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Concept

Computational anatomy

Résumé

Computational anatomy is an interdisciplinary field of biology focused on quantitative investigation and modelling of anatomical shapes variability. It involves the development and application of mathematical, statistical and data-analytical methods for modelling and simulation of biological structures. The field is broadly defined and includes foundations in anatomy, applied mathematics and pure mathematics, machine learning, computational mechanics, computational science, biological imaging, neuroscience, physics, probability, and statistics; it also has strong connections with fluid mechanics and geometric mechanics. Additionally, it complements newer, interdisciplinary fields like bioinformatics and neuroinformatics in the sense that its interpretation uses metadata derived from the original sensor imaging modalities (of which magnetic resonance imaging is one example). It focuses on the anatomical structures being imaged, rather than the medical imaging devices. It is similar in

Source officielle

https://en.wikipedia.org/wiki/Computational_anatomy

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Since 2010 approaches in deep learning have revolutionized fields as diverse as computer vision, machine learning, or artificial intelligence. This course gives a systematic introduction into influential models of deep artificial neural networks, with a focus on Reinforcement Learning.

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Séances de cours associées (1)

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Relative stability toward diffeomorphisms indicates performance in deep nets

Alessandro Favero, Mario Geiger, Leonardo Petrini, Matthieu Wyart

Understanding why deep nets can classify data in large dimensions remains a challenge. It has been proposed that they do so by becoming stable to diffeomorphisms, yet existing empirical measurements support that it is often not the case. We revisit this question by defining a maximum-entropy distribution on diffeomorphisms, that allows to study typical diffeomorphisms of a given norm. We confirm that stability toward diffeomorphisms does not strongly correlate to performance on benchmark data sets of images. By contrast, we find that the {\it stability toward diffeomorphisms relative to that of generic transformations}

R_f

correlates remarkably with the test error

\epsilon_t

. It is of order unity at initialization but decreases by several decades during training for state-of-the-art architectures. For CIFAR10 and 15 known architectures we find

\epsilon_t\approx 0.2\sqrt{R_f}

, suggesting that obtaining a small

R_f

is important to achieve good performance. We study how

R_f

depends on the size of the training set and compare it to a simple model of invariant learning.

2021

Chargement

Multiresolution model-based matching for 3D object recognition

1996

Chargement

, ,

This paper discusses the mathematical framework for designing methods of Large Deformation Diffeomorphic Matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, we prove a theorem showing that these methods may be designed by using the actions of diffeomorphisms on the image data structure to define their associated momentum representations as (cotangent-lift) momentum maps. To illustrate its use, the momentum map theorem is shown to recover the known algorithms for matching landmarks, scalar images, and vector fields. After briefly discussing the use of this approach for diffusion tensor (DT) images, we explain how to use momentum maps in the design of registration algorithms for more general data structures. For example, we extend our methods to determine the corresponding momentum map for registration using semidirect product groups, for the purpose of matching images at two different length scales. Finally, we discuss the use of momentum maps in the design of image registration algorithms when the image data is defined on manifolds instead of vector spaces.

Springer Verlag2011

Chargement

Relative stability toward diffeomorphisms indicates performance in deep nets

Alessandro Favero, Mario Geiger, Leonardo Petrini, Matthieu Wyart

R_f

correlates remarkably with the test error

\epsilon_t

. It is of order unity at initialization but decreases by several decades during training for state-of-the-art architectures. For CIFAR10 and 15 known architectures we find

\epsilon_t\approx 0.2\sqrt{R_f}

, suggesting that obtaining a small

R_f

is important to achieve good performance. We study how

R_f

depends on the size of the training set and compare it to a simple model of invariant learning.

2021