This article is concerned with finite element implementations of the three- dimensional geometrically exact rod. The special attention is paid to identifying the con- dition that ensures the frame invariance of the re...This article is concerned with finite element implementations of the three- dimensional geometrically exact rod. The special attention is paid to identifying the con- dition that ensures the frame invariance of the resulting discrete approximations. From the perspective of symmetry, this requirement is equivalent to the commutativity of the employed interpolation operator I with the action of the special Euclidean group SE（3）, or I is SE（3）-equivariant. This geometric criterion helps to clarify several subtle issues about the interpolation of finite rotation. It leads us to reexamine the finite element for- mulation first proposed by Simo in his work on energy-momentum conserving algorithms. That formulation is often mistakenly regarded as non-objective. However, we show that the obtained approximation is invariant under the superposed rigid body motions, and as a corollary, the objectivity of the continuum model is preserved. The key of this proof comes from the observation that since the numerical quadrature is used to compute the integrals, by storing the rotation field and its derivative at the Gauss points, the equiv- ariant conditions can be relaxed only at these points. Several numerical examples are presented to confirm the theoretical results and demonstrate the performance of this al- gorithm.展开更多
Image registration is an old topic but has a new application in deep-sky imaging fields named live stacking. In this Letter, we propose a live stacking algorithm based on star detection, description, and matching. A t...Image registration is an old topic but has a new application in deep-sky imaging fields named live stacking. In this Letter, we propose a live stacking algorithm based on star detection, description, and matching. A thresholding method based on Otsu and centralization is proposed to implement star detection. Then, a translation and rotation invariant descriptor is proposed to provide accurate feature matching. Extensive experiments illustrate that our proposed method is feasible in deep-sky image live stacking.展开更多
文摘This article is concerned with finite element implementations of the three- dimensional geometrically exact rod. The special attention is paid to identifying the con- dition that ensures the frame invariance of the resulting discrete approximations. From the perspective of symmetry, this requirement is equivalent to the commutativity of the employed interpolation operator I with the action of the special Euclidean group SE（3）, or I is SE（3）-equivariant. This geometric criterion helps to clarify several subtle issues about the interpolation of finite rotation. It leads us to reexamine the finite element for- mulation first proposed by Simo in his work on energy-momentum conserving algorithms. That formulation is often mistakenly regarded as non-objective. However, we show that the obtained approximation is invariant under the superposed rigid body motions, and as a corollary, the objectivity of the continuum model is preserved. The key of this proof comes from the observation that since the numerical quadrature is used to compute the integrals, by storing the rotation field and its derivative at the Gauss points, the equiv- ariant conditions can be relaxed only at these points. Several numerical examples are presented to confirm the theoretical results and demonstrate the performance of this al- gorithm.
文摘Image registration is an old topic but has a new application in deep-sky imaging fields named live stacking. In this Letter, we propose a live stacking algorithm based on star detection, description, and matching. A thresholding method based on Otsu and centralization is proposed to implement star detection. Then, a translation and rotation invariant descriptor is proposed to provide accurate feature matching. Extensive experiments illustrate that our proposed method is feasible in deep-sky image live stacking.
