This document describes an ITK implementation of an interactive method for tracing curvilinear structures. The basic tools provided in this framework are an oriented flux-based tubularity measure and a geodesic path tracer that uses the fast marching algorithm. The framework is efficient and requires minimal user interaction to trace curvilinear structures such as vessels and neurites in 2D ima...

This paper presents a general framework to segment curvilinear objects in 2D images. A pre-processing step relies on mathematical morphology to obtain a connected line which encloses curvilinear objects. Then, a graph is constructed from this line and a Markovian Random Field is defined to perform objects segmentation. Applications of our framework are numerous: they go from simple surve segmen...

This paper introduces an object recognition strategy based on the following premises: i) an object can be identified on the basis of the optical flow it induces on a stationary observer, and ii) a basis for recognition can be built on the appearance of flow corresponding to local curvilinear motion. Unlike other approaches that seek to recognize particular motions, ours focuses on the problem o...

Recently we have created a multitime maximum principle gathering together some concepts in Mechanics, Field Theory, Differential Geometry, and Control Theory. The basic tools of our theory are variational PDE systems, adjoint PDE systems, Hamiltonian PDE systems, duality, multitime maximum principle, incavity on manifolds etc. Now we justify the multitime maximum principle for curvilinear integ...

We propose a curvilinear search for nonlinear systems of equations and path-following methods that are very nonlinear with the dominant part in the tangent space. The curvilinear search is very easy to implement and should be used with the (Gauss-)Newton method. At the cost of one function evaluation the curvature along the search direction can be reduced. For zero residual nonlinear least squa...

Early attempts to derive curved beam and shell elements in a curvilinear system were dramatically unsuccessful. This was wrongly attributed to the failure of these elements to recover strain-free rigid body displacement modes in a curvilinear co-ordinate description. Recent evidence points to a ‘membrane locking’ phenomenon that arises when constrained strain fields corresponding to inextension...

ÐWe present an efficient and robust ray-casting algorithm for directly rendering a curvilinear volume of arbitrarily-shaped cells. By projecting cell-faces onto the image plane, we have effectively addressed three critical steps of the ray-casting process, namely finding the entry cell-faces for a ray, traversing along the ray from one cell to another, and reconstructing data values at the ray/...

2 Vector Analysis 6 2.1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Scalar Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 The Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 The Curl . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

The development of robust high-order finite element methods requires the curvilinear discretization for complex geometries without user intervention. In this work we present a new technique that allows for the automatic construction of high-order curvilinear meshes with two main features: first, the boundary of the mesh is globally smooth, i.e., it satisfies either the C 1 or the C 2 smoothness...

While you have probably used tensors of rank 1, i.e vectors, in special relativity, relativity is most efficiently expressed in terms of tensor algebra. General relativity, however, requires tensor algebra in a general curvilinear coordinate system. Before discussing special relativity, it will be useful to introduce some of the mathematics of differential forms in a general curvilinear set of ...