000 04449nam a22005175i 4500
001 978-3-031-02594-5
003 DE-He213
005 20240730163500.0
007 cr nn 008mamaa
008 220601s2017 sz | s |||| 0|eng d
020 _a9783031025945
_9978-3-031-02594-5
024 7 _a10.1007/978-3-031-02594-5
_2doi
050 4 _aQA1-939
072 7 _aPB
_2bicssc
072 7 _aMAT000000
_2bisacsh
072 7 _aPB
_2thema
082 0 4 _a510
_223
100 1 _aPreusser, Tobias.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978809
245 1 0 _aStochastic Partial Differential Equations for Computer Vision with Uncertain Data
_h[electronic resource] /
_cby Tobias Preusser, Robert M. Kirby, Torben Pätz.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXIV, 150 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSynthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography and Imaging,
_x2469-4223
505 0 _aPreface -- Notation -- Introduction -- Partial Differential Equations and Their Numerics -- Review of PDE-Based Image Processing -- Numerics of Stochastic PDEs -- Stochastic Images -- Image Processing and Computer Vision with Stochastic Images -- Sensitivity Analysis -- Conclusions -- Bibliography -- Authors' Biographies .
520 _aIn image processing and computer vision applications such as medical or scientific image data analysis, as well as in industrial scenarios, images are used as input measurement data. It is good scientific practice that proper measurements must be equipped with error and uncertainty estimates. For many applications, not only the measured values but also their errors and uncertainties, should be-and more and more frequently are-taken into account for further processing. This error and uncertainty propagation must be done for every processing step such that the final result comes with a reliable precision estimate. The goal of this book is to introduce the reader to the recent advances from the field of uncertainty quantification and error propagation for computer vision, image processing, and image analysis that are based on partial differential equations (PDEs). It presents a concept with which error propagation and sensitivity analysis can be formulated with a set of basic operations.The approach discussed in this book has the potential for application in all areas of quantitative computer vision, image processing, and image analysis. In particular, it might help medical imaging finally become a scientific discipline that is characterized by the classical paradigms of observation, measurement, and error awareness. This book is comprised of eight chapters. After an introduction to the goals of the book (Chapter 1), we present a brief review of PDEs and their numerical treatment (Chapter 2), PDE-based image processing (Chapter 3), and the numerics of stochastic PDEs (Chapter 4). We then proceed to define the concept of stochastic images (Chapter 5), describe how to accomplish image processing and computer vision with stochastic images (Chapter 6), and demonstrate the use of these principles for accomplishing sensitivity analysis (Chapter 7). Chapter 8 concludes the book and highlights new research topics for the future.
650 0 _aMathematics.
_911584
650 0 _aImage processing
_xDigital techniques.
_94145
650 0 _aComputer vision.
_978810
650 1 4 _aMathematics.
_911584
650 2 4 _aComputer Imaging, Vision, Pattern Recognition and Graphics.
_931569
700 1 _aKirby, Robert M.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978811
700 1 _aPätz, Torben.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978812
710 2 _aSpringerLink (Online service)
_978813
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031014666
776 0 8 _iPrinted edition:
_z9783031037221
830 0 _aSynthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography and Imaging,
_x2469-4223
_978814
856 4 0 _uhttps://doi.org/10.1007/978-3-031-02594-5
912 _aZDB-2-SXSC
942 _cEBK
999 _c84662
_d84662