Contact Representation Research Articles

Learning a Contact Potential Field for Modeling the Hand-Object Interaction.

Estimating and synthesizing the hand's manipulation of objects is central to understanding human behaviour. To accurately model the interaction between the hand and object (referred to as the "hand-object"), we must not only focus on the pose of the hand and object, but also consider the contact between them. This contact provides valuable information for generating semantically and physically plausible grasps. In this paper, we propose an explicit contact representation called Contact Potential Field (CPF). In CPF, we model the contact between a pair of hand-object vertices as a spring-mass system. This system encodes the distance of the pair, as well as a likelihood of that contact being stable. Therefore, the system of multiple extended and compressed springs forms an elastic potential field with minimal energy at the optimal grasp position. We apply CPF to two relevant tasks, namely, hand-object pose estimation and grasping pose generation. Extensive experiments on the two challenging tasks and three commonly used datasets have demonstrated that our method can achieve state-of-the-art in several reconstruction metrics, allowing us to produce more physically plausible hand-object poses even when the ground-truth exhibits severe interpenetration or disjointedness.

Contact Representation in Robotic Mechanical Systems Employing Reduced Models

Contact Representation in Robotic Mechanical Systems Employing Reduced Models

Space–time flow computation with boundary layer and contact representation: a 10-year history

In computation of flow problems with moving solid surfaces, moving-mesh methods such as the space–time (ST) variational multiscale method enable mesh-resolution control near the solid surfaces and thus high-resolution boundary-layer representation. There was, however, a perception that in computations where the solid surfaces come into contact, high-resolution boundary-layer representation and actual-contact representation without leaving a mesh protection opening between the solid surfaces were mutually exclusive objectives in a practical sense. The introduction of the ST topology change (ST-TC) method in 2013 changed the perception. The two objectives were no longer mutually exclusive. The ST-TC makes moving-mesh computation possible even without leaving a mesh protection opening. The contact is represented as an actual contact and the boundary layer is represented with high resolution. Elements collapse or are reborn as needed, and that is attainable in the ST framework while retaining the computational efficiency at a practical level. The ST-TC now has a 10-year history of achieving the two objectives that were long seen as mutually exclusive. With the ST-TC and other ST computational methods introduced before and after, it has been possible to address many of the challenges encountered in conducting flow analysis with boundary layer and contact representation, in the presence of additional intricacies such as geometric complexity, isogeometric discretization, and rotation or deformation of the solid surfaces. The flow analyses conducted with these ST methods include car and tire aerodynamics with road contact and tire deformation and ventricle-valve-aorta flow. To help widen awareness of these methods and what they can do, we provide an overview of the methods, including those formulated in the context of isogeometric analysis, and the computations performed over the 10-year history of the ST-TC.

Morphing Triangle Contact Representations of Triangulations

A morph is a continuous transformation between two representations of a graph. We consider the problem of morphing between contact representations of a plane graph. In an {mathcal {F}}-contact representation of a plane graph G, vertices are realized by internally disjoint elements from a family {mathcal {F}} of connected geometric objects. Two such elements touch if and only if their corresponding vertices are adjacent. These touchings also induce the same embedding as in G. In a morph between two {mathcal {F}}-contact representations we insist that at each time step (continuously throughout the morph) we have an {mathcal {F}}-contact representation. We focus on the case when mathcal {F} is the family of triangles in mathbb {R}^2 that are the lower-right half of axis-parallel rectangles. Such RT-representations exist for every plane graph and right triangles are one of the simplest families of shapes supporting this property. Moreover, they naturally correspond to 3-orientations. Thus, they provide a natural case to study regarding morphs of contact representations of plane graphs. We characterize the pairs of RT-representations admitting a morph between each other via the respective 3-orientations. Our characterization leads to a polynomial-time algorithm to decide whether there is a morph between two RT-representations of an n-vertex plane triangulation, and, if so, computes a morph with {mathcal {O}}(n^2) steps. Each of these steps is a linear morph moving the endpoints of each triangle at constant speed along straight-line trajectories. Our characterization also implies that for 4-connected plane triangulations there is a morph between every pair of RT-representations where the “top-most” triangle in both representations corresponds to the same vertex.

Towards color-kinematics duality in generic spacetimes

In this note, we study color-kinematics duality in generic spacetimes. We work with a contact representation for on shell correlators. The position-space integrand is encoded by enumerated differential operators. This setup generalizes certain features of S-matrix kinematics to curved space. Differences between flat and curved space are captured by commutators. We study the nonlinear sigma model at four points as an explicit example and find that color-kinematics duality holds in generic spacetimes. We illustrate our approach in the AdS transition amplitude, a type of on shell correlation function. We find a double copy procedure at four points that connects the nonlinear sigma model, the biadjoint scalar theory, and the special Galileon theory.

Simple algorithms for partial and simultaneous rectangular duals with given contact orientations

A rectangular dual of a graph G is a contact representation of G by axis-aligned rectangles such that (i) no four rectangles share a point and (ii) the union of all rectangles is a rectangle. The partial representation extension problem for rectangular duals asks whether a given partial rectangular dual can be extended to a rectangular dual, that is, whether there exists a rectangular dual where some vertices are represented by prescribed rectangles. The simultaneous representation problem for rectangular duals asks whether two (or more) given graphs that share a subgraph admit rectangular duals that coincide on the shared subgraph. Combinatorially, a rectangular dual can be described by a regular edge labeling (REL), which determines the orientations of the rectangle contacts.We describe linear-time algorithms for the partial representation extension problem and the simultaneous representation problem for rectangular duals when each input graph is given together with a REL. Both algorithms are based on formulations as linear programs, yet they have geometric interpretations and can be seen as extensions of the classic algorithm by Kant and He that computes a rectangular dual for a given graph.

Computational flow analysis with boundary layer and contact representation: II. Heart valve flow with leaflet contact

Abstract In this second part of a two-part article, we provide an overview of the heart valve flow analyses conducted with boundary layer and contact representation, made possible with the space–time (ST) computational methods described in the first part. With these ST methods, we are able to represent the boundary layers near moving solid surfaces, including the valve leaflet surfaces, with the accuracy one gets from moving-mesh methods and without the need for leaving a mesh protection gap between the surfaces coming into contact. The challenge of representing the contact between the leaflets without giving up on high-resolution flow representation near the leaflet surfaces has been overcome. The other challenges that have been overcome include the complexities of a near-actual valve geometry, having in the computational model a left ventricle with an anatomically realistic motion and an aorta from CT scans and maintaining the flow stability at the inflow of the ventricle-valve-aorta sequence, where we have a traction boundary condition during part of the cardiac cycle.

Computational flow analysis with boundary layer and contact representation: I. Tire aerodynamics with road contact

Abstract In computational flow analysis with moving solid surfaces and contact between the solid surfaces, it is a challenge to represent the boundary layers with an accuracy attributed to moving-mesh methods and to represent the contact without leaving a mesh protection gap. The space-time topology change (ST-TC) method, introduced in 2013, makes moving-mesh computation possible even when we have contact between moving solid surfaces or other kinds of flow-domain TC. The contact is represented without giving up on high-resolution flow representation near the moving surfaces. With the ST-TC and other ST computational methods introduced before and after, it has been possible to address many of the challenges encountered in conducting this class of flow analysis in the presence of additional complexities such as geometric complexity, rotation or deformation of the solid surfaces and the multiscale nature of the flow. In this first part of a two-part article, we provide an overview of the methods that made all that possible. We also provide an overview of the computations performed for tire aerodynamics with challenges that include the complexity of a near-actual tire geometry with grooves, road contact, tire deformation and rotation, road roughness and fluid films.

Forecasting Action Through Contact Representations From First Person Video.

Human actions involving hand manipulations are structured according to the making and breaking of hand-object contact, and human visual understanding of action is reliant on anticipation of contact as is demonstrated by pioneering work in cognitive science. Taking inspiration from this, we introduce representations and models centered on contact, which we then use in action prediction and anticipation. We annotate a subset of the EPIC Kitchens dataset to include time-to-contact between hands and objects, as well as segmentations of hands and objects. Using these annotations we train the Anticipation Module, a module producing Contact Anticipation Maps and Next Active Object Segmentations - novel low-level representations providing temporal and spatial characteristics of anticipated near future action. On top of the Anticipation Module we apply Egocentric Object Manipulation Graphs (Ego-OMG), a framework for action anticipation and prediction. Ego-OMG models longer term temporal semantic relations through the use of a graph modeling transitions between contact delineated action states. Use of the Anticipation Module within Ego-OMG produces state-of-the-art results, achieving 1st and 2 place on the unseen and seen test sets, respectively, of the EPIC Kitchens Action Anticipation Challenge, and achieving state-of-the-art results on the tasks of action anticipation and action prediction over EPIC Kitchens. We perform ablation studies over characteristics of the Anticipation Module to evaluate their utility.

Contact representation of short-range correlation in light nuclei studied by the high-momentum antisymmetrized molecular dynamics

The high-momentum antisymmetrized molecular dynamics (HMAMD) is a new promising framework with significant analytical simplicity and efficiency inherited from its antisymmetrized molecular dynamics in describing the high momentum correlations in various nuclear states. In the aim of further improving the numerical efficiency for the description of nucleon-nucleon correlation, we introduce a new formulation by including a new Gaussian weighted basis of high momentum pairs in the HMAMD wave function, with which very rapid convergence is obtained in numerical calculation. It is surprising that the very high-momentum components in the new HMAMD basis are found to be almost equivalent to the contact representation of the nucleon-nucleon pairs with very small nucleon-nucleon distance. The explicit formulation for the contact term significantly improves the numerical efficiency of the HMAMD method, which shows the importance of the contact correlation in the formulation of light nuclei.

Pentagon Contact Representations

Representations of planar triangulations as contact graphs of a set of internally disjoint homothetic triangles or of a set of internally disjoint homothetic squares have received quite some attention in recent years. In this paper we investigate representations of planar triangulations as contact graphs of a set of internally disjoint homothetic pentagons. Surprisingly such a representation exists for every triangulation whose outer face is a $5$-gon. We relate these representations to five color forests. These combinatorial structures resemble Schnyder woods and transversal structures, respectively. In particular there is a bijection to certain $\alpha$-orientations and consequently a lattice structure on the set of five color forests of a given graph. This lattice structure plays a role in an algorithm that is supposed to compute a contact representation with pentagons for a given graph. Based on a five color forest the algorithm builds a system of linear equations and solves it, if the solution is non-negative, it encodes distances between corners of a pentagon representation. In this case the representation is constructed and the algorithm terminates. Otherwise negative variables guide a change of the five color forest and the procedure is restarted with the new five color forest. Similar algorithms have been proposed for contact representations with homothetic triangles and with squares.

Pentagon Contact Representations

Representations of planar triangulations as contact graphs of geometric shapes have received quite some attention in recent years. The most prominent example is Koebe's 'kissing coins theorem', but representations with internally disjoint homothetic triangles or squares have also been studied. In this paper we investigate representations of planar triangulations as contact graphs of a set of internally disjoint homothetic pentagons. Surprisingly, such a representation exists for every triangulation whose outer face is a 5-gon. We relate these representations to five color forests. These combinatorial structures resemble Schnyder woods and transversal structures. In particular there is a bijection to certain α-orientations and consequently a lattice structure on the set of five color forests of a given graph. This distributive lattice plays a role in a heuristic that is supposed to compute a contact representation with pentagons for a given graph.

Contact representation in rigid block models of masonry

Rigid block models are widely used in the analysis of masonry structures, as they provide a sound and efficient approximation of the observed behaviour, namely for modelling collapse modes that do not involve the internal failure of the units. The options available for the numerical representation of contact in rigid block models are discussed, in particular the well-known point contact approaches. The accuracy of the various options is compared for static and dynamical test problems involving bending of columns and walls. Proposals are made concerning the level of contact discretisation, namely the number of contacts and weight rules, required for a good model performance.

Contact representation in rigid block models of masonry

Contact representation in rigid block models of masonry

Accurate and adaptive contact modeling for multi-rate multi-point haptic rendering of static and deformable environments

Common approaches for the haptic rendering of complex scenarios employ multi-rate simulation schemes. Here, the collision queries or the simulation of a complex deformable object are often performed asynchronously at a lower frequency, while some kind of intermediate contact representation is used to simulate interactions at the haptic rate. However, this can produce artifacts in the haptic rendering when the contact situation quickly changes and the intermediate representation is not able to reflect the changes due to the lower update rate.We address this problem utilizing a novel contact model. It facilitates the creation of contact representations that are accurate for a large range of motions and multiple simulation time-steps. We handle problematic geometrically convex contact regions using a local convex decomposition and special constraints for convex areas. We combine our accurate contact model with an implicit temporal integration scheme to create an intermediate mechanical contact representation, which reflects the dynamic behavior of the simulated objects. To maintain a haptic real time simulation, the size of the region modeled by the contact representation is automatically adapted to the complexity of the geometry in contact. Moreover, we propose a new iterative solving scheme for the involved constrained dynamics problems. We increase the robustness of our method using techniques from trust region-based optimization. Our approach can be combined with standard methods for the modeling of deformable objects or constraint-based approaches for the modeling of, for instance, friction or joints. We demonstrate its benefits with respect to the simulation accuracy and the quality of the rendered haptic forces in several scenarios with one or more haptic proxies.

Improved Approximation Algorithms for Box Contact Representations

We study the following geometric representation problem: Given a graph whose vertices correspond to axis-aligned rectangles with fixed dimensions, arrange the rectangles without overlaps in the plane such that two rectangles touch if the graph contains an edge between them. This problem is called \textsc{Contact Representation of Word Networks} (\textsc{Crown}) since it formalizes the geometric problem behind drawing word clouds in which semantically related words are close to each other. \textsc{Crown} is known to be NP-hard, and there are approximation algorithms for certain graph classes for the optimization version, \textsc{Max-Crown}, in which realizing each desired adjacency yields a certain profit. We present the first $O(1)$-approximation algorithm for the general case, when the input is a complete weighted graph, and for the bipartite case. Since the subgraph of realized adjacencies is necessarily planar, we also consider several planar graph classes (namely stars, trees, outerplanar, and planar graphs), improving upon the known results. For some graph classes, we also describe improvements in the unweighted case, where each adjacency yields the same profit. Finally, we show that the problem is APX-hard on bipartite graphs of bounded maximum degree.

Vertex Contact Representations of Paths on a Grid

We study Vertex Contact representations of Paths on a Grid (VCPG). In such a representation, the vertices of G are represented by a family of interiorly disjoint grid-paths on a square grid. Adjacencies are represented by contacts between an endpoint of one grid-path and an interior point of another grid-path. Defining u → v if the path of u ends on the path of v, we obtain an orientation on G from a VCPG. To control the bends of the grid paths the orientation is not enough. We therefore consider pairs (α,ψ): a 2-orientation α and a flow ψ in the angle graph. The 2-orientation describes the contacts of the ends of a grid-path and the flow describes the behavior of a grid-path between its two ends. We give a necessary and sufficient condition for such a pair (α,ψ) to be realizable as a VCPG. Using realizable pairs, we show that every planar (2,2)-tight graph admits a VCPG with at most 2 bends per path and that this bound is tight. In a similar way, we show that simple planar (2,1)-sparse graphs have a 4-bend representation and simple planar (2,0)-sparse graphs have 6-bend representation.

Threshold-coloring and unit-cube contact representation of planar graphs

In this paper we study threshold-coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. A pair of vertices with a small difference in their colors implies that the edge between them is present, while a pair of vertices with a big color difference implies that the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain unit-cube contact representation of several subclasses of planar graphs. Variants of the threshold-coloring problem are related to well-known graph coloring and other graph-theoretic problems. Using these relations we show the NP-completeness for two of these variants, and describe a polynomial-time algorithm for another.

Information content of contact-pattern representations and predictability of epidemic outbreaks.

To understand the contact patterns of a population—who is in contact with whom, and when the contacts happen—is crucial for modeling outbreaks of infectious disease. Traditional theoretical epidemiology assumes that any individual can meet any with equal probability. A more modern approach, network epidemiology, assumes people are connected into a static network over which the disease spreads. Newer yet, temporal network epidemiology, includes the time in the contact representations. In this paper, we investigate the effect of these successive inclusions of more information. Using empirical proximity data, we study both outbreak sizes from unknown sources, and from known states of ongoing outbreaks. In the first case, there are large differences going from a fully mixed simulation to a network, and from a network to a temporal network. In the second case, differences are smaller. We interpret these observations in terms of the temporal network structure of the data sets. For example, a fast overturn of nodes and links seem to make the temporal information more important.

Knot contact homology and representations of knot groups

We study certain linear representations of the knot group that induce augmentations of knot contact homology. This perspective on augmentations enhances our understanding of the relationship between the augmentation polynomial and the A-polynomial of the knot. For example, we show that for 2-bridge knots the polynomials agree and that this is never the case for (non-2-bridge) torus knots, nor for a family of 3-bridge pretzel knots. In addition, we obtain a lower bound on the meridional rank of the knot. As a consequence, our results give another proof that torus knots and a family of pretzel knots have meridional rank equal to their bridge number.