Introduction to Image Processing

A.Y. 2021/2022
Overall hours
MAT/03 MAT/08
Learning objectives
The course presents the main concepts that are the basis of computer graphics and digital image analysis. The emphasis will be put on the issues and basic techniques.
Expected learning outcomes
Learning the basics, geometric and numerical, for CAD; learning of the main techniques of digital image processing, implementation of algorithms for the analysis of images.
Course syllabus and organization

Single session

Lesson period
Second semester
Live lectures (on line) in the form of interactive lessons recorded and made available to students. MATLAB online laboratory.
Asynchronous lectures for deepen some topics. Blended Tutoring for teaching support.
Prerequisites for admission
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.
mod. 1
Course syllabus
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.
Teaching methods
Lectures and praticals
Teaching Resources
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.

web page:
mod. 2
Course syllabus
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.
Teaching methods
Lectures and computer sessions
Teaching Resources
(not mandatory)
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.

Ariel web page:
mod. 1
MAT/03 - GEOMETRY - University credits: 3
Lessons: 27 hours
Professor: Alzati Alberto
mod. 2
MAT/08 - NUMERICAL ANALYSIS - University credits: 3
Practicals: 12 hours
Laboratories: 24 hours
Professor: Naldi Giovanni
Monday 14.00-16.00
Office n° 2103, II floor, c/o Dip. Mat., via Saldini 50