A framework for generating 3D shapes by sequentially assembling primitives.
problem Combinatorial complexity in generating 3D shapes.
method Bayesian optimization for efficient exploration and exploitation of feasible combinations.
result Successfully generates realistic combinatorial 3D shapes.
Python tools for 3D shape analysis on Kendall's space.
problem Lack of practical utilities for advanced 3D shape analysis.
method Developed Python tools for 3D shape analysis on Kendall's 3D Shape Space.
result Efficient, accessible software solutions for researchers.
Paper adapts SVDD for 3D-shapes filtering and outlier detection.
problem Filtering and detecting outliers in 3D-shapes.
method Adapted SVDD to SimpleMKL, developing Slim-MK-SVDD for tighter boundaries.
result Slim-MK-SVDD produces a tighter boundary around data.
New method reconstructs 3D shapes from 2D images using Kendall's shape space.
problem Reconstruct 3D shapes from 2D images, especially for rare specimens.
method Kendall's shape space approach with prior information.
result More robust and plausible shapes compared to previous methods.
Paper tackles unsupervised learning of 3D shapes from single images.
problem Learning 3D shapes from single images without supervision.
method Generative models, variational auto-encoders, adversarial methods.
result Model learns 3D shapes and poses from single images, showing potential for various datasets.
Generative model disentangles 3D shapes into independent factors.
problem Learning rich representations of deformable 3D shapes.
method Supervised 3D mesh-convolutional Variational AutoEncoder with latent feature disentanglement.
result Explicit disentanglement of latent factors improves shape generation and downstream tasks.
Generative model creates detailed 3D shapes from text descriptions.
problem Creating high-resolution 3D models from natural language descriptions.
method Two-step process: first generating low-resolution shapes, then high-resolution shapes using Conditional Wasserstein GAN framework.
result Improved method generates 3D shapes more faithful to natural language.
New proof for complex 3D shapes.
problem Complex 3D shapes with infinite fundamental groups.
method Direct proof using finite covers.
result Every shape has a simpler version.
A novel 3D shape registration method using spectral graph embedding and probabilistic matching.
problem Challenges in 3D shape analysis and registration, especially with large variability.
method Combining spectral graph matching with Laplacian embedding for large graphs, using commute-time embedding and PCA.
result A method to register shapes with different samplings and isometric deformations.
MeshCNN analyzes 3D shapes using edges, overcoming irregularities.
problem Irregularities in mesh representations hinder neural network analysis.
method MeshCNN uses specialized convolution and pooling layers on mesh edges, collapsing them to focus on important features.
result MeshCNN effectively analyzes 3D shapes, learning which edges to collapse.
LION generates high-quality 3D shapes using hierarchical latent diffusion models.
problem Creating high-quality 3D shapes for digital artists.
method Hierarchical Latent Point Diffusion Model (LION) with a global shape latent and point-structured latent space.
result LION achieves state-of-the-art generation performance on ShapeNet benchmarks.
Proves unknottedness of certain 3D shapes with multiple ends.
problem Determining the structure of complex 3D shapes.
method Used mean curvature flow to analyze shapes with multiple ends.
result Proves unknottedness of shapes with multiple asymptotically conical ends.
Proposes a new layer for efficient 3D shape discrimination.
problem Irregular structure and redundancy in 3D point clouds hinder efficient inter-class discrimination.
method Integrates Blended Convolution and Synthesis layer that projects and synthesizes 3D point clouds, followed by 3D convolution in the unit ball.
result End-to-end architecture achieves compelling results on 3D shape recognition and retrieval.
Generative model learns from designs to create new shapes.
problem Designing new shapes for conceptual optimization.
method Variational autoencoder-decoder architecture for 3D shape synthesis.
result Generator maps latent space to smooth 3D surfaces for optimization.
Analyze and predict complex 3D shape deformations using LSTM autoencoders and oriented bounding boxes.
problem Detecting and predicting patterns in sequences of deforming 3D shapes.
method Use LSTM autoencoders to create low-dimensional representations of 3D shapes, incorporating oriented bounding boxes for structural components.
result The method detects patterns in plastic deformation and predicts future states of 3D shapes with improved accuracy.
Instantiation-Net reconstructs 3D mesh from single 2D image for right ventricle.
problem Reconstructing 3D shape from limited 2D images for surgical navigation.
method Combines DCNN for feature extraction and GCN for mesh reconstruction.
result Demonstrates practical strength and potential clinical use.
DISPR uses diffusion models to predict 3D cell shapes from 2D images.
problem Predicting 3D cell shapes from 2D microscopy images.
method Diffusion model trained to predict 3D shapes from 2D microscopy images as a prior.
result Adding DISPR predictions to minority cell classes improves classification accuracy.
Paper proves existence of a special 3D shape with rotational symmetry.
problem Existence of a specific type of 3D shape with rotational symmetry.
method Used a 'shooting method' similar to McGrath's approach.
result Proves existence of a closed, embedded λ-hypersurface diffeomorphic to Sn−1imesSn−1imesS1. PointGMM learns hGMMs from point clouds for 3D shape representation.
problem Lack of shape priors and non-local information in point cloud representations.
method Neural network that learns hierarchical Gaussian mixture models (hGMMs) for 3D shapes.
result Generative model learns meaningful latent space for interpolations and novel shape synthesis.
Enhanced 3D shape analysis using information geometry.
problem Challenges in comparing 3D point clouds due to their unstructured nature and complex geometry.
method Information geometric framework for 3D point cloud shape analysis using Gaussian Mixture Models (GMMs) on a statistical manifold. Proposed MSKL divergence with upper and lower bounds.
result MSKL provides stable and monotonically varying values that directly reflect geometric variation, outperforming traditional distances and existing KL approximations.
3D Adversarial Autoencoder learns compact binary descriptors from 3D point clouds.
problem Learning meaningful representations of 3D shapes for various tasks.
method End-to-end Adversarial Autoencoder model trained on 3D input and output.
result 3D Adversarial Autoencoder (3dAAE) generates state-of-the-art results for 3D points clustering and retrieval.
Constructs examples of complex 3D shapes with specific properties.
problem Creating fibered three-manifolds with certain characteristics.
method Builds examples using handlebody bundles and polytopes.
result Examples of fibered three-manifolds with specific properties.
The investigation of 3D euclidean symmetry sets (SS) and medial axis is an important area, due in particular to their various important applications. The pre-symmetry set of a surface M in 3-space (resp. smooth closed curve in 2D) is the set of pairs of points which contribute to the symmetry set, that is, the closure …
Generative models learn distributions of continuous functions.
problem Training generative models on discretized grids limits model size and data type.
method Parameterize data points by continuous functions, learn distributions over these functions.
result Models can learn rich distributions of functions independently of data type and resolution.
New method learns shape correspondences robustly from raw geometry.
problem Inaccurate and poor generalization of shape correspondences.
method Learning-based approach with feature-extraction network and functional map representation.
result Robust and accurate shape correspondence learning with less training data.
New proof shows 3D shapes can be continuously deformed.
problem Proving 3D shapes can be continuously deformed without tearing.
method Used Heegaard splitting as a main tool.
result Closed orientable 3-manifolds are parallelizable.
Found a stable 3D shape with specific properties.
problem Finding K-stable Fano threefolds.
method Analyzing specific Fano threefolds with given properties.
result Identified a K-stable Fano threefold with Picard rank 3 and anti-canonical degree 28.
Paper finds new 3D shapes that can be inside a 4D space.
problem Finding new 3D shapes with specific properties.
method Examined arithmetic hyperbolic 3-manifolds and their homology.
result Discovered infinitely many 3D shapes that are rational homology spheres and can bound geometrically.
Three proofs show all 3D shapes are parallelizable without complex tools.
problem Proving all 3D shapes are parallelizable without advanced tools.
method Minimal proofs using no spin structures or Stiefel-Whitney classes.
result Three proofs show all 3D shapes are parallelizable.
The paper uses 3D shapes to reveal sundial design adjustments based on latitude.
problem Identifying sundial design adjustments based on installation location.
method Shape analysis in a high-dimensional space, regression in shape space.
result Sundial design adjustments were latitude-dependent.
Essential surfaces found in curved 3D shapes.
problem Existence of essential closed surfaces in curved 3D shapes.
method Triangulated 3-manifolds with ideal tetrahedra and negatively curved structure.
result Essential closed surfaces proven for finite coverings.
Novel volumetric convolution for unit ball improves 3D object recognition.
problem Efficiently convolving functions in a unit ball for deep learning.
method Developed volumetric convolution using Zernike polynomials.
result Improved 3D object recognition through novel convolution.
Paper introduces a new regularization method for visual representations.
problem Learning sparse visual representations from over-complete data.
method Proposes leaky capped norm regularization (LCNR) and a majorization-minimization algorithm.
result LCNR outperforms ℓ1 regularization in monocular 3D shape recovery. Study mapping class groups of specific 3D shapes.
problem Computing mapping class groups of certain 3D manifolds.
method Analyzes simply-connected closed smooth manifolds with specific homology properties.
result Computes the mapping class group for given dimensions.
Study 3D shapes in 5D space with sharp points.
problem Understanding shapes with sharp points in higher dimensions.
method Define curvature locus using fundamental forms at sharp points.
result Local second order geometrical information captured.
New 3D shape not homotopy equivalent to any hyperbolic shape.
problem Finding 3D shapes not homotopy equivalent to hyperbolic ones.
method Constructed a locally hyperbolic 3-manifold with specific fundamental group properties.
result The constructed manifold is not homotopy equivalent to any hyperbolic manifold.
A new method for generating realistic and creative 3D shapes from point clouds.
problem Generating realistic and creative 3D shapes from point clouds.
method Learning to interpolate point clouds by encoding prior knowledge about real-world objects.
result Generated 3D shapes are both realistic and creative, unlike any existing forms.
Model reconstructs novel 3D shapes with a single prior image.
problem Generalizing single-view 3D reconstruction to new classes with limited data.
method Reframes reconstruction as refinement of a provided prior shape.
result Model reconstructs novel classes with limited training data.
New 3D shape found that behaves oddly.
problem Finding a 3D shape that isn't hyperbolic.
method Created a specific 3D shape and showed it can't be hyperbolic.
result Discovered a 3D shape that is locally hyperbolic but not hyperbolic.
VCAE improves autoencoder quality on MNIST and CelebA.
problem Overfitting and poor generative/reconstruction quality in autoencoders.
method Proposes variance-constrained autoencoder (VCAE) to enforce variance constraint on latent distribution.
result VCAE outperforms Wasserstein Autoencoder and Variational Autoencoder in quality.
Simplified proof of a theorem about 3D shapes.
problem Proving a theorem about foliations on 3-manifolds.
method Using foliated branched covers.
result A simple proof of Novikov's theorem.
New 3D shapes can't be split into torus pieces.
problem 3D shapes without torus decompositions.
method Recursive definition from compact 3-manifolds.
result Examples of 3D shapes failing torus decomposition.
New 3D shapes found without certain special flows.
problem Finding 3D shapes without specific special flows.
method Rational surgeries on the figure eight knot.
result First infinite family of hyperbolic 3-manifolds without tight projectively Anosov flows.
RCLA reduces noise in topological data analysis, preserving essential structure.
problem Noise in large datasets obscures topological features in persistent homology.
method Grid-based RCLA integrates data reduction and denoising with a threshold parameter.
result RCLA provides a theoretical guarantee and automatic parameter selection.
3D-PRNN generates shapes from depth images using recurrent neural networks.
problem Representing 3D shapes from limited sensor data.
method Generative Recurrent Neural Network (3D-PRNN) with Gaussian Fields.
result 3D-PRNN synthesizes plausible shapes from primitives, outperforming nearest-neighbor methods.
New metrics solve complex equations on special 3D shapes.
problem Finding metrics on complex 3D shapes.
method Gluing construction to solve equations.
result Solves dilatino equation on small resolutions.
The paper classifies self-replicating 3D shapes using algebraic models.
problem Understanding self-replicating 3D shapes.
method Using idempotents in the (2+1)-cobordism category to classify 3-manifolds.
result A classification theorem for self-replicating 3-manifolds.
New proofs show how to embed certain 3D shapes into a 4D ball.
problem Embedding specific 3D shapes into a 4D ball.
method Embedded surfaces in the 4-ball and branched double covers.
result New proofs of embedding theorems for rational homology balls.