizes and Retinex theory to compensate for uneven illumination. The second project used principal component analysis to compute eigenfaces for face recognition. The third project performed linear discriminant analysis and tensor-based linear discriminant analysis for binary classification and visual object recognition. Illumination compensation subtracted an estimated illumination plane from image intensities to reduce shadows. Eigenfaces were the principal components of a training set of face images. Tensor-based linear discriminant analysis treated images as higher-order tensors to outperform conventional LDA.
This document summarizes a lecture on digital typography in CS 354. It discusses how fonts are now defined mathematically using cubic Bezier curves rather than metal type. It reviews cubic Bezier curves and how continuity is achieved between curve segments. It describes the PostScript and TrueType font formats and their use of cubic and quadratic Bezier curves. The lecture contrasts modern digital typography approaches with earlier systems like Metal type and Metafont. It shows examples of serif and sans serif typefaces and discusses typographic terminology.
This document discusses image compression using the discrete cosine transform (DCT). It develops simple Mathematica functions to compute the 1D and 2D DCT. The 1D DCT transforms a list of real numbers into elementary frequency components. It is computed via matrix multiplication or using the discrete Fourier transform with twiddle factors. The 2D DCT applies the 1D DCT to rows and then columns, making it separable. These functions illustrate how Mathematica can be used to prototype image processing algorithms.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document proposes a novel image encryption technique based on multiple fuzzy graph mappings. It begins by introducing fuzzy graphs and fuzzy membership functions. It then describes how to generate multiple fuzzy graphs from a single matrix using different membership functions and parameter values. These fuzzy graphs are then mapped onto an image to encrypt it. The encryption process has three main steps: 1) pixel shuffling, 2) fuzzy graph mappings, and 3) image encryption based on the multiple fuzzy graph mappings. Experimental results demonstrate that the proposed technique is efficient and provides robust encryption.
This document discusses join-reachability problems in directed graphs. It begins by introducing graph reachability queries and the goal of efficiently answering such queries with a data structure. It then defines join-reachability queries over a collection of graphs and motivates applications involving join-reachability. The document outlines techniques for preprocessing graphs like layer decomposition and cycle removal to simplify join-reachability problems. It also discusses computing the join-reachability graph and bounds on its size. The focus is on constructing efficient data structures to answer join-reachability queries.
A Physical Approach to Moving Cast Shadow Detection (ICASSP 2009)Jia-Bin Huang
This document presents a physics-based approach for detecting moving cast shadows in video sequences. It develops a new physical model to characterize the variation in background appearance caused by cast shadows, without making assumptions about the spectral power distributions of light sources and ambient illumination. It uses a Gaussian mixture model to learn and update the shadow model parameters over time in an unsupervised manner. Experimental results on three challenging sequences demonstrate the effectiveness of the proposed method.
This document provides a summary of key concepts in digital image processing from two course units. It includes definitions of common terms like image, pixel, and color models. It also describes important techniques in image enhancement like spatial and frequency domain filtering. Key steps in digital image processing systems and transformations are outlined.
This document discusses parallel processing and compound image compression techniques. It examines the computational complexity and quantitative optimization of various image compression algorithms like BTC, DCT, DWT, DTCWT, SPIHT and EZW. The performance is evaluated in terms of coding efficiency, memory usage, image quality and quantity. Block Truncation Coding and Discrete Cosine Transform compression methods are described in more detail.
This document discusses data compression techniques including lossless compression methods like run-length encoding and statistical compression, as well as lossy compression methods like JPEG and MPEG. It also covers recent developments in data compression technology and the use of neural networks for image compression.
State-of-the-art Clustering Techniques: Support Vector Methods and Minimum Br...Vincenzo Russo
This document summarizes two state-of-the-art clustering techniques: Support Vector Clustering (SVC) and Bregman Co-clustering. SVC involves a two-phase process: 1) determining boundaries of clusters using a minimum enclosing ball approach, and 2) assigning cluster labels by finding connected components in a graph. Bregman Co-clustering aims to robustly handle missing or sparse data, high dimensionality, noise and outliers. The document discusses applications and desirable properties of these clustering methods, such as nonlinear separability and automatic detection of the number of clusters.
UMAP is a technique for dimensionality reduction that was proposed 2 years ago that quickly gained widespread usage for dimensionality reduction.
In this presentation I will try to demistyfy UMAP by comparing it to tSNE. I also sketch its theoretical background in topology and fuzzy sets.
A Diffusion Wavelet Approach For 3 D Model Matchingrafi
The document presents a novel diffusion wavelet approach for 3D model matching. It combines diffusion maps with wavelets to extract multi-scale shape features from 3D models. Fisher's discriminant ratio is used to select discriminative wavelet coefficients for model representation. Models are retrieved by comparing their representation vectors at different wavelet scales. Results show the diffusion wavelet approach outperforms spherical harmonics and wavelets for 3D model retrieval.
Adaptive Neuro-Fuzzy Inference System based Fractal Image CompressionIDES Editor
This paper presents an Adaptive Neuro-Fuzzy
Inference System (ANFIS) model for fractal image
compression. One of the image compression techniques in
the spatial domain is Fractal Image Compression (FIC)
but the main drawback of FIC using traditional
exhaustive search is that it involves more computational
time due to global search. In order to improve the
computational time and compression ratio, artificial
intelligence technique like ANFIS has been used. Feature
extraction reduces the dimensionality of the problem and
enables the ANFIS network to be trained on an image
separate from the test image thus reducing the
computational time. Lowering the dimensionality of the
problem reduces the computations required during the
search. The main advantage of ANFIS network is that it
can adapt itself from the training data and produce a
fuzzy inference system. The network adapts itself
according to the distribution of feature space observed
during training. Computer simulations reveal that the
network has been properly trained and the fuzzy system
thus evolved, classifies the domains correctly with
minimum deviation which helps in encoding the image
using FIC.
DOMAIN SPECIFIC CBIR FOR HIGHLY TEXTURED IMAGEScseij
It is A Challenging Task To Build A Cbir System Which Primarily Works On Texture Values As There
Meaning And Semantics Needs A Special Care To Be Mapped With Human Based Languages. We Have
Consider Highly Textured Images Having Properties(Entropy, Homogeneity, Contrast, Cluster Shade, Auto
Correlation)And Have Mapped Using A Fuzzy Minmax Scale W.R.T. Their Degree(High, Low,
Medium)And Technical Interpetation.This Developed System Is Performing Well In Terms Of Precision
And Recall Value Showing That Semantic Gap Has Been Reduced For Highly Textured Images Based Cbir.
This document discusses parallelizing object detection in videos for many-core systems. It presents an object detection algorithm that includes frame differencing, background differencing, post-processing, and background updating. The algorithm is parallelized by vertically partitioning video frames across cores, with some pixel overlap between partitions to reduce communication overhead. The parallel implementation achieves a speedup of 37.2x on a 64-core Tilera system processing 18 full-HD frames per second. A performance prediction equation is also developed and shown to accurately model the real performance results.
This document discusses shadow algorithms for real-time 3D graphics. It begins with an introduction to shadow mapping, a commonly used technique for generating shadows. It describes how shadow mapping works by rendering a depth map from the light's perspective and then using that depth map to determine shadowing when rendering from the camera's perspective. The document then covers specific shadow mapping algorithms and techniques used to improve realism and performance for interactive applications.
Image Restitution Using Non-Locally Centralized Sparse Representation ModelIJERA Editor
Sparse representation models uses a linear combination of a few atoms selected from an over-completed
dictionary to code an image patch which have given good results in different image restitution applications. The
reconstruction of the original image is not so accurate using traditional models of sparse representation to solve
degradation problems which are blurring, noisy, and down-sampled. The goal of image restitution is to suppress
the sparse coding noise and to improve the image quality by using the concept of sparse representation. To
obtain a good sparse coding coefficients of the original image we exploit the image non-local self similarity and
then by centralizing the sparse coding coefficients of the observation image to those estimates. This non-locally
centralized sparse representation model outperforms standard sparse representation models in all aspects of
image restitution problems including de-noising, de-blurring, and super-resolution.
Super Resolution in Digital Image processingRamrao Desai
Super-resolution aims to enhance image resolution by exploiting multiple low-resolution images. Key techniques include Bayesian methods using priors, Wiener filtering, Markov random fields, and learned models from example images. Super-resolution involves modeling blurring, sampling, and aliasing effects, and using techniques like deconvolution and example-based learning to recover high-frequency details beyond the Nyquist limit. It requires accurate motion estimation and modeling of the imaging process to combine information from multiple low-resolution images.
The document reports on the results of three image processing projects. The first project implemented Lloyd-Max quantization to reduce image file sizes and Retinex theory to compensate for uneven illumination. The second project used principal component analysis to compute eigenfaces for face recognition. The third project performed linear discriminant analysis and tensor-based linear discriminant analysis for binary classification and visual object recognition. Illumination compensation subtracted an estimated illumination plane from image intensities to reduce shadows. Eigenfaces were the principal components of a training set of face images. Tensor-based linear discriminant analysis treated images as higher-order tensors to outperform conventional LDA.
This document summarizes a lecture on digital typography in CS 354. It discusses how fonts are now defined mathematically using cubic Bezier curves rather than metal type. It reviews cubic Bezier curves and how continuity is achieved between curve segments. It describes the PostScript and TrueType font formats and their use of cubic and quadratic Bezier curves. The lecture contrasts modern digital typography approaches with earlier systems like Metal type and Metafont. It shows examples of serif and sans serif typefaces and discusses typographic terminology.
This document discusses image compression using the discrete cosine transform (DCT). It develops simple Mathematica functions to compute the 1D and 2D DCT. The 1D DCT transforms a list of real numbers into elementary frequency components. It is computed via matrix multiplication or using the discrete Fourier transform with twiddle factors. The 2D DCT applies the 1D DCT to rows and then columns, making it separable. These functions illustrate how Mathematica can be used to prototype image processing algorithms.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document proposes a novel image encryption technique based on multiple fuzzy graph mappings. It begins by introducing fuzzy graphs and fuzzy membership functions. It then describes how to generate multiple fuzzy graphs from a single matrix using different membership functions and parameter values. These fuzzy graphs are then mapped onto an image to encrypt it. The encryption process has three main steps: 1) pixel shuffling, 2) fuzzy graph mappings, and 3) image encryption based on the multiple fuzzy graph mappings. Experimental results demonstrate that the proposed technique is efficient and provides robust encryption.
This document discusses join-reachability problems in directed graphs. It begins by introducing graph reachability queries and the goal of efficiently answering such queries with a data structure. It then defines join-reachability queries over a collection of graphs and motivates applications involving join-reachability. The document outlines techniques for preprocessing graphs like layer decomposition and cycle removal to simplify join-reachability problems. It also discusses computing the join-reachability graph and bounds on its size. The focus is on constructing efficient data structures to answer join-reachability queries.
A Physical Approach to Moving Cast Shadow Detection (ICASSP 2009)Jia-Bin Huang
This document presents a physics-based approach for detecting moving cast shadows in video sequences. It develops a new physical model to characterize the variation in background appearance caused by cast shadows, without making assumptions about the spectral power distributions of light sources and ambient illumination. It uses a Gaussian mixture model to learn and update the shadow model parameters over time in an unsupervised manner. Experimental results on three challenging sequences demonstrate the effectiveness of the proposed method.
This document provides a summary of key concepts in digital image processing from two course units. It includes definitions of common terms like image, pixel, and color models. It also describes important techniques in image enhancement like spatial and frequency domain filtering. Key steps in digital image processing systems and transformations are outlined.
This document discusses parallel processing and compound image compression techniques. It examines the computational complexity and quantitative optimization of various image compression algorithms like BTC, DCT, DWT, DTCWT, SPIHT and EZW. The performance is evaluated in terms of coding efficiency, memory usage, image quality and quantity. Block Truncation Coding and Discrete Cosine Transform compression methods are described in more detail.
This document discusses data compression techniques including lossless compression methods like run-length encoding and statistical compression, as well as lossy compression methods like JPEG and MPEG. It also covers recent developments in data compression technology and the use of neural networks for image compression.
State-of-the-art Clustering Techniques: Support Vector Methods and Minimum Br...Vincenzo Russo
This document summarizes two state-of-the-art clustering techniques: Support Vector Clustering (SVC) and Bregman Co-clustering. SVC involves a two-phase process: 1) determining boundaries of clusters using a minimum enclosing ball approach, and 2) assigning cluster labels by finding connected components in a graph. Bregman Co-clustering aims to robustly handle missing or sparse data, high dimensionality, noise and outliers. The document discusses applications and desirable properties of these clustering methods, such as nonlinear separability and automatic detection of the number of clusters.
UMAP is a technique for dimensionality reduction that was proposed 2 years ago that quickly gained widespread usage for dimensionality reduction.
In this presentation I will try to demistyfy UMAP by comparing it to tSNE. I also sketch its theoretical background in topology and fuzzy sets.
A Diffusion Wavelet Approach For 3 D Model Matchingrafi
The document presents a novel diffusion wavelet approach for 3D model matching. It combines diffusion maps with wavelets to extract multi-scale shape features from 3D models. Fisher's discriminant ratio is used to select discriminative wavelet coefficients for model representation. Models are retrieved by comparing their representation vectors at different wavelet scales. Results show the diffusion wavelet approach outperforms spherical harmonics and wavelets for 3D model retrieval.
Adaptive Neuro-Fuzzy Inference System based Fractal Image CompressionIDES Editor
This paper presents an Adaptive Neuro-Fuzzy
Inference System (ANFIS) model for fractal image
compression. One of the image compression techniques in
the spatial domain is Fractal Image Compression (FIC)
but the main drawback of FIC using traditional
exhaustive search is that it involves more computational
time due to global search. In order to improve the
computational time and compression ratio, artificial
intelligence technique like ANFIS has been used. Feature
extraction reduces the dimensionality of the problem and
enables the ANFIS network to be trained on an image
separate from the test image thus reducing the
computational time. Lowering the dimensionality of the
problem reduces the computations required during the
search. The main advantage of ANFIS network is that it
can adapt itself from the training data and produce a
fuzzy inference system. The network adapts itself
according to the distribution of feature space observed
during training. Computer simulations reveal that the
network has been properly trained and the fuzzy system
thus evolved, classifies the domains correctly with
minimum deviation which helps in encoding the image
using FIC.
DOMAIN SPECIFIC CBIR FOR HIGHLY TEXTURED IMAGEScseij
It is A Challenging Task To Build A Cbir System Which Primarily Works On Texture Values As There
Meaning And Semantics Needs A Special Care To Be Mapped With Human Based Languages. We Have
Consider Highly Textured Images Having Properties(Entropy, Homogeneity, Contrast, Cluster Shade, Auto
Correlation)And Have Mapped Using A Fuzzy Minmax Scale W.R.T. Their Degree(High, Low,
Medium)And Technical Interpetation.This Developed System Is Performing Well In Terms Of Precision
And Recall Value Showing That Semantic Gap Has Been Reduced For Highly Textured Images Based Cbir.
This document provides an introduction and syllabus for a machine vision course. The 2-day course covers MATLAB basics, image processing fundamentals, and 4 projects involving content-based image retrieval, depth from stereo images, image segmentation, and object recognition. The instructor provides several demonstrations of computer vision applications and encourages students to directly start working on projects.
I am Parton R. I am a Signal Processing Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, from The University, of Edinburgh, UK. I have been helping students with their assignments for the past 6 years. I solve assignments related to Signal Processing.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Signal Processing assignments.
Fractal compression is a lossy compression method for digital images, based on fractals. The method is best suited for textures and natural images, relying on the fact that parts of an image often resemble other parts of the same image.[citation needed] Fractal algorithms convert these parts into mathematical data called "fractal codes" which are used to recreate the encoded image.
This document summarizes a method for acquiring stereo image pairs with pixel-accurate ground truth correspondence information using structured light. The method involves projecting patterns of structured light onto a scene using one or more light projectors while capturing images using a pair of cameras. By decoding the projected light patterns, each pixel can be uniquely labeled, allowing trivial determination of correspondences between camera views. The structured light patterns help overcome limitations of existing stereo datasets in evaluating stereo matching algorithms.
The learning algorithm develops basis functions for natural images that are similar to receptive fields in the primary visual cortex. The algorithm optimizes a cost function that trades off representation quality and sparseness. It searches for basis functions that lead to good sparse approximations of natural image sets. The resulting dictionaries have basis functions that are localized in space and scale, and oriented in specific directions. Applying the algorithm to different image sets produces basis functions that capture the intrinsic structures of the images, such as brushstrokes in paintings and edges in building photos.
Image De-Noising Using Deep Neural Networkaciijournal
Deep neural network as a part of deep learning algorithm is a state-of-the-art approach to find higher level
representations of input data which has been introduced to many practical and challenging learning
problems successfully. The primary goal of deep learning is to use large data to help solving a given task
on machine learning. We propose an methodology for image de-noising project defined by this model and
conduct training a large image database to get the experimental output. The result shows the robustness
and efficient our our algorithm.
- Geoffrey Hinton gives a tutorial on deep belief nets and how to learn multi-layer generative models of unlabeled data by learning one layer of features at a time using restricted Boltzmann machines (RBMs).
- RBMs make it possible to efficiently learn deep generative models one layer at a time by approximating the intractable posterior distribution over hidden units given visible data.
- Layer-by-layer unsupervised pre-training of features followed by discriminative fine-tuning improves classification performance on benchmark datasets like MNIST compared to backpropagation alone.
REMOVING OCCLUSION IN IMAGES USING SPARSE PROCESSING AND TEXTURE SYNTHESISIJCSEA Journal
The document presents a method for removing large occlusions from images using sparse processing and texture synthesis. It involves decomposing the image into structure and texture images using sparse representations. The occluded regions in the structure image are filled in using sparse reconstruction, which retains image structures. Texture synthesis is then performed on the texture image to fill in the occluded texture. Finally, the reconstructed structure and texture images are combined to produce the occlusion-free output image. The method is shown to effectively remove large occlusions while avoiding blurring and retaining both structures and textures. It outperforms other inpainting methods in terms of visual quality.
T. Lucas Makinen x Imperial SBI WorkshopLucasMakinen1
1) The document discusses using neural networks to compress cosmological simulations into informative summaries or statistics in order to perform inference on cosmological parameters.
2) It describes using "Information Maximizing Neural Networks" which are trained to maximize the Fisher information of the summaries with respect to the parameters in order to capture the most cosmologically relevant information.
3) The document also introduces using graph neural networks to represent cosmological simulations as graphs with nodes for halos and edges for their connections, finding that the graph structure captures cosmological information in a way that is insensitive to network architecture details.
Data Science - Part XVII - Deep Learning & Image ProcessingDerek Kane
This lecture provides an overview of Image Processing and Deep Learning for the applications of data science and machine learning. We will go through examples of image processing techniques using a couple of different R packages. Afterwards, we will shift our focus and dive into the topics of Deep Neural Networks and Deep Learning. We will discuss topics including Deep Boltzmann Machines, Deep Belief Networks, & Convolutional Neural Networks and finish the presentation with a practical exercise in hand writing recognition technique.
This document discusses a method called cone tracing, which is a variant of ray tracing that can be used to render realistic soft shadows and glossy reflections more efficiently than traditional ray tracing. The key aspects are:
- Cone tracing models light as conical volumes rather than individual rays, reducing the number of intersections needed while avoiding noise.
- The paper presents a rendering engine that uses both cone tracing and ray tracing modules to produce shadows and reflections. Cone tracing is used to determine occlusion and reflection colors at ray intersection points.
- Intersection algorithms are approximated for cones, which have linear widening, rather than solved directly through systems of equations like with rays. This achieves accurate results more efficiently
Image Denoising Based On Sparse Representation In A Probabilistic FrameworkCSCJournals
Image denoising is an interesting inverse problem. By denoising we mean finding a clean image, given a noisy one. In this paper, we propose a novel image denoising technique based on the generalized k density model as an extension to the probabilistic framework for solving image denoising problem. The approach is based on using overcomplete basis dictionary for sparsely representing the image under interest. To learn the overcomplete basis, we used the generalized k density model based ICA. The learned dictionary used after that for denoising speech signals and other images. Experimental results confirm the effectiveness of the proposed method for image denoising. The comparison with other denoising methods is also made and it is shown that the proposed method produces the best denoising effect.
Deferred Pixel Shading on the PLAYSTATION®3Slide_N
This document summarizes a deferred pixel shading algorithm implemented on the PlayStation 3 system. The algorithm runs pixel shaders on the Synergistic Processing Elements of the Cell processor concurrently with the GPU for rendering images. Experimental results found that running the pixel shading on 5 SPEs achieved a performance of up to 85Hz at 720p resolution, comparable to running on a high-end GPU. This indicates that the Cell processor can effectively enhance GPU performance by offloading pixel shading work.
This paper proposes an algorithm to optimize the trade-off between space and time for a class of electronic structure calculations involving tensor contractions. The algorithm starts with an operation-based representation and applies transformations to minimize the total memory requirement by reducing the size of intermediate arrays through loop fusion techniques. This approach addresses the challenge of large temporary memory requirements for coupled cluster and other electronic structure models.
The development of multimedia system technology in Content based Image Retrieval (CBIR) System is
one in every of the outstanding area to retrieve the images from an oversized collection of database. The feature
vectors of the query image are compared with feature vectors of the database images to get matching images.It is
much observed that anyone algorithm isn't beneficial in extracting all differing kinds of natural images. Thus an
intensive analysis of certain color, texture and shape extraction techniques are allotted to spot an efficient CBIR
technique that suits for a selected sort of images. The Extraction of an image includes feature description and
feature extraction. During this paper, we tend to projected Color Layout Descriptor (CLD), grey Level Co-
Occurrences Matrix (GLCM), Marker-Controlled Watershed Segmentation feature extraction technique that
extract the matching image based on the similarity of Color, Texture and shape within the database. For
performance analysis, the image retrieval timing results of the projected technique is calculated and compared
with every of the individual feature.
This document is an internship report submitted by Raghunandan J to Eckovation about a project on classifying handwritten digits using a convolutional neural network. It provides an introduction to convolutional neural networks and explains each layer of a CNN including the input, convolutional layer, pooling layer, and fully connected layer. It also gives examples of real-world applications that use artificial neural networks like Google Maps, Google Images, and voice assistants.
Image Super-Resolution Reconstruction Based On Multi-Dictionary LearningIJRESJOURNAL
ABSTRACT: In order to overcome the problems that the single dictionary cannot be adapted to variety types of images and the reconstruction quality couldn’t meet the application, we propose a novel Multi-Dictionary Learning algorithm for feature classification. The algorithm uses the orientation information of the low resolution image to guide the image patches in the database to classify, and designs the classification dictionary which can effectively express the reconstructed image patches. Considering the nonlocal similarity of the image, we construct the combined nonlocal mean value(C-NLM) regularizer, and take the steering kernel regression(SKR) to formulate a local regularization ,and establish a unified reconstruction framework. Extensive experiments on single image validate that the proposed method, compared with several other state-of-the-art learning based algorithms, achieves improvement in image quality and provides more details.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
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1. MANAGING MEGABYTES
A Better Way to
Compress Images
Mathematics is providing a novel technique for achieving
compression ratios of 10, 000 to 1-and higher
Michael F. Barnsley and Alan D.
Sloan
THE NATURAL WORLD is filled Georgia Institute of Technology is devel- geometry provides just such a
with intricate detail. Consider the oping the system, with funding provided collection of shapes. For a hint of this,
geometry on the back of your hand: the by the Defense Advanced Research Proj- glance at the pictures in The Fractal
pores, the fine lines, and the color ects Agency (DARPA) and the Georgia Geometry of Nature by Benoit
variations. A camera can capture that Tech Research Corporation (GTRC). Our Mandelbrot, who coined the term fractal
detail and, at your leisure, you can study description is necessarily simplified, but to describe objects that are very
the photo to see things you never noticed it will show you how a fractal image- "fractured" (see references for additional
before. Can personal computers be made compression scheme operates and how to books and articles). Some elementary
to carry out similar functions of image use it to create exciting images. fractal images accompany this article.
storage and analysis? If so, then image Using fractals to simulate landscapes
compression will certainly play a central Describing Natural Objects Traditional and other natural effects is not new; it has
role. computer graphics encodes images in been a primary practical application. For
The reason is that digitized images- terms of simple geometrical shapes: instance, through experimentation, you
images converted into bits for processing points, line segments, boxes, circles, and find that a certain fractal generates a pat-
by a computer-demand large amounts of so on. More advanced systems use three- tern similar to tree bark. Later, when you
computer memory. For example, a high- dimensional elements, such as spheres want to render a tree, you put the treebark
detail gray-scale aerial photograph might and cubes, and add color and shading to fractal to work.
be blown up to a 3'h-foot square and then the description. What is new is the ability to start with
resolved to 300 by 300 pixels per square Graphics systems founded on tradi- an actual image and find the fractals that
inch with 8 significant bits per pixel. tional geometry are great for creating will imitate it to any desired degree of ac-
Digitization at this level requires 130 pictures of man-made objects, such as curacy. Since our method includes a com-
megabytes of computer memory-too bricks, wheels, roads, buildings, and pact way of representing these fractals,
much for personal computers to handle. cogs. However, they don't work well at we end up with a highly compressed data
For real-world images such as the all when the problem is to encode a sun- set for reconstructing the original image.
aerial photo, current compression set, a tree, a lump of mud, or the intricate
techniques can achieve ratios of structure of a black spleenwort fern.
between 2 to 1 and 10 to 1. By these Think about using a standard graphics Overview of Fractal Compression We
methods, our photo would still require system to encode a digitized picture of a start with a digitized image. Using image-
between 65 and 13 megabytes. cloud: You'd have to tell the computer processing techniques such as color
In this article, we describe some of the address and color attribute of each separation, edge detection, spectrum
the main ideas behind a new method for point in the cloud. But that's exactly what analysis, and texture-variation analysis,
image compression using fractals. The an uncompressed digitized image is-a we break up the image into segments.
method has yielded compression ratios in long list of addresses and attributes.
excess of 10,000 to 1 (bringing our aerial (Some of the same techniques continued
To escape this difficulty, we need a
photo down to a manageable 13,000 richer library of geometrical shapes.
bytes). The color pictures in figures 1 These shapes need to be flexible and
through 5 were encoded using the new Michael F. Barnsley and Alan D.
controllable so that they can be made to Sloan are professors of mathematics at
technique; actual storage requirements conform to clouds, mosses, feathers,
for these images range from 100 to 2000 the Georgia Institute of Technology
leaves, and faces, not to mention waving (Atlanta, GA 30332) and officers of
bytes. sunflowers and glaring arctic wolves. Iterated Systems Inc. (1266 Holly Lane
A mathematics research team at the Fractal NE, Atlanta, GA 30329).
3. IMAGE COMPRESSION
W [Yx] _ Ca d ] [ x Y ] + al a+a2b+e=
0,a+a2b+e=
-y,a+_y2b+e =1 ',,
_ ax+by+e - I
cx+dy+f I ' and find c , d , and f in similar fashion
from these equations:
where the coefficients a, b, c, d , e, and f a,c+a2d + f = a2, (4)
are real numbers. 0,c+02d + f = N2, (5)
If we know in advance the y,c+ti2d + f = y 2. (6)
translations, rotations, and scalings that
combine to produce W, we can generate We recommend the use of an equation
coefficient values as follows: solver such as TK Solver Plus
(Universal Technical Systems,
a = r cos 6, b = -s sin ~, Rockford, Illinois) or Eureka (Borland Figure 6: An aff ne transformation W
c=rsin0,d=scos0, International, Scoffs Valley, California) moves the smiling face F to a new
for finding the coefficient values. Doing face W(F). The transformation is
where r is the scaling factor on x, s is the it manually can be tedious. called contractive because it moves
scaling factor on y, 9 is the angle of Now that we know what a contractive points closer together.
rotation on x, 0 is the angle of rotation continued
on y, e is the translation on x, and f i s
the translation on y.
How can you find an affine transfor-
mation that produces a desired effect?
Let's show how to find the affine trans- ((31,82)
formation that takes the big leaf to the
little leaf in figure 7. We wish to find the
numbers a, b, c, d, e, and f for which ~ - ( « 1 , C - 0
the transformation W has the property fY1,l`z) _ i- (a~,az)
W(big leaf) = little leaf.
Begin by introducing x and y coordinate
axes, as already shown in the figure.
Mark three points on the big leaf (we've
chosen the leaf tip, a side spike, and the
point where the stem joins the leaf) and
determine their coordinates (a,,a2),
(N1,N2), and (y,,72). Mark the corre-
sponding points on the little leaf and
determine their coordinates (ix,,a2),
(N2), and (j,,y2), respectively.
Determine values for the
coefficients a, b, and e by solving the Figure 7: Two leaves fix an affine transformation
three linear equations ivy W.
Table 1: IFS codes for a Sierpinski triangle. f P Table 3 : I F S codes
for a fern. d e f P
W a b c d e W abc
1 0.5 0 0 0.5 0 0 0.33 1 000 0.16 0 0 0.01
2 0.5 0 0 0.5 1 0 0.33 2 0.2 -0.26 0.23 0.22 0 1.6 0.07
3 0.5 0 0 0.5 0.5 0.5 0.34 3 -0.15 0.28 0.26 0.24 0 0.44 0.07
4 0.85 0.04 -0.04 0.85 0 1.6 0.85
Table 2 : I F S codes for a square. e f P Table 4 : I F S
codes for fractal tree. e t P
W a b c d W a bcd
1 0.5 0 0 0.5 0 0 0.25 1 0 0 0 0.5 0 0 0.05
2 0.5 0 0 0.5 0.5 0 0.25 2 0.1 0 0 0.1 0 0.2 0.15
3 0.5 0 0 0.5 0 0.5 0.25 3 0.42 -0.42 0.42 0.42 0 0.2 0.4
4 0.5 0 0 0.5 0.5 0.5 0.25 4 0.42 0.42 -0.42 0.42 0 0.2 0.4
4. IMAGE COMPRESSION
affine transformation is and how to find formations. In the present case we might (i) Initialize: x=0, y=0.
one that maps a source image onto a de- have p,, ps , and p,. Notice that the
sired target image, we can describe an probabilities must add up to 1. That is, (ii) For n=1 to 2500, do steps (iii)-(vii).
iterated function system. An IFS is a col- p, +
p,+p,=1. (iii) Choose k to be one of the numbers
lection of contractive affine transforma- 1, 2 , . . ., m, with probability P,
tions. Here's an example of an IFS of Of course, the above notation for an (iv) Apply the transformation W, to the
three transformations: IFS is cumbersome. Table 1 expresses point (x,y) to obtain
the same information in tabular form. y=y.
Other examples of IFS codes are given
W' 1yI _ [0.0 0.5] Cy] + [00] ' in tables 2 through 4. Notice that an IFS (vi) If n > 10, plot (x,y).
can contain any number of affine (vii) Loop.
transformations. Applying this procedure to the trans-
The Random Iteration Algorithm Now formation in table 1 produces the figure
WZ Cy] = [o:o oa] Cy] + Co] ' let's see how to decode an arbitrary IFS shown in figure 8-a fractal known as the
code using the random iteration method. Sierpinski triangle. Increasing the number
Remember that in general an IFS can of iterations n adds points to the image.
W, [y] _ 00 0.5 Cy] + 1.55] contain any number, say m, of affine Figure 9 shows the result of the random
transformations, W,, W2, W3,.. ., W,., iteration algorithm applied to the data in
Each transformation must also have an each with an associated probability. The table 3, at several stages during the
associated probability, pi, determining its following code summarizes the method: process. By increasing the scale factor
"importance" relative to the other trans used in plotting, you can zoom in on the
image (see figure 10). The text box on
page 221 contains a BASIC implementa-
tion of the method with additional com-
ments on programming.
You may wonder why the first 10
points are not plotted (step (vi)). This is
to give the randomly dancing point time
to settle down on the image. It is like a
soccer ball thrown onto a field of expert
players: Until someone gains control of
the ball, its motion is unpredictable, or at
least is independent of the players' ac-
tions. But eventually a player gets the
ball, and its motion then becomes a
direct result of the skill of the players.
The fact that our transformation is
contractive guarantees that the "ball" will
eventually get to one of the "players,"
and that it will stay under control after
Figure 8: The result of applying the random iteration algorithm to the IFS code that.
in table 1. It is called the Sierpinski triangle. How do we know that the random iter-
co nt inue d
Figure 9: A fern appears when the random iteration algorithm is applied to the IFS code in table
3.
5. IMAGE COMPRESSION
at on algorithm will produce the same plane, with its vertices at (0,0), (1,0), (1, tions 1 through 3 and 4 through 6. The
image over and over again, independent 1), and (0,1) (see figure 11). The ob- values one finds in the present case are
of the particular sequence of random jective is to choose a set of contractive
choices that are made? This remarkable affine transformations, in this case W , given in table 2. When the random itera-
result was first suggested by computer- W2, W,, W4, so that S is approximated as tion algorithm is applied to this IFS
graphical mathematics experiments and well as possible by the union of the four code, the square is regenerated.
later given a rigorous theoretical subimages WI(S) U W2(S) U W3(S) U The preceding example typifies the
foundation by Georgia Tech W4(S). Figure 11 shows, on the left, S general situation: You need to find a set
mathematician John Elton. together with four noncovering affine of affine transformations that shrink dis-
The Collage Theorem transformations of it; on the right, the tances and that cause the target image to
affine transformations have been be approximated by the union of the af-
adjusted to make the union of the fine transformations of the image. The
Our next goal is to show a systematic transformed images cover up the square. Collage Theorem says that the more ac-
method for finding the affine transforma- curately the image is described in this
tions that will produce an IFS encoding To find the coefficients of these trans-
formations, we use the method described way, the more accurately the transforma-
of a desired image. This is achieved with tions provide an IFS encoding of it.
the help of the Collage Theorem. earlier in the section on iterated function Figure 12 provides another
To illustrate the method, we start systems, leading to simultaneous equa illustration of the Collage Theorem. At
from a picture of a filled-in square S in the bottom left is shown a polygonalized
leaf boundary, together with four affine
transformations of that boundary. The
transformed leaves taken together do
not form a very good approximation of
the leaf, in consequence, the
corresponding IFS image (bottom right),
computed using the random iteration
algorithm, does not look much like the
original leaf image. However, as the
collage is made more accurate (upper
left), the decoded image (upper right)
becomes more accurate.
So, there's a fundamental stability
here. You don't have to get the IFS code
exactly right in order to capture a good
likeness of your original image. More-
over, the IFS code is robust: Small per-
turbations in the code will not result in
unacceptable damage to the image. In
each of the above examples, we have
used four transformations to encode the
image. However, any number can be
used.
For example, the spiral image in
figure 13 can be encoded with just two
contractive affine transformations. See if
you can find them. Then determine the
Figure 10: Successive zooms on pieces of an IFS-encoded fern. IFS transformation coefficients and
input them to the random iteration
algorithm to get the spiral back again.
Figure 11: The collage theorem is used to encode a classical square S. The correct IFS code is obtained when the four affine
transformations of S cover S, as shown on the right.
6. IMAGE COMPRESSION
Assigning Probabilities filled in. Let the affine transformations W, amount of time that the randomly dancii.
corresponding to an image I be g point should spend in the subimage W,
Once you have defined your transforma- is approximately equal to
tions, you need to assign probabilities to W, [xY] - [c, d,] [xy] +
them. Different choices of probabilities do
not in general lead to different images, but
they do affect the rate at which various where i = 1, 2, 3,.. ., n. Then the continued
regions or attributes of the image are
IFS Decoding Listing A: A BASIC program demonstrating the use of the random
iteration algorithm to reconstruct an IFS-compressed image.
in BASIC 10 'Allow for a maximum of 4 transformations in the IFS
20 DIM a(4), b(4), c(4), d(4), e(4), f(4), p(4)
isting A is a BASIC 30
implementation of the random iteration 40 'Transformation data, Sierpinski triangle 50
'First comes the number of transformations 60 'then
algorithm. It includes the data for the the coefficients a through f and probability 70 'The pk
Sierpinski triangle, but you can use it to values for pk should be in descending order. 80 DATA
process any IFS tables. In particular, you 3
90 DATA .5,0,0,.5,0,0,.34 100 DATA .5,0,0,.5,1,0,.33
will want to try the data in tables 2, 3, 110 DATA .5,0,0,.5,.5,.5,.33
and 4. Be sure to set the variable m
correctly; it tells the program how many
120
transformations are in the IFS. 130 'Read in the
It is also essential that the probabilities 140 data READ m
in p ( ) add up to 1. For speed, the 150 pt = 0 'Cumulative probability
160 FOR j = 1 TO m
transformations should be listed in de- 170 READ a(j), b(j), c(j), d(j), e(j), f(j), pk
scending order of probability: the highest 180 pt = pt + pk
probability transformation first, and the 190 P(j) =
lowest probability last. 200 pt NEXT j
210
The program includes variables for 220
resealing and translating the origin to 230 'Set up for Graphics
accommodate the range of the points be- 240
258 SCREEN 3 'Select graphics screen
ing plotted to the limits of your screen. If 260
the image is too wide, decrease xscale; if
xscale = 350 'Map [0,11 onto [0,3501
the points are too close horizontally, yscale = 325 'Map [8,11 onto [0,3251
increase xscale. Adjust yscale similarly to 270 xoffset = 0
280 'Initialize x and y
get a good vertical point spread. To move 290 x = 8
the image, adjust xoffset and yoffset. 300 y = 0
You can do these adjustments by trial 310
and error: Run the program; interrupt it 320
330 'Do 2500
and change the offsets and scale factors; 340 iterations FOR n =
and run it again. Or, you can replace the 350 1 TO 2580 pk = RND
plot command pset with a command to 360 'The next line works for m<=4. It must be
print the values of x and y and run the 370 modified 'for values of m > 4.
380 IF pk <= p(1) THEN k = 1 ELSE IF pk <= p(2) THEN k
program to get an exact idea of the range = ELSE IF pk <= p(3) THEN k = 3 ELSE k = 4
2
of points being plotted, so you can adjust
the scale and offsets more precisely. 390 newx = a (k) * x + b (k) * y + e
(k)
Another way to arrange the program 400 newy = c (k) * x + d (k)
is to have it read all the data-m, a () , ( ), * y + f (k) 410 x =
c( ), d( ), e( ), f( ), p( ) > xscale, yscale, newx
xoffset, and yoffset-from a disk file 420 y = newy
430 Use PRINT x,y instead of the PSET line
specified by the user. Instead of reading 440 'to see the range of coordinates. Then fix yscal
in the coefficients a, b, c, and d, you may 450 'xscale, yscale, xoffset, and yoffset e
want to read in angles 0 and 0 and scale 460 IF n > 10 THEN PSET (x *
470 NEXT n
factors r and s, and then calculate the 480
coefficients. 490 LOCATE 24, 35
The random iteration method is com- 500
510 PRINT "Press any key to end.";
putation-intensive, so we recommend use 520 WHILE INKEY$
of a compiler such as Microsoft's 530 WEND
QuickBASIC or Borland's Turbo BASIC. 540
550 'Return to text screen SCREEN 0
If your computer has a floatingpoint 560 END
coprocessor and your compiler supports
one, so much the better.
7. IMAGE COMPRESSION
So long as ad - cd is not 0, it is a stan-
dard calculus result that our ratio equals
the determinant of the transformation
matrix for W,.. So a good choice for the
probability p; is
a; d; - b;
c;
I akdk-b,Ckl
provided none of these numbers p;
comes out to be 0. A 0 value should be
replaced by a very small positive value,
such as 0.001, and the other probabilities
correspondingly adjusted to keep the
sum of all the probabilities equal to 1.
We now summarize the compression
and decompression process: An input
image is broken up into segments
through image-processing techniques.
These image components are looked up
in the IFS library using the Collage
Theorem, and their IFS codes are
recorded. When the image is to be
reconstructed, the IFS codes are input to
Figure 12: The Collage Theorem is applied to a leaf. The collage at lower left isn't the random iteration algorithm. The
much good, so the corresponding IFS image, shown at lower right, is a poor accuracy of the reconstructed image
approximation. But as the collage improves, upper left, so does the IFS image. depends only on the tolerance setting
Applications
For graphics applications, we use a more
sophisticated procedure that allows full-
color images to be encoded. Combina-
torial searching algorithms can be used to
automate the collage mapping stage. Fig-
ures 2, 3, and 4 were obtained using IFS
theory at compression ratios in excess of
10,000 to 1. These images were based on
photographs in recent issues of National
Geographic. A full-sequence video ani-
mation, A Cloud Study, was shown at
SIGGRAPH '87. This was encoded at a
ratio exceeding 1,000,000 to 1 and can be
transmitted in encoded form at video
rates over ISDN lines (ISDN stands for
integrated services digital network, a
concept for integrated voice and data
communications). A frame from the ani-
mation is shown in figure 5.
The IFS compression technique is
computation-intensive in both the
encoding and decoding phases.
Computations for the color images were
all carried out on Masscomp 5600
workstations (dual 68020-based systems)
with Aurora graphics. Complex color
images require about 100 hours each to
encode and 30 minutes to decode on the
Masscomp.
For practical applications, you need
custom hardware that can speed the en-
coding and decoding process. An experi-
mental prototype, the IFSIS (iterated
Figure 13: Can you find the IFS codes for this spiral image? Only two function system-image synthesizer), de-
transformations are needed. codes at the rate of several frames per
second. The IFSIS device was produced
from a cooperative effort between
8. IMAGE COMPRESSION
DARPA, Atlantic Aerospace Electronics Corporation, and Iterated Systems, and it was
demonstrated on October 5, 1987, at thethirdannualmeetingoftheAppliedand Computational
Mathematics Program of DARPA. It can be connected to a personal computer through a serial
port; the personal computer sends the IFS codes to the device, whichrespondsbyproducingcom-
plex color images on a monitor.
The IFSIS is a proof of concept for faster devices with higher resolution. Once the higher-
performance IFSIS devices are combined with ISDN telecommunication, full-color animation at
video rates over phone lines will be a reality.
Another area for future application of IFS encoding is automatic image analysis. What's in a
picture? Does it show a spotted sandpiper or a robin? The more complex the image or the more
subtle the question, the harder it becomes for an algorithmic answer to be formulated. But here's
the point: Whatever the answer, it will proceed faster if stable, compressed images are used. The
reason for this is that image-recognition problems involve combinatorial searching, and searching
times increase factorially with the size of the image file.
During the spring of 1987, Iterated Systems was incorporated to develop commercial
applications of IFS image compression. It is exciting to see how an abstract field of mathematics
research is leading to new technology with implications ranging from commercial and industrial
work to personal computing. E
ACKNOWLEDGMENTS
Figures 2 through S were encoded by graduate students Francois Malassenet, Laurie Reuter, and
Arnaud Jacquin. All color images were produced in the Computergraphical Mathematics
Laboratory at Georgia Institute of Technology and are copyright 1987, GTRC.
BIBLIOGRAPHY
Barnsley, M. F. and S. Demko. "Iterated
Function Systems and the Global Con-
struction of Fractals." The Proceedings of
the Royal Society of London, A399, 1985,
pp. 243-275.
Barnsley, M. F., V. Ervin, D. Hardin, and
J. Lancaster. "Solution of an Inverse
Problem for Fractals and Other Sets."
Proceedings of the National Academy of
Science, vol. 83, April 1985.
Barnsley, M. F. Fractals Everywhere. Ac-
ademic Press, 1988. Forthcoming. Elton, J.
"An Ergodic Theorem for Iterated Maps."
BYTE
Journal of Ergodic Theory and Dynamical
Systems. Forthcoming. Mandelbrot, B. The
Fractal Geometry of Nature. San Francisco,
CA: W. H. Freeman and Co., 1982.
THE SMALL SYSTEMS JOURNAL
Reprinted with permission from the January 1988 issue of BYTE magazine. Copyright c 1988 by
McGraw-Hill, Inc., New York, 10020. All rights reserved.
9. COMPUTER
GRAPHICS
WORLD GRAPHICS
TECHNOLOGY
Chaotic Compression
A new twist on fractal theory speeds
complex image transmission to video rates
pounding the problems of cost takes three hours at a total trans-
By Michael F. Barnsley & and delay, extended transmission mission cost of $42 (25 cents per
Alan D. Sloan times expose data to degradation. minute) to send our sample image
A one-megabyte-per-second 1000 miles on a 2400-bps toll line.
Ethernet line transmits the same The same image can be sent to the
T he massive volumes of data
associated with computer graphics
image in one second, but two
users who are each exchanging one
minute of animation of such
images consume an hour of time.
same address in 16 seconds at a
cost of 51 cents on a 56,000-bps
T1 line.
Confounding Performance
severely check the use of low- Given these burdens, it's easy to Paradoxically, continuing improve-
bandwidth communications see"why there is no multiple-user ments in computer graphics hard-
network for animating high- ware and software only compound
devices for image transfer. resolution images at video rates.
Multiple users can easily overload Transmission times are propor- the problem. Faster hardware in-
tional to transmission bandwidths. creases the rate of graphics
even the markedly higher production and thus increases
bandwidth of local area networks. At current rates, for example, it demand on transmission. The
Potential applications go quest for realism
unrealized as the cost of Ten thousand-to-one compression ratios can be realized with
transmitting graphics increases a new method based on chaos theory, fractal geometry, and affine
directly with improved per- transformations. While transmission can approach or exceed video
formance and greater complexity. rates, the challenge now is to reconstruct images as rapidly.
Below: "Sunflower Field" and "Arctic Wolf," images compressed
But algorithms based on fractal at 10,000:1 at Georgia Tech.
geometry can encode image data at
high compression ratios-in excess
of 10,000 to one. It is possible to
transmit such compressed image
files at video rates (30 frames per
second) over normal telephone
lines. A new graphics device, the
Iterated Function System Image
Synthesizer, makes Transmission
A Perspective on it possible to
A 1000-by-1000-resolution com-
puter graphics image with eight
bits of color information per pixel
needs one megabyte of data for
specification. The transmission of
this image over a 2400-bit-per-
second line takes over 55 minutes.
Com
Michael F. Barnsley and Alan D. Sloan are
professors of mathematics at the Georgia
Institute of Technology (Atlanta). Barnsley
and Sloan are also officers of Iterated Sys-
tems Inc. (Atlanta).
Reprinted from the November, 1987 edition of Computer
Graphics World Copyright 1987 by PennWell Publishing
Company
10. drives graphics software to on a line between P(n) and Vk
produce images of increasing where Vl = A, V2 = B, and Va = C.
complexity. Greater image
complexity means more Throw away the first 25 points and
information that must be trans- have been working on image com- plot the rest. The result is indepen-
mitted for each image. pression standards. But the com- dent of the initial point P(0) as well
Sophisticated printers also increase pression ratios being discussed are as the sequence of random
transmission requirements. A new basically pretty low.
For example, one exact numbers which were chosen in its
color printer from Tektronix is a generation.
case in point. Producing an A-size, compression method-a type of
method calling for exact When suitably generalized, this
24-bit-deep color printout at 300
dpi can chew up over 9M of data. reconstruction of an image-calls for process leads to full-color images
Even at the Integrated Services a ratio of just two to one. There are like the sunflowers and Arctic wolf
several exact methods, but they on the preceding page. Inspired by
Digital Network bandwidth of National Geographic photographs,
64,000 bps, it will take over 15 aren't particularly useful. In one
minutes to supply the necessary experiment, a photo montage was Georgia Institute of Technology
run-length encoded, producing a graduate students Laurie Reuter and
data to the printer. Data
compression and reconstruction 60-percent increase in data length. Arnaud Jacquin encoded each of
clearly offer the greatest potential Unix provides a Huffman encoder these images at a ratio exceeding
for relief from the costs associated which yields a compression ratio of 10,000 to one. Both images are
decoded by a random iteration al-
with even the fastest communica- An experimental device reconstructs
tions technologies.
Digital data compression compressed video images at the rate
consists of encoding and decoding of about four frames per second.
phases. In the encoding phase, an
input string of integer-based (I) bits Such ratios are common to exact An experimental prototype device
is transformed into a coded string compression methods. introduced at the Meeting of the
of complex number-based (C) bits. General Electric has announced the Applied and Computational Mathe-
The ratio of I to C bits is the Digital Video Interactive com- matics Program of the Defense Ad-
compression ratio. In the decoding pression system developed at the vanced Research Projects Agency
phase, the compressed string David Sarnoff Research Center (DARPA) in October, the Iterated
regenerates the original data. If the ("DVI Video/Graphics," July, Function System Image Synthesizer
compression ratio is two to one, p.125). As the DVI compression (IFSIS) decoded video images at the
then in the time it would take to ratio increases above 10 to one, the rate of about four frames per
transmit one uncompressed image, loss of high-frequency information second. Because of the extreme
two compressed images can be becomes more apparent. But fine compression ratios, this device can
transmitted. detail isn't as critical for motion be coupled loosely to any host,
High-ratio image compression video as for still images, so the DVI which will treat it as if it were a
slashes transmission time and can produce a credible video at a printer-only it produces complex
costs. For example, an 100-to-one ratio. color images instead of text.
uncompressed minute of 30 The new method described here
has been used to encode complex Networking and high-resolution,
frames-per-second animation for a real-time animated graphics can be
24-bit-deep, 1000-by-1000 color graphics at exact compression
ratios of 10,000 to one. It can be realized simultaneously by means of
image takes seven months to used with classical compression IFSIS-type devices. The demon-
transmit over a 24-bps line at a techniques to increase yields even
further-up to one million to one in stration at the DARPA meeting
cost of $75,000. Compressed at a served as proof-of-concept for
10,000-toone ratio, the same the case of "A Cloud Study,"
shown at SIGGRAPH '87. The faster transmission devices with
minute of animation takes 30 method is based on chaotic higher resolution. Once the higher-
minutes to transmit at a cost of dynamic systems theory. A simple
example illustrates the procedure. performance IFSIS devices are
about $7.50. On a 1.544 million- combined with 64,000-bps
bps line, uncompressed Given a triangle with vertices A, B,
and C, choose an initial point P(0) telecommunications, fullcolor
transmission takes eight hours at a animation transmission and
cost of $339; compressed at 10,000 at random in the triangle. An itera-
tive procedure (affine reconstruction at video rates over
to one, it takes just three seconds phone lines will become a commer-
11. drives graphics software to on a line between P(n) and Vk
produce images of increasing where Vl = A, VZ = B, and V$ = C.
complexity. Greater image
complexity means more Throw away the first 25 points and
information that must be trans- have been working on image com- plot the rest. The result is indepen-
mitted for each image. pression standards. But the com- dent of the initial point P(0) as well
Sophisticated printers also increase pression ratios being discussed are as the sequence of random
transmission requirements. A new basically pretty low.
For example, one exact numbers which were chosen in its
color printer from Tektronix is a generation.
case in point. Producing an A-size, compression method-a type of
method calling for exact When suitably generalized, this
24-bit-deep color printout at 300
dpi can chew up over 9M of data. reconstruction of an image-calls for process leads to full-color images
Even at the Integrated Services a ratio of just two to one. There are like the sunflowers and Arctic wolf
several exact methods, but they on the preceding page. Inspired by
Digital Network bandwidth of National Geographic photographs,
64,000 bps, it will take over 15 aren't particularly useful. In one
minutes to supply the necessary experiment, a photo montage was Georgia Institute of Technology
run-length encoded, producing a graduate students Laurie Reuter and
data to the printer. Data
compression and reconstruction 60-percent increase in data length. Arnaud Jacquin encoded each of
clearly offer the greatest potential Unix provides a Huffman encoder these images at a ratio exceeding
for relief from the costs associated which yields a compression ratio of 10,000 to one. Both images are
decoded by a random iteration al-
with even the fastest communica- An experimental device reconstructs
tions technologies.
Digital data compression consists compressed video images at the rate
of encoding and decoding phases. of about four frames per second.
In the encoding phase, an input
string of integer-based (I) bits is Such ratios are common to exact An experimental prototype device
transformed into a coded string of compression methods. introduced at the Meeting of the
complex number-based (C) bits. General Electric has announced the Applied and Computational Mathe-
The ratio of I to C bits is the Digital Video Interactive com- matics Program of the Defense Ad-
compression ratio. In the decoding pression system developed at the vanced Research Projects Agency
phase, the compressed string David Sarnoff Research Center (DARPA) in October, the Iterated
regenerates the original data. If the ("DVI Video/Graphics," July, Function System Image Synthesizer
compression ratio is two to one, p.125). As the DVI compression (IFSIS) decoded video images at the
then in the time it would take to ratio increases above 10 to one, the rate of about four frames per
transmit one uncompressed image, loss of high-frequency information second. Because of the extreme
two compressed images can be becomes more apparent. But fine compression ratios, this device can
transmitted. detail isn't as critical for motion be coupled loosely to any host,
High-ratio image compression video as for still images, so the DVI which will treat it as if it were a
slashes transmission time and can produce a credible video at a printer-only it produces complex
costs. For example, an 100-to-one ratio. color images instead of text.
uncompressed minute of 30 The new method described here
has been used to encode complex Networking and high-resolution,
frames-per-second animation for a
graphics at exact compression real-time animated graphics can be
24-bit-deep, 1000-by-1000 color ratios of 10,000 to one. It can be realized simultaneously by means of
image takes seven months to used with classical compression IFSIS-type devices. The demon-
transmit over a 24-bps line at a techniques to increase yields even
further-up to one million to one in stration at the DARPA meeting
cost of $75,000. Compressed at a
the case of "A Cloud Study," served as proof-of-concept for
10,000-toone ratio, the same shown at SIGGRAPH '87. The faster transmission devices with
minute of animation takes 30 method is based on chaotic higher resolution. Once the higher-
minutes to transmit at a cost of dynamic systems theory. A simple
example illustrates the procedure. performance IFSIS devices are
about $7.50. On a 1.544 million-
Given a triangle with vertices A, B, combined with 64,000-bps
bps line, uncompressed and C, choose an initial point P(0) telecommunications, fullcolor
transmission takes eight hours at a at random in the triangle. An itera- animation transmission and
cost of $339; compressed at 10,000 tive procedure (affine
transformation) transforms a point reconstruction at video rates over
to one, it takes just three seconds
phone lines will become a commer-