Unit MATHEMATICAL METHODS FOR ARTIFICIAL INTELLIGENCE
- Course
- Informatics
- Study-unit Code
- A002083
- Curriculum
- Artificial intelligence
- Teacher
- Gianluca Vinti
- CFU
- 12
- Course Regulation
- Coorte 2021
- Offered
- 2022/23
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
APPLIED IMAGE AND SIGNAL PROCESSING
| Code | A002085 |
|---|---|
| CFU | 6 |
| Teacher | Gianluca Vinti |
| Teachers |
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| Hours |
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| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Academic discipline | MAT/05 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | English |
| Contents | Introduction to the course • Summary of the Fourier transform and its properties. • Exact sampling and approximate sampling • Generalized sampling operators and sampling- Kantorovich: their properties and main results. • Notions on images and on the applications of the theorem of sampling to images • MATLAB and its applications to image processing • GIMP, IMAGEJ, and their applications to image processing • Image Processing Algorithms: registration, segmentation, thresholding, morphological operators, smoothing and sharpening operators, etc. • Image acquisition instrumentation: CT, RNM, Thermography. • Medical diagnostics: -General introduction to medical diagnostics - Vascular, diagnostic and interventional surgery • Possible visits: - Visit to the Diagnostic Imaging Department: radiography (RX), computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, cardioCT. -Visit to the section of vascular surgery: endovascular treatments -Visit the ophthalmology section • Visit to the Center for Research on Atomic Pollution and the Environment (Hot-Box, thermography, thermal bridges and pollution). • Non-invasive diagnostics in the engineering field: image processing for seismic vulnerability • Laboratories of Applied Mathematics on topics of the course |
| Reference texts | Notes and slides of the teacher. It will be recommended some books. |
| Educational objectives | Learning outcomes: The course provides knowledge of the major concepts of image processing with particular reference to the medical ones. The main knowledge (descriptor Dublin 1) will be acquired: • knowledge of the reconstruction of signals and images by sampling; • Knowledge of the main concepts and analysis techniques and image processing; • knowledge of the main problems of medical diagnostics and application of algorithms for the improvement of image; The main skills acquired (ability to apply the knowledge gained descriptor Dublin 2, and to take with independent judgment the appropriate approach, the Dublin descriptor 3) will be: • analytical skills and image processing whose purpose is to medical diagnosis; • ability to develop a line of reasoning that leads the student to identify the methods of solving the problem in question; • ability to identify the right approach to the solution of the problem with an eye toward the medical diagnostics. |
| Prerequisites | Knowledge of reconstruction of signals and images by sampling; Knowledge of the main concepts and analysis techniques and image processing; Knowledge of the main problems of medical diagnostics and of the application of algorithms for the improvement of image. |
| Teaching methods | The course is structured as follows: 1) Lectures on all the topics of the course; 2) Classroom workshop: 2/3 workshops on problems where topics from the course are used 3) Guided tours of 4 hours each at the departments of the Santa Maria della Misericordia Hospital in Perugia (radiology and / or vascular and / or ophthalmology surgery) and / or at Engineering. |
| Other information | Attendance is strongly recommended for all lessons. |
| Learning verification modality | Oral exam. The verification of the educational objectives of teaching (examination) include an oral exam. The oral exam will be held on the dates set out in the examinations of the CdS calendar. The oral examination, consists of a discussion of the duration not exceeding 40 minutes each aimed at verifying: i) the level of knowledge of the theoretical and laboratory course content (Dublin descriptor 1), ii) the level of expertise in exposing the logical and mathematical reasoning skills (descriptor Dublin 2), iii) the independence of judgment (Dublin descriptor 3) to propose the most appropriate approach to argue what is required. The oral examination also aims to verify the student's ability to present with properties of language questions proposed by the Commission, to support a dialectical relationship during discussion and dimostrate logical-deductive ability and synthetic exposition (descriptor Dublin 4). The final mark will be made by the Commission in thirty. |
| Extended program | Introduction to the course • Summary of the Fourier transform and its properties. • Exact sampling and approximate sampling • Generalized sampling operators and sampling- Kantorovich: their properties and main results. • Notions on images and on the applications of the theorem of sampling to images • MATLAB and its applications to image processing • GIMP, IMAGEJ, and their applications to image processing • Image Processing Algorithms: registration, segmentation, thresholding, morphological operators, smoothing and sharpening operators, etc. • Image acquisition instrumentation: CT, RNM, Thermography. • Medical diagnostics: -General introduction to medical diagnostics - Vascular, diagnostic and interventional surgery • Possible visits: - Visit to the Diagnostic Imaging Department: radiography (RX), computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, cardioCT. -Visit to the section of vascular surgery: endovascular treatments -Visit the ophthalmology section • Visit to the Center for Research on Atomic Pollution and the Environment (Hot-Box, thermography, thermal bridges and pollution). • Non-invasive diagnostics in the engineering field: image processing for seismic vulnerability • Laboratories of Applied Mathematics on topics of the course |
NUMERICAL METHODS FOR INFORMATION TECHNOLOGIES
| Code | A002084 |
|---|---|
| CFU | 6 |
| Teacher | Bruno Iannazzo |
| Teachers |
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| Hours |
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| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Academic discipline | MAT/08 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | English (or Italian if all students require it). |
| Contents | Selected topics in Numerical Analysis related to approximation, linear algebra and non-linear optimization and their applications to data science and information technologies |
| Reference texts | For the numerical analysis topics: J. Stoer, R. Bulirsch. Introduction to numerical analysis. Springer. 2013; material provided by the teacher. For the optional topics, we will use a specific reference, that will be communicated during the lectures. |
| Educational objectives | Get into mathematical aspects related to some important data science and information technologies applications. Getting in touch with all mathematical modeling aspects: abstraction, modelisting interpretation, computer simulation (using the software Matlab or Octave). |
| Prerequisites | Numerical analysis (e.g. LU factorization, interpolation theory). Linear algebra, calculus with several real variables. Elementary computer science. The optional part may have different prerequisites (e.g. differential geometry). |
| Teaching methods | Face-to-face lectures and laboratory sessions, using Matlab/Octave |
| Learning verification modality | The exams consists in a detailed discussion of some topics of the course. In the evaluation, the comprehension will be priviledged with respect to the memorization. The exam's duration is about one hour. For students attending the course, the exams will have two terms: - mid-term, where the student will give an half-hour seminar of on a topic related to the course but not taught (for instance, an application or the proof of a theorem); - a final exam that consists in a group project or a seminar on the contend of a scientific publication; some extra grades can be obtained through (non-mandatory): - a simple laboratory test during the laboratory sessions (it might be substituted with some further lectures); - the solution of some exercises given during the course. |
| Extended program | Least square approximation and singular value decomposition (principal component analysis). QR factorization and Nonnegative matrix factorization. Matrices with positivity structure, eigenvalue computation. Non-linear optimization. During the course, some applications to data science and information technologies will be taken into account: data fitting, complex networks; classification problems; machine learning. Spline interpolation. B-splines. Trigonometric interpolation. Fast Fourier Transform. Application to digital filtering, curves and surfaces in computer graphics. Manifold optimization. |