The lecture of this PhD course will follow this schedule:
Thursday 23/11/2023 8.30  12.30 and 14.00  18.00
Friday 24/11/2023 8.30  12.30 and 14.00  18.00
Monday 27/11/2023 8.30  12.30 and 14.00  18.00
The room for all these lectures is:
Aula Seminari, First floor, Building U14, Viale Sarca 336, 20125, Milan (Italy)
Department of Informatics, Systems and Communication (DISCo)
University of MilanBicocca
Course Syllabus
Titolo
Geometry processing and machine learning for geometric data
Docente(i)
Simone Melzi, Riccardo Marin (UNIVERSITY OF TÜBINGEN)
Lingua
Inglese
Breve descrizione
Course Organization:
The course will consists of three full days lessons with 4 hours in the morning (8.30  12.30) and 4 hours in the afternoon (14.00  18.00).
Course Overview:
After an introduction to geometric data and related applications (respectively sections 1 and 2) the rest of the course will be divided in five sections (sections from 3 to 7) each of which consists of 2 hours of theory and 2 hours of lab in which an implementation of the main algorithms and results discussed in the related theory will be rpovided and discussed witht he teachers. At the end of the course, each student will own a personal implementation/demo of at least one architecture or algorithm related to the topic of each section.
Table of Contents:

Introduction to 3D data, possible representations and geometric quantities (2h):
1.1 point clouds
1.2 meshes
1.3 graphs
1.4 volumetric
1.5 implicit surfaces 
Applications (2h):
2.1 retrieval/classification
2.2 segmentation
2.3 matching
2.4 look for appropriate representation/features 
Spectral graph\geometry processing (2h+2h LAB):
3.1 introduction to graph Laplacian
3.2 LBO (cotangent weights)
3.3 eigendecomposition
3.4 spectral representation
3.5 exploit spectral quantities 
Pointbased architecture (2h+2h LAB):
4.1 missed connectivity, problems and desired properties
4.2 permutation invariance and rigidtransformations invariance
4.3 PointNet
4.4 Pointnet++
4.5 pointMLP 
Convolution on 3D data (2h+2h LAB):
5.1 introduction to convolution
5.2 pooling, unpooling and properties
5.3 extrinsic convolutions
5.4 geometric data and missing fixed template
5.5 spectral and alternative convolutions
5.6 diffusion based convolutions 
Other architectures on 3D data (2h+2h LAB):
6.1 limitations of Points and Meshes and Explicit access to geometry
6.2 implicit representations as possible solutions
6.3 conversions: implicit vs explicit
6.4 use cases and applications
6.5 learning on grids
6.6 neural fields 
Graphs as geometric data and Graph Neural Networks (2h+2h LAB):
7.1 introduction to graphs
7.2 tasks on graph retrieval/classification, scene understanding, segmentation
7.3 the problem of learning on graphs
7.4 GNN as MLP on Graphs,
7.5 convolution on a mesh is a convolution on a graph
7.6 other graphs networks: Graph Attention Networks and Set transformers
Final Evaluation
Evaluation will be based on a simple project.
 topic selected by the student in coordination with lecturer(s)
 may be theoretical, practical, or a combination
 may start from one of the demo presented in the labs
The evaluation based on the following criteria:
 quality: of the work, presentation, and report
 significance: of the topic chosen
 novelty: of the techniques and results
CFU / Ore
2 / 24
Periodo di erogazione
November (attempt dates 23,24,27,28)
Sustainable Development Goals
Title
Geometry processing and machine learning for geometric data
Teacher(s)
Simone Melzi, Riccardo Marin (UNIVERSITY OF TÜBINGEN)
Language
English
Short description
Course Organization:
The course will consists of three full days lessons with 4 hours in the morning (8.30  12.30) and 4 hours in the afternoon (14.00  18.00).
Course Overview:
After an introduction to geometric data and related applications (respectively sections 1 and 2) the rest of the course will be divided in five sections (sections from 3 to 7) each of which consists of 2 hours of theory and 2 hours of lab in which an implementation of the main algorithms and results discussed in the related theory will be rpovided and discussed witht he teachers. At the end of the course, each student will own a personal implementation/demo of at least one architecture or algorithm related to the topic of each section.
Table of Contents:

Introduction to 3D data, possible representations and geometric quantities (2h):
1.1 point clouds
1.2 meshes
1.3 graphs
1.4 volumetric
1.5 implicit surfaces 
Applications (2h):
2.1 retrieval/classification
2.2 segmentation
2.3 matching
2.4 look for appropriate representation/features 
Spectral graph\geometry processing (2h+2h LAB):
3.1 introduction to graph Laplacian
3.2 LBO (cotangent weights)
3.3 eigendecomposition
3.4 spectral representation
3.5 exploit spectral quantities 
Pointbased architecture (2h+2h LAB):
4.1 missed connectivity, problems and desired properties
4.2 permutation invariance and rigidtransformations invariance
4.3 PointNet
4.4 Pointnet++
4.5 pointMLP 
Convolution on 3D data (2h+2h LAB):
5.1 introduction to convolution
5.2 pooling, unpooling and properties
5.3 extrinsic convolutions
5.4 geometric data and missing fixed template
5.5 spectral and alternative convolutions
5.6 diffusion based convolutions 
Other architectures on 3D data (2h+2h LAB):
6.1 limitations of Points and Meshes and Explicit access to geometry
6.2 implicit representations as possible solutions
6.3 conversions: implicit vs explicit
6.4 use cases and applications
6.5 learning on grids
6.6 neural fields 
Graphs as geometric data and Graph Neural Networks (2h+2h LAB):
7.1 introduction to graphs
7.2 tasks on graph retrieval/classification, scene understanding, segmentation
7.3 the problem of learning on graphs
7.4 GNN as MLP on Graphs,
7.5 convolution on a mesh is a convolution on a graph
7.6 other graphs networks: Graph Attention Networks and Set transformers
Final Evaluation
Evaluation will be based on a simple project.
 topic selected by the student in coordination with lecturer(s)
 may be theoretical, practical, or a combination
 may start from one of the demo presented in the labs
The evaluation based on the following criteria:
 quality: of the work, presentation, and report
 significance: of the topic chosen
 novelty: of the techniques and results
CFU / Hours
2 / 24
Teaching period
November (attempt dates 23,24,27,28)