Basics of Linear Algebra, Mathematical Analysis, Numerical Analysis
Assessment methods and Criteria
The final examination consists of two parts: an oral exam and a lab exam. -The lab exam consists in developing a project and some exercises in the format of open-ended. The lab portion of the final examination serves to assess the capability of the student to put a problem of digital image processing into context, find a solution and to give a report on the results obtained. - The oral exam can be taken only for the first module. In the oral exam, the student will be required to illustrate results presented during the course and will be required to solve problems regarding Computational and differential Geometry in order to evaluate her/his knowledge and comprehension of the arguments covered as well as the capacity to apply them. The student may choose instead to take one midterm exam.
The complete final examination is passed if all two parts (oral, lab) are successfully passed. Final marks are given using the numerical range 0-30, and will be communicated immediately after the two parts.
A brief overview of Euclidean and affine Geometry, geometric transformations. Differential geometry of curves and surfaces in E3. Bézier curves and Bernstein polynomials. Spline (degree 2 and 3), Bézier surfaces patches, Coons surfaces. Points and curves interpolation, Hermite interpolation.
Lessons and praticals
A.Goetz: "Introduction to Differential Geometry" Addison Wesley Publ. Comp. (1970) M.M. Mortenson, Modelli Geometrici in Computer Graphics, McGraw-Hill, 1989. G. Farin, D. Hansford, The essentials of CAGD, AK Peters, 2000. J.J. Risler: Méthodes Mathématiques pour la C.A.O., Recherches en Mathématiques Appliqées, 18, Masson, 1991.
Main properties of digital images and image representation. Basic algorithms for image analysis (edge detection, denoising, segmentation). Image coding and image transforms, introduction to discrete Fourier, Wavelet, and frame transform. Notes on segmentation and the calculus of variations. Introduction to image processing in MATLAB.
Lessons and computer sessions
K.R. Castleman, Digital Image Processing, Prentice Hall, 1996. W.L. Briggs, Van E. Henson, The DFT, SIAM, 1995. S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1999.