Bayesian analysis of geological shapes for improved oil prediction.
problem Simplistic classifications of geological shapes hinder accurate oil prediction.
method Deriving integrated likelihood for cross-sectional shapes given class parameters using Bayesian statistics.
result First coherent statistical analysis of geological shapes.
We analyze and correct bias in template shape estimation using geometric statistics.
problem Asymptotic bias in template shape estimation.
method Tools from geometric statistics, stratified geometry of shape space, Taylor expansion, bootstrap procedures.
result Proposed methods to quantify and correct bias in template shape estimation.
Paper tackles shape graph registration using neural networks.
problem Constrained registration of shape graphs with varying nodes and edges.
method Shape-Graph Matching Network (SGM-net) with an elastic shape metric loss function.
result State-of-the-art matching performance and reduced computational cost.
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.
Wide and deep neural network predicts Alzheimer's progression from shape and clinical data.
problem Predicting Alzheimer's disease progression from shape and clinical data.
method Fused anatomical shape and tabular clinical data in a neural network, employing survival analysis loss.
result The model outperforms shape and clinical models individually.
Bayesian method classifies shapes in 2D and 3D.
problem Shape classification in 2D and 3D.
method Bayesian framework for modeling and classification.
result Efficiency and efficacy evaluated on Kimia database.
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…
New framework classifies high-dimensional shapes using ray intersections, establishing data requirements.
problem Classifying high-dimensional shapes in real-world data.
method Ray-based classification (RBC) framework using intersections of one-dimensional representations (rays) with shape boundaries.
result Established bounds on the number of rays necessary for shape classification, defined by key angular metrics.
A new algorithm for parallel transport on shape spaces is presented and compared to existing methods.
problem Statistical analysis of shape data, especially in time series and optimization.
method Pole ladder algorithm for parallel transport on Kendall shape spaces, compared to integration methods.
result The pole ladder algorithm is a more efficient method for parallel transport.
A novel method classifies shapes by their square-root velocity function.
problem Classifying shapes in infinite-dimensional, curved spaces.
method Square-root velocity function, tangent spaces, principal components, combining pairwise classifiers.
result Improves classification accuracy by separating shapes and reducing dimensionality.
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.
Develops new shape metrics for high-dimensional objects.
problem Lack of single metrics to describe shape in high dimensions.
method Introduces hyper-Sphericity and hyper-Shape Proportion metrics.
result Discriminates between different shapes in high dimensions.
Study finds cherry-picking load shaping strategies outperforms others in reducing grid CO2 emissions.
problem Lack of detailed counterfactual data makes it hard to assess load shaping strategies' effectiveness.
method Calibrated granular ERCOT simulations for counterfactual analysis of load shaping strategies.
result LMP-based load shaping outperforms other strategies in reducing grid CO2 emissions.
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.
This work characterizes how data augmentation shapes neural representations.
problem Understanding the impact of data augmentation on neural network representations.
method Embedding neural network hidden representations into a metric space invariant to transformations, analyzing shape-space trajectories.
result Increasing data augmentation strength leads to well-behaved trajectories in the embedded space, and different augmentation types steer representations in distinct directions.
New method for partial matching of shapes with Varifolds.
problem Matching structures with topological or shape differences.
method Varifold shape representation and LDDMM framework.
result Effective partial matching despite topological differences.
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 benchmark for non-rigid 3D human shape retrieval.
problem Distinguishing between body shapes of 3D human models.
method Extended benchmark with 145 new models and FAUST dataset.
result Improved comparison of 25 shape retrieval methods.
A novel method predicts shape development using Riemannian shape spaces.
problem Predicting future shape development from a single observation.
method Proposes a novel prediction method that encodes shapes in a Riemannian shape space and learns hierarchical statistical models.
result Outperforms deep learning-supported variants and state-of-the-art methods in predicting shape development.
SVarM uses varifold representations for shape classification and regression.
problem Challenges in analyzing geometric data due to non-Euclidean shape spaces.
method Develops a neural network-based framework for varifold representations of shapes.
result Demonstrates strong performance and robustness in shape classification and regression.
A new method for analyzing shapes using FDA techniques.
problem Statistical shape analysis of deformed contours.
method Functional Data Analysis (FDA) with basis expansion and principal component analysis.
result Successfully identifies deformation parameters and captures contour distributions.
The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.
problem Reconstructing full-field structural mode shapes from sparse sensor data.
method Physics-Constrained Single-Output Gaussian Process (CONS-SOGP) framework.
result The proposed method provides more accurate and reliable mode shapes.
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.
A new metric captures shape information in manifold learning.
problem Capturing shape information in high-dimensional data.
method Metric based on angular changes along geodesic lines.
result Feasibility and merits of proposed dimensionality reduction scheme.
Method learns shape changes over time from longitudinal data.
problem Tackles learning shape trajectories from repeated observations.
method Combines statistical and deformation models on a diffeomorphism manifold.
result Shows gender and genetic differences in hippocampal atrophy progression.
A neural network learns efficient parametrizations of product shape spaces.
problem Efficiently parametrize complex shape spaces with high computational costs.
method Developed a neural network architecture that separately learns approximations for low-dimensional factors and combines them.
result Demonstrated the effectiveness of the approach on synthetic and real data.
Machine learning methods struggle with geometric data, but shape space analysis provides a framework for studying and analyzing geometric variability.
problem Machine learning methods struggle with geometric data
method Shape space analysis provides a mathematical and computational framework
result Characterizes shape variability, compares geometric objects, and analyzes structural trajectories
Improves functional linear regression with shape transfer learning.
problem Data scarcity in functional linear models.
method Shape-based transfer learning from auxiliary to target domains.
result Enhances robustness and generalizability of functional linear models.
New kernel method for shape classification on Kendall shape space.
problem Classification of shapes on non-Euclidean Kendall shape space.
method Extrinsic Veronese Whitney Gaussian kernel for KRRC on Σ2k. result KRRC classifier performs well on real Kendall shape data.
This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and computational anatomy, of what can be described as geometrico-functional data, that is a da…
Efficient method for shape modeling invariant to rigid motion.
problem Statistical shape modeling for rigidly moving shapes.
method Non-Euclidean Lie group analysis of metric distortion and curvature.
result Outperforms state-of-the-art classifiers in sparse data.
Extends square root velocity transform to handle curves in shape spaces of manifold-valued data.
problem Handling curves that leave the shape space in shape analysis.
method Generalizes absolutely continuous curves to strong Riemannian manifolds and extends SRVT to handle these curves.
result Computations in the SRVT framework can now be applied to curves in shape spaces of manifold-valued data.
Hierarchical geodesic model for analyzing shapes on manifolds.
problem Analyzing temporal observations on manifold-valued data.
method Adapted functional-based metric for efficiency; variational time discretization of geodesics.
result Performed hypothesis tests and estimated mean trends in longitudinal analysis.
This work increases shape bias in CNNs trained on ImageNet, improving robustness without accuracy gain.
problem Shape bias in CNNs trained on ImageNet.
method Uses domain-adversarial training to remove texture clues and increase shape bias.
result The method increases robustness of CNNs without improving accuracy.
3D point cloud attacks examine how neural networks can be fooled.
problem Understanding how 3D neural networks can be exploited by attackers.
method Examined two categories of attacks: distributional and shape attacks.
result Some shape attacks can fool 3D point cloud classification models even after preprocessing.
A new method for selecting model order in statistical shape models.
problem Choosing the right model order in PDMs for optimal performance.
method Information-theoretic criteria for selecting model order.
result The new method provides a better trade-off between overfitting and underfitting.
A novel regression algorithm uses shape analysis to predict curves without training data.
problem Predicting curves without training data for regression problems.
method Shape analysis of trained models to generate new shapes for prediction.
result Successfully predicts curves based on shape analysis of existing models.
Deep neural network predicts cardiac shape from MRI images and patient data.
problem Automatic 3D cardiac shape analysis for large-scale studies.
method Uses deep neural networks combining MRI images and patient metadata.
result Significant agreement with reference shapes in cardiac parameters.
Deep learning predicts AF recurrence from MRI images without pre-processing.
problem Estimating AF recurrence from MRI images efficiently and accurately.
method Deep learning approach to predict shape descriptors directly from MRI images.
result Deep learning method produces similar outcomes to state-of-the-art methods.
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.
Bayesian nonparametric method partitions shapes using curves.
problem Capturing complex shapes in multi-dimensional data.
method Proposes a novel spline partitioning approach using curves.
result Demonstrates improved shape modeling compared to existing methods.
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.
Combines spatial context priors with data term for better dendritic spine segmentation.
problem Poor segmentation results due to overlapping pixel intensity distributions.
method Combines nonparametric context priors with learned-intensity data term and nonparametric shape priors.
result Significant improvements in dendritic spine segmentation.
Modeling functional data, this study uncovers the size-and-shape of functions under noisy observations.
problem Uncertainty in recovering a fixed effect function from noisy observations.
method Bayesian functional mixed model with priors on unitary transformations.
result It is possible to recover the size-and-shape of a square-integrable function μ. Introduces Star-Shaped DDPMs for non-Gaussian distributions.
problem Difficulties in defining DDPMs for non-Gaussian distributions.
method Star-shaped diffusion process, duality with specific Markovian diffusions, efficient algorithms.
result SS-DDPMs can model distributions like Beta, von Mises-Fisher, Dirichlet, Wishart.
A method for reconstructing surfaces from sparse 3D points using statistical shape models.
problem Reconstructing surfaces from sparse 3D point clouds, especially in medical applications.
method Formulate surface reconstruction as a probabilistic problem using Gaussian Mixture Models (GMM) with anisotropic covariances oriented by surface normals.
result Superior accuracy and robustness on sparse data compared to Iterative Closest Points method.
Develops multiscale covariance tensor fields for data shape analysis.
problem Quantifying variation of data at all scales.
method Localized covariance tensor fields (CTF) and strong stability theorems.
result CTFs are robust to sampling, noise, and outliers.
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.