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We describe new approaches for distances between pairs of 2-dimensional surfaces (embedded in 3-dimensional space) that use local structures and global information contained in inter-structure geometric relationships. We present algorithms to automatically determine these distances as well as geometric correspondences. This is motivated by the aspiration of students of natural science to understand the continuity of form that unites the diversity of life. At present, scientists using physical traits to study evolutionary relationships among living and extinct animals analyze data extracted from carefully defined anatomical correspondence points (landmarks). Identifying and recording these landmarks is time consuming and can be done accurately only by trained morphologists. This renders these studies inaccessible to non-morphologists, and causes phenomics to lag behind genomics in elucidating evolutionary patterns. Unlike other algorithms presented for morphological correspondences our approach does not require any preliminary marking of special features or landmarks by the user. It also differs from other seminal work in computational geometry in that our algorithms are polynomial in nature and thus faster, making pairwise comparisons feasible for significantly larger numbers of digitized surfaces. We illustrate our approach using three datasets representing teeth and different bones of primates and humans, and show that it leads to highly accurate results.
Purpose: Whole-heart MRA techniques typically target pre-determined motion states and address cardiac and respiratory dynamics independently. We propose a novel fast reconstruction algorithm, applicable to ungated free-running sequences, that leverag
Accurate isolation and quantification of intraocular dimensions in the anterior segment (AS) of the eye using optical coherence tomography (OCT) images is important in the diagnosis and treatment of many eye diseases, especially angle closure glaucom
Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape representations
We propose a method to learn object representations from 3D point clouds using bundles of geometrically interpretable hidden units, which we call geometric capsules. Each geometric capsule represents a visual entity, such as an object or a part, and
Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element approximations