Mathematical Methods In Computer Vision

Mathematical Methods in Computer Vision

This volume comprises some of the key work presented at two IMA Workshops on Computer Vision during fall of 2000. Recent years have seen significant advances in the application of sophisticated mathematical theories to the problems arising in image processing. Basic issues include image smoothing and denoising, image enhancement, morphology, image compression, and segmentation (determining boundaries of objects-including problems of camera distortion and partial occlusion). Several mathematical approaches have emerged, including methods based on nonlinear partial differential equations, stochastic and statistical methods, and signal processing techniques, including wavelets and other transform theories. Shape theory is of fundamental importance since it is the bottleneck between high and low level vision, and formed the bridge between the two workshops on vision. The recent geometric partial differential equation methods have been essential in throwing new light on this very difficult problem area. Further, stochastic processes, including Markov random fields, have been used in a Bayesian framework to incorporate prior constraints on smoothness and the regularities of discontinuities into algorithms for image restoration and reconstruction. A number of applications are considered including optical character and handwriting recognizers, printed-circuit board inspection systems and quality control devices, motion detection, robotic control by visual feedback, reconstruction of objects from stereoscopic view and/or motion, autonomous road vehicles, and many others.

Mathematical Methods in Image Processing and Inverse Problems

This book contains eleven original and survey scientific research articles arose from presentations given by invited speakers at International Workshop on Image Processing and Inverse Problems, held in Beijing Computational Science Research Center, Beijing, China, April 21–24, 2018. The book was dedicated to Professor Raymond Chan on the occasion of his 60th birthday. The contents of the book cover topics including image reconstruction, image segmentation, image registration, inverse problems and so on. Deep learning, PDE, statistical theory based research methods and techniques were discussed. The state-of-the-art developments on mathematical analysis, advanced modeling, efficient algorithm and applications were presented. The collected papers in this book also give new research trends in deep learning and optimization for imaging science. It should be a good reference for researchers working on related problems, as well as for researchers working on computer vision and visualization, inverse problems, image processing and medical imaging.

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging