There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into a system of ranked taxa: domain, kingdom, phylum, class, etc. Cluster analysis is the formal study of methods and algorithms for grouping, or clustering, objects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes data clustering (unsupervised learning) from classification or discriminant analysis (supervised learning). The aim of clustering is to find structure in data and is therefore exploratory in nature. Clustering has a long and rich history in a variety of scientific fields. One of the most popular and simple clustering algorithms, K-means, was first published in 1955. In spite of the fact that K-means was proposed over 50 years ago and thousands of clustering algorithms have been published since then, K-means is still widely used. This speaks to the difficulty in designing a general purpose clustering algorithm and the ill-posed problem of clustering. We provide a brief overview of clustering, summarize well known clustering methods, discuss the major challenges and key issues in designing clustering algorithms, and point out some of the emerging and useful research directions, including semi-supervised clustering, ensemble clustering, simultaneous feature selection during data clustering, and large scale data clustering.

Data clustering: 50 years beyond K-means

The practice of classifying objects according to perceived similarities is the basis for much of science. Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms in to taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and methods for grouping objects according to measured or perceived intrinsic characteristics. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes cluster analysis (unsupervised learning) from discriminant analysis (supervised learning). The objective of cluster analysis is to simply find a convenient and valid organization of the data, not to establish rules for separating future data into categories.

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Data Clustering: 50 Years Beyond K-means

Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

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Computer Vision: Algorithms and Applications

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

Statistical modeling methods are becoming indispensable in today's large-scale image analysis. In this paper, we explore a computationally efficient parameter estimation algorithm for two-dimensional (2-D) and three-dimensional (3-D) hidden Markov models (HMMs) and show applications to satellite image segmentation. The proposed parameter estimation algorithm is compared with the first proposed algorithm for 2-D HMMs based on variable state Viterbi. We also propose a 3-D HMM for volume image modeling and apply it to volume image segmentation using a large number of synthetic images with ground truth. Experiments have demonstrated the computational efficiency of the proposed parameter estimation technique for 2-D HMMs and a potential of 3-D HMM as a stochastic modeling tool for volume images.

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A computationally efficient approach to the estimation of two- and three-dimensional hidden Markov models

In the early 1990s, the establishment of the Internet brought forth a revolutionary viewpoint of information storage, distribution, and processing: the World Wide Web is becoming an enormous and expanding distributed digital library. Along with the development of the Web, image indexing and retrieval have grown into research areas sharing a vision of intelligent agents. Far beyond Web searching, image indexing and retrieval can potentially be applied to many other areas, including biomedicine, space science, biometric identification, digital libraries, the military, education, commerce, culture and entertainment. Machine Learning and Statistical Modeling Approaches to Image Retrieval describes several approaches of integrating machine learning and statistical modeling into an image retrieval and indexing system that demonstrates promising results. The topics of this book reflect authors' experiences of machine learning and statistical modeling based image indexing and retrieval. This book contains detailed references for further reading and research in this field as well.

Machine Learning and Statistical Modeling Approaches to Image Retrieval

This paper investigates the connection between additive fuzzy systems and kernel machines. We prove that, under quite general conditions, these two seemingly quite distinct models are essentially equivalent. As a result, algorithms based upon support vector (SV) learning are proposed to build fuzzy systems for classification and function approximation. The performance of the proposed algorithm is illustrated using extensive experimental results.

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Kernel machines and additive fuzzy systems: classification and function approximation

A method and system for generating and searching a tree-structured index of window vectors that represent database sequences comprise a window vector generation module, a tree-structured index generation module, a query sequence partitioning module, and a retrieval component. The window vector generation module partitions a database sequence into a plurality of overlapping windows. Each window has a fixed length W comprising a fixed number of nucleotides, and the offset among windows is determined by a parameter Δ. The window vector generation module then maps each database sequence window into a window vector. The database sequence window vector indicates the frequency of appearance of each k-tuple in the corresponding database sequence window. The tree-structured index generation module then generates a tree-structured index using the database sequence window vectors. The query sequence partitioning module partitions a query sequence into a plurality of windows and maps each query sequence window into a query sequence window vector. Each query sequence window vector is then compared against the tree-structured index to locate the database sequences that are similar to the query sequence. The list database sequences that are similar to the sequence is then returned as the result of the search.

Sequence database search with sequence search trees

The detection of mesoscale oceanic structures, such as upwellings or eddies, from satellite images has significance for marine environmental studies, coastal resource management, and ocean dynamics studies. Nevertheless, there is a lack of tools that allow us to retrieve automatically relevant mesoscale structures from large satellite image databases. This paper focuses on the development and validation of a content-based image retrieval system to classify and retrieve oceanic structures from satellite images. The images were obtained from the National Oceanic and Atmospheric Administration satellite's Advanced Very High Resolution Radiometer sensor. The study area is about W2° - 21°, N19° - 45°. This system conducts labeling and retrieval of the most relevant and typical mesoscale oceanic structures, such as upwellings, eddies, and island wakes located in the Canary Islands area and in the Mediterranean and Cantabrian seas. Our work is based on several soft computing technologies such as fuzzy logic and neurofuzzy systems.

James Z. Wang

Papers

A computationally efficient approach to the estimation of two- and three-dimensional hidden Markov models

Machine Learning and Statistical Modeling Approaches to Image Retrieval

Kernel machines and additive fuzzy systems: classification and function approximation

Sequence database search with sequence search trees

Fuzzy Content-Based Image Retrieval for Oceanic Remote Sensing