Metrics of Curves for Shape Analysis and Shape Optimization

Scuola Normale Superiore
LEVEL
PhD
TYPE
Course
MODES
-
LANGUAGE
-
ECTS
30
PERIOD
30/09/2021 to 29/05/2022

Course Description

We will see the mathematics that stands behind some sections of Computer Vision, and in particular the so called “Shape Spaces theory” we will address mostly the case in which the shape space is a space of closed immersed curves in the plane. To this end, we will consider this Shape Space of Immersed Curves as an infinite dimensional Differentiable Manifold we will develop a convenient calculus we will endow this manifold with some choices of Riemannian metrics that have been proposed in the current literature. These models justify the methods called active contours that are used for Shape Optimization the active contour methods try to minimize a functional using a gradient descent approach the functional is designed to achieve a task , such as image segmentation or tracking. These Riemannian Manifold models at the same time define some tools that are useful in Shape Analysis, such as “distance between two curves” or “geodetic of curves”. Time remaining, we will address some possible definitions of probabilities on spaces of curves.

Subject area

Biology
Digital communications IA electronics
Mathematics

Educational-info

Competences

We will review some elements in Riemannian Geometry, Functional Analysis, Global Analysis, consequently we will explore some contemporary research themes.

Prerequisites

at least a bachelor

Duration

20h

ECTS

30

Validation mode

Oral Examination,Written Examination,Written report

Maximum number of students

10

Organizer

Partner

Scuola Normale Superiore

Faculty

Scuola Normale Superiore

Department

Classe di Scienze

Contact or registration links