Publication

Landmark-Based Shape Encoding and Sparse-Dictionary Learning in the Continuous Domain

Résumé

We provide a generic framework to learn shape dictionaries of landmark-based curves that are defined in the continuous domain. We first present an unbiased alignment method that involves the construction of a mean shape as well as training sets whose elements are subspaces that contain all affine transformations of the training samples. The alignment relies on orthogonal projection operators that have a closed form. We then present algorithms to learn shape dictionaries according to the structure of the data that needs to be encoded: 1) projection-based functional principal-component analysis for homogeneous data and 2) continuous-domain sparse shape encoding to learn dictionaries that contain imbalanced data, outliers, or different types of shape structures. Through parametric spline curves, we provide a detailed and exact implementation of our method. We demonstrate that it requires fewer parameters than purely discrete methods and that it is computationally more efficient and accurate. We illustrate the use of our framework for dictionary learning of structures in biomedical images as well as for shape analysis in bioimaging.

À propos de ce résultat
Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.
Concepts associés (34)
Computational anatomy
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.
Dictionnaires chinois
vignette|upright 1.5|Page du manuscrit de Dunhuang (probablement du ) du Yiqiejing yinyi, le plus ancien dictionnaire chinois de terminologie bouddhiste. Les dictionnaires chinois remontent à la dynastie Han, c'est-à-dire à environ 2000 ans, ce qui en fait la langue qui a la plus ancienne tradition lexicographique.
Statistical shape analysis
Statistical shape analysis is an analysis of the geometrical properties of some given set of shapes by statistical methods. For instance, it could be used to quantify differences between male and female gorilla skull shapes, normal and pathological bone shapes, leaf outlines with and without herbivory by insects, etc. Important aspects of shape analysis are to obtain a measure of distance between shapes, to estimate mean shapes from (possibly random) samples, to estimate shape variability within samples, to perform clustering and to test for differences between shapes.
Afficher plus
Publications associées (35)

Dictionary Learning for Two-Dimensional Kendall Shapes

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Anna You-Lai Song

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between algorithmic simplici ...
SIAM PUBLICATIONS2020

Deep Micro-Dictionary Learning and Coding Network

Yan Yan, Wei Wang, Wei Xiao

In this paper, we propose a novel Deep Micro-Dictionary Learning and Coding Network (DDLCN). DDLCN has most of the standard deep learning layers (pooling, fully, connected, input/output, etc.) but the main difference is that the fundamental convolutional l ...
IEEE2019

Dictionary Learning Based on Sparse Distribution Tomography

Michaël Unser, Pedram Pad

We propose a new statistical dictionary learning algorithm for sparse signals that is based on an α-stable innovation model. The parameters of the underlying model—that is, the atoms of the dictionary, the sparsity index α and the dispersion of the transfo ...
P. Pad2017
Afficher plus
MOOCs associés (15)
Algèbre Linéaire (Partie 1)
Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.
Algèbre Linéaire (Partie 1)
Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.
Algèbre Linéaire (Partie 2)
Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.
Afficher plus

Graph Chatbot

Chattez avec Graph Search

Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.

AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.