Introduction to Image Processing
A.Y. 2024/2025
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.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Prerequisites for admission
Basics of Linear Algebra, Mathematical Analysis, Numerical Analysis, Statistics.
Assessment methods and Criteria
The final examination consists of two parts: an oral exam (first part), and a lab and written exam (second part)
-The lab exam consists in developing a project (maximum points of the laboratory test 18/30), and the written test of some some open-ended questions (maximum points of the written test 15/30). 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 (of the oral exam) to take one midterm written exam.
The complete final examination is passed if all parts (oral, lab, written) are successfully passed. Final marks are given using the numerical range 0-30, the value is obtained with an appropriate average of the values of each test, and it will be communicated immediately after the all parts.
-The lab exam consists in developing a project (maximum points of the laboratory test 18/30), and the written test of some some open-ended questions (maximum points of the written test 15/30). 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 (of the oral exam) to take one midterm written exam.
The complete final examination is passed if all parts (oral, lab, written) are successfully passed. Final marks are given using the numerical range 0-30, the value is obtained with an appropriate average of the values of each test, and it will be communicated immediately after the all parts.
prima parte
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:
http://www.mat.unimi.it/users/alzati/personale/elab.html
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:
http://www.mat.unimi.it/users/alzati/personale/elab.html
seconda parte
Course syllabus
Main properties of digital images and image representation. Point operators and local operators. Basic algorithms for image analysis (edge detection, denoising, segmentation).
Mathematical morphology. Image coding and image transforms, introduction to discrete Fourier, Wavelet, and frame transform. Notes on neural networks based algorithms. Introduction to image processing in MATLAB.
Mathematical morphology. Image coding and image transforms, introduction to discrete Fourier, Wavelet, and frame transform. Notes on neural networks based algorithms. Introduction to image processing in MATLAB.
Teaching methods
Lectures and computer sessions
Teaching Resources
Lecture Notes
References (not mandatory)
Kristian Bredies, Dirk Lorenz, Mathematical Image Processing,
Springer-Birkhäuser, 2018.
Digital Image Processing
3rd Ed. (DIP/3e) by Gonzalez and Woods
W.L. Briggs, Van E. Henson, The DFT, SIAM, 1995.
S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1999.
Ariel web page
References (not mandatory)
Kristian Bredies, Dirk Lorenz, Mathematical Image Processing,
Springer-Birkhäuser, 2018.
Digital Image Processing
3rd Ed. (DIP/3e) by Gonzalez and Woods
W.L. Briggs, Van E. Henson, The DFT, SIAM, 1995.
S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1999.
Ariel web page
prima parte
MAT/03 - GEOMETRY - University credits: 3
Lessons: 27 hours
Professor:
Alzati Alberto
seconda parte
MAT/08 - NUMERICAL ANALYSIS - University credits: 3
Practicals: 12 hours
Laboratories: 24 hours
Laboratories: 24 hours
Professor:
Naldi Giovanni
Educational website(s)
Professor(s)
Reception:
Monday 14.00-16.00
Office n° 2103, II floor, c/o Dip. Mat., via Saldini 50