Related papers: Symmetry in Image Registration and Deformation Mod…
The definition of Linear Symmetry-Based Disentanglement (LSBD) proposed by (Higgins et al., 2018) outlines the properties that should characterize a disentangled representation that captures the symmetries of data. However, it is not clear…
Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The…
How can intelligent agents solve a diverse set of tasks in a data-efficient manner? The disentangled representation learning approach posits that such an agent would benefit from separating out (disentangling) the underlying structure of…
This communication describes a representation of images as a set of edges characterized by their position and orientation. This representation allows the comparison of two images and the computation of their similarity. The first step in…
In this article we study the problem of thoracic image registration, in particular the estimation of complex anatomical deformations associated with the breathing cycle. Using the intimate link between the Riemannian geometry of the space…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
Aerial image registration or matching is a geometric process of aligning two aerial images captured in different environments. Estimating the precise transformation parameters is hindered by various environments such as time, weather, and…
Visual odometry techniques typically rely on feature extraction from a sequence of images and subsequent computation of optical flow. This point-to-point correspondence between two consecutive frames can be costly to compute and suffers…
Due to the abundance of 2D product images from the Internet, developing efficient and scalable algorithms to recover the missing depth information is central to many applications. Recent works have addressed the single-view depth estimation…
Anatomical variabilities seen in longitudinal data or inter-subject data is usually described by the underlying deformation, captured by non-rigid registration of these images. Stationary Velocity Field (SVF) based non-rigid registration…
Unlike image or text domains that benefit from an abundance of large-scale datasets, point cloud learning techniques frequently encounter limitations due to the scarcity of extensive datasets. To overcome this limitation, we present…
Some new properties of symmetries that disappear as point symmetries after the first reduction of order of an ODE and reappear after the second are analyzed from the aspect of three-dimensional subalgebra of symmetries of differential…
This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
We consider the problem of nonlinear dimensionality reduction: given a training set of high-dimensional data whose ``intrinsic'' low dimension is assumed known, find a feature extraction map to low-dimensional space, a reconstruction map…
Attributes and objects can compose diverse compositions. To model the compositional nature of these general concepts, it is a good choice to learn them through transformations, such as coupling and decoupling. However, complex…
Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…
Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one…
In an influential paper, Tadmor, Nezzar and Vese (Multiscale Model. Simul. (2004)) introduced a hierarchical decomposition of an image as a sum of constituents of different scales. Here we construct analogous hierarchical expansions for…
We describe a method for recovering the irradiance underlying a collection of images corrupted by atmospheric turbulence. Since supervised data is often technically impossible to obtain, assumptions and biases have to be imposed to solve…