Related papers: Particle-Based Shape Modeling for Arbitrary Region…
The human nose exhibits a huge variation in shape among individuals. All these variants alter the airflow through the nasal cavity and can impact how we smell odors. To acquire a better understanding of physiological and pathological…
The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape…
Anatomical shape analysis plays a pivotal role in clinical research and hypothesis testing, where the relationship between form and function is paramount. Correspondence-based statistical shape modeling (SSM) facilitates population-level…
Statistical shape modeling (SSM) enables population-based quantitative analysis of anatomical shapes, informing clinical diagnosis. Deep learning approaches predict correspondence-based SSM directly from unsegmented 3D images but require…
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…
We propose a new shape analysis approach based on the non-local analysis of local shape variations. Our method relies on a novel description of shape variations, called Local Probing Field (LPF), which describes how a local probing operator…
To date, the comparison of Statistical Shape Models (SSMs) is often solely performance-based, carried out by means of simplistic metrics such as compactness, generalization, or specificity. Any similarities or differences between the actual…
Model reduction of large nonlinear systems often involves the projection of the governing equations onto linear subspaces spanned by carefully-selected modes. The criteria to select the modes relevant for reduction are usually…
Fragment-based shape signature techniques have proven to be powerful tools for computer-aided drug design. They allow scientists to search for target molecules with some similarity to a known active compound. They do not require reference…
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
The study of physiology demonstrates that the form (shape)of anatomical structures dictates their functions, and analyzing the form of anatomies plays a crucial role in clinical research. Statistical shape modeling (SSM) is a widely used…
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…
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of…
Despite progress in the rapidly developing field of geometric deep learning, performing statistical analysis on geometric data--where each observation is a shape such as a curve, graph, or surface--remains challenging due to the…
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive…
Identification of regions of interest (ROI) associated with certain disease has a great impact on public health. Imposing sparsity of pixel values and extracting active regions simultaneously greatly complicate the image analysis. We…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
This article describes a volumetric approach for procedural shape modeling and a new Procedural Shape Modeling Language (PSML) that facilitates the specification of these models. PSML provides programmers the ability to describe shapes in…
Statistical Shape Models of faces and various body parts are heavily used in medical image analysis, computer vision and visualization. Whilst the field is well explored with many existing tools, all of them aim at experts, which limits…