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.
In shape analysis, the concept of shape spaces has always been vague, requiring a case-by-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes in a manifold. This notion encompasses every shape space studied so far in the literature, and offers a rigorou…
Paper introduces a method to generate stable shapes using Grassmann manifolds.
problem Generating stable shapes with minimal extraneous transformations.
method Continuous normalization flows on Grassmann manifolds to eliminate extraneous transformations.
result The method significantly outperforms state-of-the-art methods in generating high-quality samples.
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.
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.
This paper tackles shape denoising in computer vision and medical imaging.
problem Handling shapes with missing pieces or outliers in shape modeling.
method Introduces six types of noise and an objective measure for shape denoising.
result Evaluates seven shape denoising methods, six of which are based on deep learning.
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.
New star-shaped acceptability indexes generalize existing methods.
problem Generalizing existing acceptability measures.
method Characterizing acceptability indexes through star-shaped risk measures and sets.
result Introducing concrete examples linked to various financial measures.
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.
Generator network replicates AAM's face recognition neuron responses.
problem Replicating AAM's face recognition neuron responses using a deep generative model.
method Using a variational auto-encoder, learned generator network from face images generated by AAM, capturing shape variations without explicit shape model.
result Inferred latent variables of the learned generator network have strong linear relationship with AAM's shape and appearance variables.
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.
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.
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.
BézierGAN generates smooth curves from low-dimensional parameters.
problem Designing smooth curves for aerodynamic and hydrodynamic shapes.
method Generative model that maps low-dimensional latent representation to Bézier curve points.
result Generates diverse and realistic curves with consistent shape variation.
We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape features in a visually intuitive manner. This method have implications in shape an…
Framework detects shape shifts in functional profiles using Fréchet mean and shape invariant model.
problem Detecting shape shifts in functional profiles.
method Combining Fréchet mean and shape invariant model for interpretable parameterization of profile deviations.
result Potential shifts in shape deformation process distinguished by significant shifts in amplitude and/or phase.
We consider the problem of modelling noisy but highly symmetric shapes that can be viewed as hierarchies of whole-part relationships in which higher level objects are composed of transformed collections of lower level objects. To this end, we propose the stochastic wreath process, a fully generative probabilistic model…
Generates tubular and membranous shapes using curvature functionals.
problem Difficult analysis of tubular and membranous shapes.
method Modeling as curvature optimization problem, phase-field formulation, GPU algorithm.
result Wide continuum of shape textures discovered.
Paper analyzes shapes of brain arterial networks using statistical methods.
problem Quantifying and comparing shapes of brain arterial networks.
method Mathematical representation of BAN shapes as elastic shape graphs, development of Riemannian metrics and geometrical tools.
result Age has a clear, quantifiable effect on BAN shapes, with increased variance in shapes as age increases.
Generative model creates realistic images with 3D understanding.
problem Lack of 3D understanding in existing image generation models.
method Disentangled 3D representation using shape, viewpoint, and texture.
result Generates more realistic images and enables 3D operations.
Generative model combines shape and intensity priors for left atrium segmentation.
problem Challenges in segmenting left atrium MRI images due to shape variation and multimodality.
method Generative image model with mixture of Gaussians for shape priors and autoencoders for intensity priors.
result Maximizes posterior probability using a mixture of Gaussians for shape priors and autoencoders for intensity priors.
A new method for analyzing shapes and forms using additive models on manifolds.
problem Analyzing shapes and forms under geometric transformations.
method Extending generalized additive regression to models for shapes/forms using squared geodesic distance and Riemannian L2-Boosting algorithm. result Automated model selection and intuitive visualization of covariate effects in shape/form space.
Generalizes shape analysis to Lie groups and homogeneous spaces.
problem Shape analysis on non-Euclidean spaces.
method Square Root Velocity Transform (SRVT) generalization to Lie groups and homogeneous manifolds.
result Shape analysis on Lie groups and homogeneous spaces.
Introduces fine shape theory to simplify shape and antishape invariants.
problem Complexity and limitations of existing shape theories for metrizable spaces.
method Develops fine shape theory with a simple definition, aiming to supersede known shape theories.
result Fine shape theory unifies Čech cohomology and Steenrod-Sitnikov homology as invariants.
Coarse homotopy theory connects Euclidean cones to shape theory of compact spaces.
problem Establishing connections between coarse homotopy theory and shape theory.
method Using pointed shape invariants and inverse mapping telescopes.
result Proving two compact spaces are strong shape equivalent if their Euclidean cones are coarsely homotopy equivalent.
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 learns shape drift for quantifying domain uncertainty in hemodynamics.
problem Quantifying domain uncertainty in medical image segmentation for biomarker estimation.
method Conditional stochastic interpolant framework based on LDDMM registration.
result Generative model can create random perturbations of shapes for biomarker estimation.
Meta-learning for efficient reward shaping in RL.
problem Challenges in designing effective reward shaping functions in RL.
method Meta-learning framework to automatically learn reward shaping on multiple tasks.
result Significantly improved learning efficiency and interpretable visualizations across various RL settings.
Hybrid clustering merges K-means and hierarchical methods for diverse group shapes.
problem Clustering homogeneous spherical groups in large datasets.
method First, K-means partitions the dataset into spherical groups. Then, hierarchical clustering merges these groups with a data-driven distance measure. result Hybrid approach reveals general-shaped groups in datasets.
Smooth generative model of shapes with uncertainty from silhouette images.
problem Challenges in modeling shapes represented as silhouette images due to intractable posteriors.
method Gaussian Process Deep Belief Networks (GPDBN) that learn from small data and propagate uncertainty.
result Proposed model provides favorable results compared to state-of-the-art models.
New shape representation for airfoils improves design and manufacturing.
problem Designing and manufacturing airfoils efficiently and accurately.
method Combining physics-based and data-driven techniques on a Grassmannian manifold.
result Rich set of novel 2D airfoil deformations not previously captured.
The paper learns pose variations within shape populations using constrained mixtures of factor analyzers.
problem Learning pose variations within a shape population with articulated parts and relative rotations.
method Formulated as mixtures of factor analyzers, segmentation by component posterior probabilities, and constraints on factor loading matrices for rotation matrices.
result Automatic learning of pose variations from shape populations, resulting in smooth and realistic animations.
Study shows one-dimensional location-scale-shape models are flat in Wasserstein geometry.
problem Investigating curvature in location-scale-shape models under Wasserstein metric.
method Introduced location-scale-shape model and investigated its geometry.
result Location-scale-shape model is intrinsically flat but extrinsically curved in Wasserstein geometry.
Bézier-GAN optimizes airfoil design by reducing shape complexity.
problem High computational cost in aerodynamic shape optimization.
method Generative adversarial networks (GANs) to learn compact shape representations.
result Empirically accelerates optimization convergence by at least two times.
The paper characterizes law-invariant star-shaped risk measures.
problem Understanding and characterizing law-invariant star-shaped risk measures.
method Developed characterizations for positively homogeneous and star-shaped functionals, derived Kusuoka-type representations, and offered representations of general law-invariant star-shaped functionals.
result Characterizations of law-invariant star-shaped functionals, including their connections to Value-at-Risk and Expected Shortfall.
In 1998 Smoczyk [Smo98] showed that, among others, the blowup limits at singularities are convex for the mean curvature flow starting from a closed star-shaped surface in R3. We prove in this paper that this is true for the mean curvature flow of star-shaped hypersurfaces in Rn+1 in arbitrary …
The shape equation and linking conditions for a vesicle with two-phase domains are derived. We refine the conjecture on the general neck condition for the limit shape of a budding vesicle proposed by Jülicher and Lipowsky [Phys. Rev. Lett. \textbf{70}, 2964 (1993); Phys. Rev. E \textbf{53}, 2670 (1996)], and then we us…
Reduces 3-body problem to shape and spherical geometry.
problem Investigates the motion of three bodies in a plane.
method Geometric reduction using equivariant Riemannian geometry.
result Time parametrization of moduli curve determined by shape curve and potential function.
Unsupervised clustering of curves according to their shapes is an important problem with broad scientific applications. The existing model-based clustering techniques either rely on simple probability models (e.g., Gaussian) that are not generally valid for shape analysis or assume the number of clusters. We develop an…
Extends shape analysis to framed space curves using quaternionic arithmetic.
problem Matching and classifying shapes of framed space curves.
method Extends square root transform to framed curves using quaternionic arithmetic and Hopf fibration properties. Describes geodesics in framed curve space explicitly.
result Explicit descriptions of geodesics in framed curve space and averages of collections of curves.
The paper generalizes convex and star-shaped concepts to symplectic spaces and studies variational problems.
problem Generalizing convex and star-shaped concepts to symplectic vector spaces.
method Study of variational problems for symplectically convex and star-shaped curves.
result Extremal points of the variational problem are rigid multiply traversed conics for a range of parameters.
The paper characterizes dynamic return and star-shaped risk measures via BSDEs.
problem Characterizing dynamic return and star-shaped risk measures.
method Characterization of star-shaped functionals and BSDEs.
result Existence of convex BSDEs with non-empty set of supersolutions.
Geomstats introduces shape module for analyzing shapes of objects.
problem Analyzing shapes of objects represented as landmarks, curves, and surfaces.
method Implementing shape spaces, group actions, fiber bundles, quotient spaces, and Riemannian metrics.
result Users can compare, average, and interpolate shapes inside shape spaces.
LIMP learns latent shapes with metric preservation, improving generative models.
problem Insufficient training data for high-fidelity latent representations.
method Metric preservation as a prior, geometric distortion criterion, geodesic loss.
result Synthetic samples of higher quality achieved through metric preservation.
Extended orbit model theory for shape analysis using graded group action framework.
problem Limitations of standard orbit model theory in shape analysis.
method Developed graded group action (GGA) framework with regularity conditions.
result Uniqueness result for momentum map trajectory in multi-scale shape spaces.
This paper proves rational eigenvalues for shape operators in certain spaces.
problem Understanding rational properties of shape operators in symmetric spaces.
method Analyzing normal holonomy and shape operators in singular orbits of isotropy representations.
result Shape operators have rational eigenvalues in specific normal holonomy factors.
A new shape space allows optimization of non-smooth shapes in fluid mechanics.
problem Optimizing non-smooth shapes in fluid mechanics.
method Constructing a product manifold to include piecewise-smooth shapes.
result Numerical results show applicability in minimizing viscous energy dissipation.
Machine learning shapes bodies via inverse scattering.
problem Generating 3D human bodies with customizable characteristics.
method Combining inverse scattering with machine learning.
result Generates geometric bodies from characteristic parameters.