相关论文: An optimization-based registration approach to geo…
This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…
Registration is a transformation estimation problem between two point clouds, which has a unique and critical role in numerous computer vision applications. The developments of optimization-based methods and deep learning methods have…
Landmark matching via geodesic shooting is a prerequisite task for numerous registration based applications in biomedicine. Geodesic shooting has been developed as one solution approach and formulates the diffeomorphic registration as an…
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
Image registration is a process of aligning two or more images of same objects using geometric transformation. Most of the existing approaches work on the assumption of location invariance. These approaches require object-centric images to…
The goal of this paper is to address the problem of global point cloud registration (PCR) i.e., finding the optimal alignment between point clouds irrespective of the initial poses of the scans. This problem is notoriously challenging for…
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…
This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…
We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by…
Volume-based reconstruction is usually expensive both in terms of memory consumption and runtime. Especially for sparse geometric structures, volumetric representations produce a huge computational overhead. We present an efficient way to…
In this work, we explore the numerical solution of geometric shape optimization problems using neural network-based approaches. This involves minimizing a numerical criterion that includes solving a partial differential equation with…
We study the problem of fitting an ultrametric distance to a dissimilarity graph in the context of hierarchical cluster analysis. Standard hierarchical clustering methods are specified procedurally, rather than in terms of the cost function…
Commercial off the shelf (COTS) 3D scanners are capable of generating point clouds covering visible portions of a face with sub-millimeter accuracy at close range, but lack the coverage and specialized anatomic registration provided by more…
Point cloud registration aims at estimating the geometric transformation between two point cloud scans, in which point-wise correspondence estimation is the key to its success. In addition to previous methods that seek correspondences by…
Various tasks in scientific computing can be modeled as an optimization problem on the indefinite Stiefel manifold. We address this using the Riemannian approach, which basically consists of equipping the feasible set with a Riemannian…
We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…
During recent years the field of fine-grained complexity has bloomed to produce a plethora of results, with both applied and theoretical impact on the computer science community. The cornerstone of the framework is the notion of…
Pose Graph Optimization (PGO) is an important non-convex optimization problem and is the state-of-the-art formulation for SLAM in robotics. It also has applications like camera motion estimation, structure from motion and 3D reconstruction…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…