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Partial Differential Equation Methods for Image Inpainting
This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate students in mathematics with an interest in image processing and mathematical analysis.
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging
This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model...
Medical Image Understanding and Analysis
This book constitutes the refereed proceedings of the 26th Conference on Medical Image Understanding and Analysis, MIUA 2022, held in Cambridge, UK, in July 2022. The 65 full papers presented were carefully reviewed and selected from 95 submissions. They were organized according to following topical sections: biomarker detection; image registration, and reconstruction; image segmentation; generative models, biomedical simulation and modelling; classification; image enhancement, quality assessment, and data privacy; radiomics, predictive models, and quantitative imaging. Chapter “FCN-Transformer Feature Fusion for Polyp Segmentation” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
From Photography to 3D Models and Beyond: Visualizations in Archaeology
This book explores the history of visual technology and archaeology and outlines how the introduction of interactive 3D computer modelling to the discipline parallels very closely the earlier integration of photography into archaeological fieldwork.
Medical Image Understanding and Analysis
This book constitutes the refereed proceedings of the 23rd Conference on Medical Image Understanding and Analysis, MIUA 2019, held in Liverpool, UK, in July 2019. The 43 full papers presented were carefully reviewed and selected from 70 submissions. There were organized in topical sections named: oncology and tumour imaging; lesion, wound and ulcer analysis; biostatistics; fetal imaging; enhancement and reconstruction; diagnosis, classification and treatment; vessel and nerve analysis; image registration; image segmentation; ophthalmic imaging; and posters.
Artificial Intelligence, Blockchain, Computing and Security Volume 1
This book contains the conference proceedings of ICABCS 2023, a non-profit conference with the objective to provide a platform that allows academicians, researchers, scholars and students from various institutions, universities and industries in India and abroad to exchange their research and innovative ideas in the field of Artificial Intelligence, Blockchain, Computing and Security. It explores the recent advancement in field of Artificial Intelligence, Blockchain, Communication and Security in this digital era for novice to profound knowledge about cutting edges in artificial intelligence, financial, secure transaction, monitoring, real time assistance and security for advanced stage lear...
Statistical and Computational Inverse Problems
This book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results. The techniques are applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems. Contains detailed examples throughout and includes a chapter on case studies where such methods have been implemented in biomedical engineering.
Indra's Pearls
Felix Klein, one of the great nineteenth-century geometers, rediscovered in mathematics an idea from Eastern philosophy: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple co-existing symmetries. For a century these ideas barely existed outside the imagination of mathematicians. However in the 1980s the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.
Mathematical Aspects of Deep Learning
A mathematical introduction to deep learning, written by a group of leading experts in the field.
