Abstract
Image processing and computer vision are growing research fields that take advantage of the increasing power or modern computers linked with sophisticated techniques coming from many fields of expertise and in particular from mathematics. We present an introduction to some problems in computer vision and image processing and to some mathematical techniques and concepts that are nowadays routinely used to approach them.
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Notes
- 1.
All derivatives have to be understood in a weak sense throughout the text.
- 2.
Note that the unknown is now named u and hence I might denote the input image from now on.
- 3.
- 4.
The determination of the true 3D motion of objects is known as scene flow and will not be analyzed in these notes. The interested reader can refer to [26] and references therein.
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Acknowledgements
The author is grateful to the organizers and scientific committee of the Jacques-Louis Lions Spanish-French school for the invitation. This research was Partially supported by Spanish MINECO grant MTM 2014-54388. This work is dedicated to the memory of Vicent Caselles.
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Baeza, A. (2016). Mathematical Methods in Image Processing and Computer Vision. In: Higueras, I., Roldán, T., Torrens, J. (eds) Numerical Simulation in Physics and Engineering. SEMA SIMAI Springer Series, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-32146-2_3
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