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An Image Processing Tour of College Mathematics (Chapman & Hall/CRC Mathematical and Computational Imaging Sciences Series)
by Yevgeniy V. GalperinAn Image Processing Tour of College Mathematics aims to provide meaningful context for reviewing key topics of the college mathematics curriculum, to help students gain confidence in using concepts and techniques of applied mathematics, to increase student awareness of recent developments in mathematical sciences, and to help students prepare for graduate studies. The topics covered include a library of elementary functions, basic concepts of descriptive statistics, probability distributions of functions of random variables, definitions and concepts behind first- and second-order derivatives, most concepts and techniques of traditional linear algebra courses, an introduction to Fourier analysis, and a variety of discrete wavelet transforms – all of that in the context of digital image processing. Features Pre-calculus material and basic concepts of descriptive statistics are reviewed in the context of image processing in the spatial domain. Key concepts of linear algebra are reviewed both in the context of fundamental operations with digital images and in the more advanced context of discrete wavelet transforms. Some of the key concepts of probability theory are reviewed in the context of image equalization and histogram matching. The convolution operation is introduced painlessly and naturally in the context of naïve filtering for denoising and is subsequently used for edge detection and image restoration. An accessible elementary introduction to Fourier analysis is provided in the context of image restoration. Discrete wavelet transforms are introduced in the context of image compression, and the readers become more aware of some of the recent developments in applied mathematics. This text helps students of mathematics ease their way into mastering the basics of scientific computer programming.
Image Processing using Pulse-Coupled Neural Networks: Applications in Python
by Thomas Lindblad Jason M. KinserImage processing algorithms based on the mammalian visual cortex are powerful tools for extraction information and manipulating images. This book reviews the neural theory and translates them into digital models. Applications are given in areas of image recognition, foveation, image fusion and information extraction. The third edition reflects renewed international interest in pulse image processing with updated sections presenting several newly developed applications. This edition also introduces a suite of Python scripts that assist readers in replicating results presented in the text and to further develop their own applications.
Image Processing with Cellular Topology
by Vladimir KovalevskyThis book explains why the finite topological space known as abstract cell complex is important for successful image processing and presents image processing methods based on abstract cell complex, especially for tracing and encoding of boundaries of homogeneous regions. Many examples are provided in the book, some teach you how to trace and encode boundaries in binary, indexed and colour images. Other examples explain how to encode a boundary as a sequence of straight-line segments which is important for shape recognition. A new method of edge detection in two- and three-dimensional images is suggested. Also, a discussion problem is included in the book: A derivative is defined as the limit of the relation of the increment of the function to the increment of the argument as the latter tends to zero. Is it not better to estimate derivatives as the relation of the increment of the function to the optimal increment of the argument instead of taking exceedingly small increment which leads to errors? This book addresses all above questions and provide the answers.
Image Schema Theory and Mathematical Cognition (Mathematics in Mind)
by Marcel DanesiThis book uses blending theory in math cognition, and assesses the main aspect of this theory, called image schema theory. Applied work in math pedagogy has used this theory, but no work has assessed its validity. This book provides an overall assessment of the theory with regard to its validity in the study of math cognition. Overall, this book presents image schema theory as it has evolved today to mathematicians, cognitive scientists, and math educators, deriving from it any concrete implications for modeling math in computer science and, on the other side, for making math pedagogy more effective.
Image Statistics in Visual Computing
by Tania Pouli Erik Reinhard Douglas W. CunninghamTo achieve the complex task of interpreting what we see, our brains rely on statistical regularities and patterns in visual data. Knowledge of these regularities can also be considerably useful in visual computing disciplines, such as computer vision, computer graphics, and image processing. The field of natural image statistics studies the regular
Images and Identities: Puerto Rican in Two World Contexts
by Asela Rodriguez LagunaFirst published in 1987. Routledge is an imprint of Taylor & Francis.
An Imaginary Tale: The Story of √-1
by Paul J. NahinToday complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.Some images inside the book are unavailable due to digital copyright restrictions.
An Imaginary Tale
by Paul J. NahinToday complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.Some images inside the book are unavailable due to digital copyright restrictions.
An Imaginary Tale
by Paul J. NahinToday complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them.In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times.Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.
Imagine Math
by Michele EmmerImagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. This book is intended to contribute to grasping how much that is interesting and new is happening in the relationships between mathematics, imagination and culture. With a look at the past, at figures and events, that help to understand the phenomena of today. It is no coincidence that this volume contains an homage to the great Italian artist of the 1700s, Andrea Pozzo, and his perspective views. Theatre, art and architecture are the topics of choice, along with music, literature and cinema. No less important are applications of mathematics to medicine and economics. The treatment is rigorous but captivating, detailed but full of evocations, an all-embracing look at the world of mathematics and culture
Imagine Math 6: Between Culture And Mathematics
by Michele Emmer Marco AbateImagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine combining music, art, poetry, literature, architecture and cinema with mathematics. Imagine the unpredictable and sometimes counterintuitive applications of mathematics in all areas of human endeavour. Imagination and mathematics, imagination and culture, culture and mathematics.This sixth volume in the series begins with a homage to the architect Zaha Hadid, who died on March 31st, 2016, a few weeks before the opening of a large exhibition of her works in Palazzo Franchetti in Venice, where all the Mathematics and Culture conferences have taken place in the last years. A large section of the book is dedicated to literature, narrative and mathematics including a contribution from Simon Singh. It discusses the role of media in mathematics, including museums of science, journals and movies. Mathematics and applications, including blood circulation and preventing crimes using earthquakes, is also addressed, while a section on mathematics and art examines the role of math in design. A large selection presents photos of mathematicians and mathematical objects by Vincent Moncorge. Discussing all topics in a way that is rigorous but captivating, detailed but full of evocations, it offers an all-embracing look at the world of mathematics and culture.
Imagine Math 8: Dreaming Venice
by Michele Emmer Marco AbateThis eighth volume of Imagine Math is different from all the previous ones. The reason is very clear: in the last two years, the world changed, and we still do not know what the world of tomorrow will look like. Difficult to make predictions. This volume has a subtitle Dreaming Venice. Venice, the dream city of dreams, that miraculous image of a city on water that resisted for hundreds of years, has become in the last two years truly unreachable. Many things tie this book to the previous ones. Once again, this volume also starts like Imagine Math 7, with a homage to the Italian artist Mimmo Paladino who created exclusively for the Imagine Math 8 volume a new series of ten original and unique works of art dedicated to Piero della Francesca. Many artists, art historians, designers and musicians are involved in the new book, including Linda D. Henderson and Marco Pierini, Claudio Ambrosini and Davide Amodio. Space also for comics and mathematics in a Disney key. Many applications, from Origami to mathematical models for world hunger. Particular attention to classical and modern architecture, with Tullia Iori.As usual, the topics are treated in a way that is rigorous but captivating, detailed and full of evocations. This is an all-embracing look at the world of mathematics and culture.
Imaging Heat and Mass Transfer Processes
by Pradipta Kumar Panigrahi Krishnamurthy MuralidharImaging Heat and Mass Transfer Processes: Visualization and Analysis applies Schlieren and shadowgraph techniques to complex heat and mass transfer processes. Several applications are considered where thermal and concentration fields play a central role. These include vortex shedding and suppression from stationary and oscillating bluff bodies such as cylinders, convection around crystals growing from solution, and buoyant jets. Many of these processes are unsteady and three dimensional. The interpretation and analysis of images recorded are discussed in the text.
Imaging the Cheops Pyramid
by H. D. BuiIn this book Egyptian Archeology and Mathematics meet. The author is an expert in theories and applications in Solid Mechanics and Inverse Problems, a former professor at Ecole Polytechnique and now works with Electricité de France on maintenance operations on nuclear power plants. In the Autumn of 1986, after the end of the operation on the King's chamber conducted under the Technological and Scientific Sponsorship of EDF, to locate a cavity, he was called to solve a mathematical inverse problem, to find the unknown tomb of the King and the density structure of the whole pyramid based on measurements of microgravity made inside and outside of the pyramid. This book recounts the various search operations on the pyramid of Cheops made at the request of the Egyptian and French authorities in 1986-1987. After the premature end of the Cheops operation in the Autumn of 1986, following the fiasco of unsuccessful drillings in the area suspected by both architects G. Dormion and J.P. Goidin and microgravity auscultation, EDF and CPGF (a geophysical company) teams continued their researches with measurements already made, trying this time an inversion of the Newton gravity equation for the entire pyramid and using another theoretical team led by the author. The inverse problem solution confirmed the results of auscultations, but found no cavity. However, the image of the average density at the surface of the entire pyramid forms a sort of square "spiral" probably related to the construction method. In 2000, Jean-Pierre Houdin considered the author's results of 1988 as a confirmation of his theory of the internal ramp tunnel. Since then the author has done additional research and found that classical theories of the construction based on degrees and the particular mode of stones filling can also report the same densitogram. The book is richly illustrated with color figures. It is dotted with information concerning Physics, Mechanics and the History of Egyptian Antiquities. The book ends with the greatest mystery of the pyramid about the unknown tomb of the King and a dream to see the tomb at an unexpected place.
Imaging, Vision and Learning Based on Optimization and PDEs: IVLOPDE, Bergen, Norway, August 29 – September 2, 2016 (Mathematics and Visualization)
by Xue-Cheng Tai Egil Bae Marius LysakerThis volume presents the peer-reviewed proceedings of the international conference Imaging, Vision and Learning Based on Optimization and PDEs (IVLOPDE), held in Bergen, Norway, in August/September 2016. The contributions cover state-of-the-art research on mathematical techniques for image processing, computer vision and machine learning based on optimization and partial differential equations (PDEs). It has become an established paradigm to formulate problems within image processing and computer vision as PDEs, variational problems or finite dimensional optimization problems. This compact yet expressive framework makes it possible to incorporate a range of desired properties of the solutions and to design algorithms based on well-founded mathematical theory. A growing body of research has also approached more general problems within data analysis and machine learning from the same perspective, and demonstrated the advantages over earlier, more established algorithms. This volume will appeal to all mathematicians and computer scientists interested in novel techniques and analytical results for optimization, variational models and PDEs, together with experimental results on applications ranging from early image formation to high-level image and data analysis.
Imagining Numbers: (particularly The Square Root Of Minus Fifteen)
by Barry MazurHow the elusive imaginary number was first imagined, and how to imagine it yourselfImagining Numbers (particularly the square root of minus fifteen) is Barry Mazur's invitation to those who take delight in the imaginative work of reading poetry, but may have no background in math, to make a leap of the imagination in mathematics. Imaginary numbers entered into mathematics in sixteenth-century Italy and were used with immediate success, but nevertheless presented an intriguing challenge to the imagination. It took more than two hundred years for mathematicians to discover a satisfactory way of "imagining" these numbers. With discussions about how we comprehend ideas both in poetry and in mathematics, Mazur reviews some of the writings of the earliest explorers of these elusive figures, such as Rafael Bombelli, an engineer who spent most of his life draining the swamps of Tuscany and who in his spare moments composed his great treatise "L'Algebra". Mazur encourages his readers to share the early bafflement of these Renaissance thinkers. Then he shows us, step by step, how to begin imagining, ourselves, imaginary numbers.
IMF: Recent Economic Developments (Imf Working Papers #Imf Staff No. 97/107)
by International Monetary FundA report from the International Monetary Fund.
IMF: Recent Economic Developments (Imf Working Papers #Imf Staff No. 97/107)
by International Monetary FundA report from the International Monetary Fund.
IMF: Recent Economic Developments (Imf Staff Country Reports #Imf Staff No. 97/107)
by International Monetary FundA report from the International Monetary Fund.
IMF: Recent Economic Developments (Imf Working Papers #Imf Staff No. 97/107)
by International Monetary FundA report from the International Monetary Fund.
IMF: Recent Economic Developments (Imf Working Papers #Imf Staff No. 97/107)
by International Monetary FundA report from the International Monetary Fund.
IMF: Recent Economic Developments (Imf Working Papers #Imf Staff No. 97/107)
by International Monetary FundA report from the International Monetary Fund.
IMF: Recent Economic Developments (Imf Working Papers #Imf Staff No. 97/107)
by International Monetary FundA report from the International Monetary Fund.
Imitation Market Modeling in Digital Economy: Game Theoretic Approaches (Lecture Notes in Networks and Systems #368)
by Elena G. PopkovaThis book includes the best studies on the results of the International Scientific and Practical Conference “New behaviors of market players in the digital economy,” which was held by the Institute of Scientific Communications on July 8, 2021, online, in YouTube format. This book is devoted to the study of digital economy markets from the standpoint of various market players—society (consumers), entrepreneurship, and the state—from the standpoint of various sciences—economic, managerial, social, and legal—which ensures the multidisciplinarity of the book. The uniqueness of the book lies in the application of a new scientific and methodological approach to the study of digital economy markets—simulation modeling. The advantages of a game-based scientific and methodological approach to reducing the uncertainty of economic processes and systems—a combination of quantitative and qualitative analytical methods, a systematic consideration of economic processes and systems from a socio-economic point of view—make it especially suitable for studying digital economy markets. The book identifies the impact of globalization and digitalization on the modern economy and industry markets. The trends and features of the use of advanced technologies in the digital economy markets are studied. The modern practices of business management and business integration in the digital economy are considered. The foundations of economic security and sustainable development of markets and enterprises in the digital economy are revealed. The book is suitable for scientists studying the markets of the digital economy, who will find in it scientific and methodological recommendations and developments on the application of game theory, as well as ready simulation models of the digital economy markets.
Immanent Reasoning or Equality in Action: A Plaidoyer For The Play Level (Logic, Argumentation And Reasoning Ser. #18)
by Shahid Rahman Zoe McConaughey Ansten Klev Nicolas ClerboutThis monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory (CTT). The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion.One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning.According to this perspective the emergence of concepts are not only games of giving and asking for reasons (games involving Why-questions), they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How.