Related papers: Algorithms to automatically quantify the geometric…
We demonstrate applications of the Gaussian process-based landmarking algorithm proposed in [T. Gao, S.Z. Kovalsky, and I. Daubechies, SIAM Journal on Mathematics of Data Science (2019)] to geometric morphometrics, a branch of evolutionary…
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…
We present results of a long-term team collaboration of mathematicians and biologists. We focus on building a mathematical framework for the shape space constituted by a collection of homologous bones or teeth from many species. The…
Three-dimensional shape reconstruction of 2D landmark points on a single image is a hallmark of human vision, but is a task that has been proven difficult for computer vision algorithms. We define a feed-forward deep neural network…
We propose a fully automatic method for fitting a 3D morphable model to single face images in arbitrary pose and lighting. Our approach relies on geometric features (edges and landmarks) and, inspired by the iterated closest point…
Face alignment aims to estimate the locations of a set of landmarks for a given image. This problem has received much attention as evidenced by the recent advancement in both the methodology and performance. However, most of the existing…
In this paper, we address the problem of building dense correspondences between human images under arbitrary camera viewpoints and body poses. Prior art either assumes small motion between frames or relies on local descriptors, which cannot…
Landmark digitization is essential in geometric morphometrics, enabling the quantification of biological shapes, such as facial structures, for in-depth morphological analysis. Traditional landmarking, which identifies specific anatomical…
In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…
In this work, we focus on the task of learning and representing dense correspondences in deformable object categories. While this problem has been considered before, solutions so far have been rather ad-hoc for specific object types (i.e.,…
We present an algorithm that automatically establishes dense correspondences between a large number of 3D faces. Starting from automatically detected sparse correspondences on the outer boundary of 3D faces, the algorithm triangulates…
The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be…
Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
Anatomical landmark correspondences in medical images can provide additional guidance information for the alignment of two images, which, in turn, is crucial for many medical applications. However, manual landmark annotation is…
To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…
Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…
Finding localized correspondences across different images of the same object is crucial to understand its geometry. In recent years, this problem has seen remarkable progress with the advent of deep learning-based local image features and…
Recent technological developments have spurred great advances in the computerized tracking of joints and other landmarks in moving animals, including humans. Such tracking promises important advances in biology and biomedicine. Modern…
Statistical shape modeling is an essential tool for the quantitative analysis of anatomical populations. Point distribution models (PDMs) represent the anatomical surface via a dense set of correspondences, an intuitive and easy-to-use…