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.
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.
Statistical shape models enhance machine learning algorithms providing prior information about deformation. A Point Distribution Model (PDM) is a popular landmark-based statistical shape model for segmentation. It requires choosing a model order, which determines how much of the variation seen in the training data is a…
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.
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.
Mathematical methods of population genetics and framework of exchangeability provide a Markov chain model for analysis and interpretation of stochastic behaviour of equity markets, explaining, in particular, market shape formation, statistical equilibrium and temporal stability of market weights.
Study compares geometric approaches for shape and deformation statistics.
problem Characterizing statistical models of shapes and deformations.
method Information geometry and Wasserstein geometry.
result Wasserstein estimator is robust against waveform perturbation.
In this paper, we describe a novel shape classification method which is embedded in the Bayesian paradigm. We discuss the modelling and the resulting shape classification algorithm for two and three dimensional data shapes. We conclude by evaluating the efficiency and efficacy of the proposed algorithm on the Kimia sha…
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.
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.
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.
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.
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.
Shape information is of great importance in many applications. For example, the oil-bearing capacity of sand bodies, the subterranean remnants of ancient rivers, is related to their cross-sectional shapes. The analysis of these shapes is therefore of some interest, but current classifications are simplistic and ad hoc.…
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.
Active-set algorithm improves Cox regression for shape-restricted covariates.
problem Improving Cox regression for shape-restricted covariates.
method Shape-restricted inference using active-set optimization for spline basis expansion.
result Active-set algorithm produces accurate linear covariate effect estimates.
Left atrium shape has been shown to be an independent predictor of recurrence after atrial fibrillation (AF) ablation. Shape-based representation is imperative to such an estimation process, where correspondence-based representation offers the most flexibility and ease-of-computation for population-level shape statisti…
New model combines shape and feature-based measures for better time series classification.
problem Limited approaches in time series classification lead to poor results for some classes.
method Proposes a new model that automatically decides between shape and feature-based measures.
result Improves classification accuracy statistically significantly on real-world datasets.
The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to early formulations of the problem - with an object to be classified described as …
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.
Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their asymmetric generalizations. Properties of these estimators depend on the choice of pena…
We propose a method to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this tr…
Surveying nonparametric inference with shape constraints, past and future.
problem Statistical inference under shape constraints.
method Historical overview and future directions.
result Outlook on future research directions.
This article presents certain recent methodologies and some new results for the statistical analysis of probability distributions on manifolds. An important example considered in some detail here is the 2-D shape space of k-ads, comprising all configurations of k planar landmarks (k>2)-modulo translation, scaling a…
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.
New findings challenge the traditional U-shaped curve of model complexity and error, revealing a second descent in error as model size increases.
problem The traditional U-shaped curve of model complexity and prediction error is incomplete, with recent work suggesting a second descent in error as model size increases.
method Careful consideration of multiple complexity axes and a nonparametric statistics perspective were used to interpret the observed double descent curves.
result The observed double descent curves in classical statistical machine learning methods fold back into traditional convex shapes, resolving tensions with statistical intuition.
Kernel-based tests for shape constraints in finance.
problem Enforcing shape relations on latent functions in financial econometrics.
method Kernel-based nonparametric framework for mean-variance optimization.
result Established statistical properties and a joint Wald-type statistic for testing shape constraints.
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.
The paper proposes a new method for modeling and quantifying uncertainty in multiple closed curves.
problem Modeling and uncertainty quantification of multiple closed curves.
method A multiple-output, multi-dimensional Gaussian process modeling framework.
result The proposed method provides meaningful uncertainty quantification for curve and shape-related tasks.
Paper proposes a shape-constrained approach to distributionally robust learning.
problem Challenges in statistical learning under distribution shift.
method Shape-constrained approach to distributionally robust learning (DRL). Assumes isotonic density ratio.
result Improved accuracy demonstrated in empirical studies.
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.
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
We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of t…
Informative and discriminative feature descriptors play a fundamental role in deformable shape analysis. For example, they have been successfully employed in correspondence, registration, and retrieval tasks. In the recent years, significant attention has been devoted to descriptors obtained from the spectral decomposi…
The incredible variety of galaxy shapes cannot be summarized by human defined discrete classes of shapes without causing a possibly large loss of information. Dictionary learning and sparse coding allow us to reduce the high dimensional space of shapes into a manageable low dimensional continuous vector space. Statisti…
NAMLSS models provide interpretable neural regression for location, scale, and shape.
problem Lack of interpretability in deep learning models for complex data distributions.
method Combines classical statistical methods with DNNs for distributional regression.
result Achieves visual interpretability and predictive power of deep learning models.
New method estimates shape distance in neural representations with limited data.
problem Measuring geometric similarity between high-dimensional network representations.
method Method-of-moments estimator with tunable bias-variance tradeoff.
result New estimator achieves lower bias than standard methods in high-dimensional settings.
DNAMite creates interpretable, calibrated survival analysis models.
problem Limited interpretability in survival analysis models, especially for healthcare applications.
method Feature discretization and kernel smoothing in embedding module for flexible shape functions.
result DNAMite produces calibrated shape functions interpretable as contributions to cumulative incidence function.
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.
These are the proceedings of the workshop "Math in the Black Forest", which brought together researchers in shape analysis to discuss promising new directions. Shape analysis is an inter-disciplinary area of research with theoretical foundations in infinite-dimensional Riemannian geometry, geometric statistics, and geo…
A novel multi-resolution cluster detection (MCD) method is proposed to identify irregularly shaped clusters in space. Multi-scale test statistic on a single cell is derived based on likelihood ratio statistic for Bernoulli sequence, Poisson sequence and Normal sequence. A neighborhood variability measure is defined to …
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and ca…
In the series of our earlier papers on the subject, we proposed a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We developed algorithms that allowed to detect objects of unknown shapes in the presence of non…
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.
Unified treatment of elastic metrics for curves in any dimension.
problem Defining metrics on spaces of Euclidean curves for statistical analysis.
method Developing a unified approach to elastic metrics, extending results on existence of solutions and algorithms for computing distances and geodesics.
result Unified treatment of elastic metrics for all parameter choices, extending previous work.
Unified framework for hard affine SDP constraints in vRKHSs.
problem Incorporating shape constraints into predictive models for rich function classes.
method Unified convex optimization framework using second-order cone tightening.
result Unified and modular approach for handling multiple shape constraints.
Study characterizes bladder motion using dynamic MRI and statistical analysis.
problem Limited volume coverage in dynamic MRI sequences hinders 3D shape reconstruction.
method 3D dense velocity measurements, LDDMM framework, statistical characterization, mean curvature changes, surface deformation analysis.
result Stable shape descriptor for characterizing bladder surface dynamics.
A universal method for hypothesis tests and confidence sets without regularity conditions.
problem Difficult inference in irregular statistical models.
method Modified likelihood ratio statistic (split LRT).
result Works for any parametric and some nonparametric models.