相关论文: A discrete framework to find the optimal matching …

Optimization on Hadamard manifolds -- the natural Riemannian setting for globally geodesically convex problems -- relies on exponential maps to retract tangent vectors and parallel transport to connect tangent spaces across the manifold.…

Nowadays, high-speed machining is usually used for production of hardened material parts with complex shapes such as dies and molds. In such parts, tool paths generated for bottom machining feature with the conventional parallel plane…

We provide a simple unified approach to obtain (i) Discrete polygonal isoperimetric type inequalities of arbitrary high order. (ii) Arbitrary high order isoperimetric type inequalities for smooth curves, where both upper and lower bounds…

Matching deformable objects using their shapes is an important problem in computer vision since shape is perhaps the most distinguishable characteristic of an object. The problem is difficult due to many factors such as intra-class…

This paper proposes a general framework of Riemannian adaptive optimization methods. The framework encapsulates several stochastic optimization algorithms on Riemannian manifolds and incorporates the mini-batch strategy that is often used…

A unified framework to derive optimized compact schemes for a uniform grid is presented. The optimal scheme coefficients are determined analytically by solving an optimization problem to minimize the spectral error subject to equality…

Riemannian cubics in tension are critical points of the linear combination of two objective functionals, namely the squared norms of the velocity and acceleration of a curve on a Riemannian manifold. We view this variational problem of…

This work deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…

In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in…

This paper considers the problem of finding a meaningful template function that represents the common pattern of a sample of curves. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping…

In this paper, we consider the problem of finding dense intrinsic correspondence between manifolds using the recently introduced functional framework. We pose the functional correspondence problem as matrix completion with manifold…

The reach of a submanifold of $\mathbb{R}^N$ is defined as the largest radius of a tubular neighbourhood around the submanifold that avoids self-intersections. While essential in geometric and topological applications, computing the reach…

In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which are used in computer aided geometric design. We consider these curves in the framework of the similarity geometry and characterize…

We present a robust method to find region-level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the…

The minimal path method has proven to be particularly useful and efficient in tubular structure segmentation applications. In this paper, we propose a new minimal path model associated with a dynamic Riemannian metric embedded with an…

Determining the quantum circuit complexity of a unitary operation is closely related to the problem of finding minimal length paths in a particular curved geometry [Nielsen et al, Science 311, 1133-1135 (2006)]. This paper investigates many…

In a recent article, we have shown that a variety of localized polynomial frames, including isotropic as well as directional systems, are suitable for detecting jump discontinuities along circles on the sphere. More precisely, such edges…

We present an efficient, parallel, constrained optimization technique for approximating CAD curves with super-convergent rates. The optimization function is a disparity measure in terms of a piece-wise polynomial approximation and a curve…

Kernel-based non-linear dimensionality reduction methods, such as Local Linear Embedding (LLE) and Laplacian Eigenmaps, rely heavily upon pairwise distances or similarity scores, with which one can construct and study a weighted graph…

This paper addresses the morphing of manifold-valued images based on the time discrete geodesic paths model of Berkels, Effland and Rumpf 2015. Although for our manifold-valued setting such an interpretation of the energy functional is not…