Accurate 3D Shape Correspondence by a Local Description Darcyan Principal Curvature Fields (original) (raw)
Related papers
2017
In this paper, we address the problem of the correspondence b etween 3D non-rigid human shapes. We propose a local surface description around the 3D human body extremi i s. It is based on the mean of principal curvature fields values on the intrinsic Darcyan parametriz ation constructed around these points. The similarity between the resulting descriptors is, then, measured in the sense of theL2 distance. Experiments on a several human objects from the TOSCA dataset confirm the accuracy of t he proposed approach.
Non-rigid Shape Correspondence Using Pointwise Surface Descriptors and Metric Structures
Mathematics and Visualization, 2012
Finding a correspondence between two non-rigid shapes is one of the cornerstone problems in the field of three-dimensional shape processing. We describe a framework for marker-less non-rigid shape correspondence, based on matching intrinsic invariant surface descriptors, and the metric structures of the shapes. The matching task is formulated as a quadratic optimization problem that can be used with any type of descriptors and metric. We minimize it using a hierarchical matching algorithm, to obtain a set of accurate correspondences. Further, we present the correspondence ambiguity problem arising when matching intrinsically symmetric shapes using only intrinsic surface properties. We show that when using isometry invariant surface descriptors based on eigendecomposition of the Laplace-Beltrami operator, it is possible to construct distinctive sets of surface descriptors for different possible correspondences. When used in a proper minimization problem, those descriptors allow us to explore a number of possible correspondences between two given shapes.
A Survey on Shape Correspondence
We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours, or point sets. This survey is motivated in part by recent developments in space-time registration, where one seeks a correspondence between non-rigid and time-varying surfaces, and semantic shape analysis, which underlines a recent trend to incorporate shape understanding into the analysis pipeline. Establishing a meaningful correspondence between shapes is often difficult since it generally requires an understanding of the structure of the shapes at both the local and global levels, and sometimes the functionality of the shape parts as well. Despite its inherent complexity, shape correspondence is a recurrent problem and an essential component of numerous geometry processing applications. In this survey, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria arising from the problem definition. The main categories of classification are defined in terms of the input and output representation, objective function, and solution approach. We conclude the survey by discussing open problems and future perspectives.
An Adaptive Descriptor for Functional Correspondence Between Non-Rigid 3D Shapes
2018 IEEE International WIE Conference on Electrical and Computer Engineering (WIECON-ECE), 2018
In this paper, we propose an adaptive descriptor for functional correspondence between non-rigid 3D shapes. This descriptor is computed based on a norm between points in Global Point Signature (GPS) domain. We calculate the initial descriptors by utilizing initial correspondences estimating in GPS domain. Moreover, we present an iteration method for extending the initial descriptor based on candidate correspondences. Our method is implemented and benchmarked with others; the results shows that our paradigm improves overall matching canability,
Robust 2D Shape Correspondence Using Geodesic Shape Context
context
A meaningful correspondence and similarity measure between shapes is particularly useful in applications such as morphing, object recognition, shape registration and retrieval. In this paper, we present a robust shape descriptor for points along a 2D contour, based on the curvature distribution collected over bins arranged geodesically along the contour. Convolution, binning and hysteresis thresholding of curvatures are applied to render the descriptor more robust against noise and non-rigid shape deformation. Once the shape descriptor is computed for every point or feature vertex of the two shapes to be matched, a one-to-one correspondence can be quickly established through best matching of the descriptors, aided by a proximity heuristic. Our approach does not rely on the linear ordering of the points along a contour, facilitating its 3D generalization. It is also capable of matching all the points along the contour, not just a specified set of feature vertices. Our shape descriptor is intuitive, fast to compute, shape distinguishing, and easy to implement. The performance of our approach, when applied to shape correspondence and shape retrieval on the Brown database and the articulated shapes database of Ling et al., shows that it is robust against both rigid and common non-rigid transformations such as bending and moderate stretching.
Hierarchical Framework for Shape Correspondence
Numerical Mathematics: Theory, Methods and Applications
Detecting similarity between non-rigid shapes is one of the fundamental problems in computer vision. In order to measure the similarity the shapes must first be aligned. As opposite to rigid alignment that can be parameterized using a small number of unknowns representing rotations, reflections and translations, non-rigid alignment is not easily parameterized. Majority of the methods addressing this problem boil down to a minimization of a certain distortion measure. The complexity of a matching process is exponential by nature, but it can be heuristically reduced to a quadratic or even linear for shapes which are smooth two-manifolds. Here we model the shapes using both local and global structures, employ these to construct a quadratic dissimilarity measure, and provide a hierarchical framework for minimizing it to obtain sparse set of corresponding points. These correspondences may serve as an initialization for dense linear correspondence search.
Matching 3d shapes using 2d conformal representations
2004
Matching 3D shapes is a fundamental problem in Medical Imaging with many applications including, but not limited to, shape deformation analysis, tracking etc. Matching 3D shapes poses a computationally challenging task. The problem is especially hard when the transformation sought is diffeomorphic and non-rigid between the shapes being matched. In this paper, we propose a novel and computationally efficient matching technique which guarantees that the estimated non-rigid transformation between the two shapes being matched is a diffeomorphism.
An Efficient Approach to Correspondences between Multiple Non‐Rigid Parts
Computer Graphics Forum, 2014
Identifying multiple deformable parts on meshes and establishing dense correspondences between them are tasks of fundamental importance to computer graphics, with applications to e.g. geometric edit propagation and texture transfer. Much research has considered establishing correspondences between non‐rigid surfaces, but little work can both identify similar multiple deformable parts and handle partial shape correspondences. This paper addresses two related problems, treating them as a whole: (i) identifying similar deformable parts on a mesh, related by a non‐rigid transformation to a given query part, and (ii) establishing dense point correspondences automatically between such parts. We show that simple and efficient techniques can be developed if we make the assumption that these parts locally undergo isometric deformation. Our insight is that similar deformable parts are suggested by large clusters of point correspondences that are isometrically consistent. Once such parts are i...
Image and Vision Computing, 2008
Robust solutions for correspondence matching of deformable objects are prerequisite for many applications, particularly for analyzing and comparing soft tissue organs in the medical domain. However, this has proved very difficult for 3D model surfaces, especially for approximate symmetric organs such as the liver, the stomach and the head. In this paper, we propose a novel approach to establish the 3D point-correspondence for polygonal free-form models based on an analysis of the relative angle distribution around each vertex with respect to relative reference frame calculated from principal component analysis (PCA). Two kinds of distributions, the Relative Angle-Context Distribution (RACD) and the Neighborhood Relative Angle-Context Distribution (NRACD) have been defined respectively from the probability mass function of relative angles context. RACD describes the global geometric features while NRACD provides a hierarchical local to global shape description. The experiments and evaluation of adopting these features for the human head and liver models show that both distributions are capable of building robust point correspondence while the NRACD gives better performance because it contains additional information on the spatial relationship among vertices and has the ability to provide an effective neighborhood shape description. Furthermore, we propose a similarity measure between correspondence ready models based on relative angle-context distribution factors. The experimental results demonstrate that this approach is very promising for model analysis, 3D model retrieval and classification.