Introduction to Image Processing
A.Y. 2026/2027
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 cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Prerequisites for admission
Basic notions of Geometry, Mathematical Analysis, Statistics, and Numerical Analysis (for reference: courses in Mathematical Analysis 1, Geometry 1, Mathematical Analysis 2, Geometry 2, Numerical Analysis 1)
Assessment methods and Criteria
The examination typically consists of a written component (covering the first part of the course) or, alternatively, an oral exam, together with a laboratory assessment and a written test (covering the second part of the course).
For the first part of the course:
a written test at the end of this part of the course;
if the written test is not passed, an oral examination must be taken during the scheduled exam sessions.
The oral examination concerns only the first part of the course. During the oral exam, students will be asked to present some of the results included in the syllabus, as well as to solve a number of differential and computational geometry problems, in order to assess their knowledge and understanding of the topics covered and their ability to apply them.
A single midterm written test, consisting of open-ended questions, is provided as an alternative to the oral examination.
The laboratory assessment consists in the development of a project (maximum score: 18/30), while the written test consists of open-ended questions (maximum score: 15/30).
The laboratory assessment aims to evaluate the student's ability to frame a digital image analysis problem, identify an appropriate solution, and report on the obtained results.
The exam is considered passed if both the first and the second parts of the course are successfully completed. The final grade is expressed out of 30 and is determined as a suitable weighted average of the marks obtained. It will be communicated immediately after all required components have been successfully completed.
For the first part of the course:
a written test at the end of this part of the course;
if the written test is not passed, an oral examination must be taken during the scheduled exam sessions.
The oral examination concerns only the first part of the course. During the oral exam, students will be asked to present some of the results included in the syllabus, as well as to solve a number of differential and computational geometry problems, in order to assess their knowledge and understanding of the topics covered and their ability to apply them.
A single midterm written test, consisting of open-ended questions, is provided as an alternative to the oral examination.
The laboratory assessment consists in the development of a project (maximum score: 18/30), while the written test consists of open-ended questions (maximum score: 15/30).
The laboratory assessment aims to evaluate the student's ability to frame a digital image analysis problem, identify an appropriate solution, and report on the obtained results.
The exam is considered passed if both the first and the second parts of the course are successfully completed. The final grade is expressed out of 30 and is determined as a suitable weighted average of the marks obtained. It will be communicated immediately after all required components have been successfully completed.
Elaborazione dell'immagine (prima parte)
Course syllabus
Review of Euclidean and affine geometry; geometric transformations.
Bézier curves and Bernstein polynomials.
Spline curves, with particular emphasis on degrees 2 and 3.
Bézier surfaces and their joining.
Coons patches.
Interpolation of points and curves; cubic Hermite interpolation.
Planar representation of 3D objects.
Projective cameras and an introduction to epipolar geometry.
Bézier curves and Bernstein polynomials.
Spline curves, with particular emphasis on degrees 2 and 3.
Bézier surfaces and their joining.
Coons patches.
Interpolation of points and curves; cubic Hermite interpolation.
Planar representation of 3D objects.
Projective cameras and an introduction to epipolar geometry.
Teaching methods
Lectures and classroom exercise sessions
Teaching Resources
Reference texts (for consultation)
M. M. Mortenson: "Modelli geometrici in computer graphics" ed. Mc Graw-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
R. Hartley-A.Zisserman: "Multiple View Geometry in computer vision" Cambridge Univ. Press, 2002.
M. M. Mortenson: "Modelli geometrici in computer graphics" ed. Mc Graw-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
R. Hartley-A.Zisserman: "Multiple View Geometry in computer vision" Cambridge Univ. Press, 2002.
Elaborazione dell'immagine (seconda parte)
Course syllabus
Representation and properties of digital images. Point operators and local operators.
Selected algorithms for image analysis (segmentation, edge detection, denoising). Mathematical morphology.
Encoding and transforms. Introduction to the discrete Fourier transform, wavelets, and frames. Introduction to algorithms based on neural networks: MLP networks and convolutional networks.
Introduction to image analysis in MATLAB.
Selected algorithms for image analysis (segmentation, edge detection, denoising). Mathematical morphology.
Encoding and transforms. Introduction to the discrete Fourier transform, wavelets, and frames. Introduction to algorithms based on neural networks: MLP networks and convolutional networks.
Introduction to image analysis in MATLAB.
Teaching methods
Lectures and in-class exercise sessions, computer-based laboratory.
Teaching Resources
Notes
Reference texts (for consultation)
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.
Reference texts (for consultation)
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.
Modules or teaching units
Elaborazione dell'immagine (prima parte)
MATH-02/B - Geometry - University credits: 3
Lessons: 27 hours
Professor:
Alzati Alberto
Elaborazione dell'immagine (seconda parte)
MATH-05/A - Numerical Analysis - University credits: 3
Exercises: 12 hours
Laboratories: 24 hours
Laboratories: 24 hours
Professor:
Naldi Giovanni
Professor(s)
Reception:
Monday 14.00-16.00
Office n° 2103, II floor, c/o Dip. Mat., via Saldini 50