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The reconstruction of an object's shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process of aligning intra-operative…
Predictive models can be particularly helpful for robots to effectively manipulate terrains in construction sites and extraterrestrial surfaces. However, terrain state representations become extremely high-dimensional especially to capture…
A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport w.r.t. geometric distance and local feature similarity. Geometric invariance and modelling of…
This paper presents a new joint inversion approach to shape-based inverse problems. Given two sets of data from distinct physical models, the main objective is to obtain a unified characterization of inclusions within the spatial domain of…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
In this work, we describe a Bayesian framework for reconstructing the boundaries of piecewise smooth regions in the X-ray computed tomography (CT) problem in an infinite-dimensional setting. In addition to the reconstruction, we are also…
Recent studies have shown the benefits of using additional elevation data (e.g., DSM) for enhancing the performance of the semantic segmentation of aerial images. However, previous methods mostly adopt 3D elevation information as additional…
This paper further develops the Method of Matched Sections (MMS), a robust numerical framework for the solution of boundary value problems governed by partial differential equations. It demonstrates its unique applicability to the…
We propose a novel approach to generate samples from the conditional distribution of patient-specific cardiovascular models given a clinically aquired image volume. A convolutional neural network architecture with dropout layers is first…
We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion…
Defined mathematically as critical points of surface area subject to a volume constraint, constant mean curvatures (CMC) surfaces are idealizations of interfaces occurring between two immiscible fluids. Their behavior elucidates phenomena…
Predicting realistic ground views from satellite imagery in urban scenes is a challenging task due to the significant view gaps between satellite and ground-view images. We propose a novel pipeline to tackle this challenge, by generating…
Surface extraction from implicit neural representations modelling a single class surface is a well-known task. However, there exist no surface extraction methods from an implicit representation of multiple classes that guarantee topological…
Selective segmentation is an important application of image processing. In contrast to global segmentation in which all objects are segmented, selective segmentation is used to isolate specific objects in an image and is of particular…
This paper introduces Neural Subdivision, a novel framework for data-driven coarse-to-fine geometry modeling. During inference, our method takes a coarse triangle mesh as input and recursively subdivides it to a finer geometry by applying…
Surface-based geodesic topology provides strong cues for object semantic analysis and geometric modeling. However, such connectivity information is lost in point clouds. Thus we introduce GeoNet, the first deep learning architecture trained…
We address the problems of measuring geometric similarity between 3D scenes, represented through point clouds or range data frames, and associating them. Our approach leverages macro-scale 3D structural geometry - the relative configuration…
Symmetry detection, especially partial and extrinsic symmetry, is essential for various downstream tasks, like 3D geometry completion, segmentation, compression and structure-aware shape encoding or generation. In order to detect partial…
In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D…
Camouflaged objects are typically assimilated into their backgrounds and exhibit fuzzy boundaries. The complex environmental conditions and the high intrinsic similarity between camouflaged targets and their surroundings pose significant…