Topic

# Displacement (vector)

About: Displacement (vector) is a research topic. Over the lifetime, 24669 publications have been published within this topic receiving 264944 citations.

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TL;DR: The model predicts the mass specific energy fluctuations of the center of mass per distance to be similar for runners and hoppers and similar to empirical data obtained for animals of various size.

Abstract: A simple spring-mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed. The bouncing mechanism itself results in a confinement of the free parameter space where solutions can be found. In particular, bouncing frequency and vertical displacement are closely related. Only a few parameters, such as the vector of the specific landing velocity and the specific leg length, are sufficient to determine the point of operation of the system. There are more physiological constraints than independent parameters. As constraints limit the parameter space where hopping is possible, they must be tuned to each other in order to allow for hopping at all. Within the range of physiologically possible hopping frequencies, a human hopper selects a frequency where the largest amount of energy can be delivered and still be stored elastically. During running and hopping animals use flat angles of the landing velocity resulting in maximum contact length. In this situation ground reaction force is proportional to specific contact time and total displacement is proportional to the square of the step duration. Contact time and hopping frequency are not simply determined by the natural frequency of the spring-mass system, but are influenced largely by the vector of the landing velocity. Differences in the aerial phase or in the angle of the landing velocity result in the different kinematic and dynamic patterns observed during running and hopping. Despite these differences, the model predicts the mass specific energy fluctuations of the center of mass per distance to be similar for runners and hoppers and similar to empirical data obtained for animals of various size.

1,582 citations

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TL;DR: A way to approach the problem of dense optical flow estimation by integrating rich descriptors into the variational optical flow setting, while reaching out to new domains of motion analysis where the requirement of dense sampling in time is no longer satisfied is presented.

Abstract: Optical flow estimation is classically marked by the requirement of dense sampling in time. While coarse-to-fine warping schemes have somehow relaxed this constraint, there is an inherent dependency between the scale of structures and the velocity that can be estimated. This particularly renders the estimation of detailed human motion problematic, as small body parts can move very fast. In this paper, we present a way to approach this problem by integrating rich descriptors into the variational optical flow setting. This way we can estimate a dense optical flow field with almost the same high accuracy as known from variational optical flow, while reaching out to new domains of motion analysis where the requirement of dense sampling in time is no longer satisfied.

1,429 citations

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Yale University

^{1}TL;DR: This paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images, and an algorithm consistent with that framework, based on a scale-based separation of the image intensity information and the process of measuring motion.

Abstract: THE ROBUST MEASUREMENT OF VISUAL MOTION FROM DIGITIZED IMAGE SEQUENCES HAS BEEN AN IMPORTANT BUT DIFFICULT PROBLEM IN COMPUTER VISION. THIS PAPER DESCRIBES A HIERARCHICAL COMPUTATIONAL FRAMEWORK FOR THE DETERMINATION OF DENSE DISPLACEMENT FIELDS FROM A PAIR OF IMAGES, AND AN ALGORITHM CONSIST- ENT WITH THAT FRAMEWORK. OUR FRAMEWORK IS BASED ON THE SEPARATION OF THE IMAGE INTENSITY INFORMATION AS WELL AS THE PROCESS OF MEASURING MOTION ACCORDING TO SCALE. THE LARGE SCALE INTENSITY INFORMATION IS FIRST USED TO OBTAIN ROUGH ESTIMATES OF IMAGE MOTION, WHICH ARE THEN REFINED BY USING INTENSITY INFORMATION AT SMALLER SCALES. THE ESTIMATES ARE IN THE FORM OF DISPLACEMENT (OR VELOCITY) VECTORS FOR PIXELS AND ARE ACCOMPANIED BY A DIRECTION-DEPENDENT CONFIDENCE MEASURE. A SMOOTHNESS CONSTRAINT IS EMPLOYED TO PROPAGATE THE MEASUREMENTS WITH HIGH CONFIDENCE TO THEIR NEIGBORING AREAS WHERE THE CONFIDENCES ARE LOW. AT ALL LEVELS, THE COMPUTATIONS ARE PIXEL-PARALLEL, UNIFORM ACROSS THE IMAGE, AND BASED ON INFORMATION FROM A SMALL NEIGHBORHOOD OF A PIXEL. FOR OUR ALGORITHM, THE LOCAL DISPLACEMENT VECTORS ARE DETERMIND BY MINI- MIZING THE SUM-OF-SQUARED DIFFERENCES (SSD) OF INTENSITIES, THE CONFIDENCE MEASURES ARE DERIVED FROM THE SHAPE OF THE SSD SURFACE, AND THE SMOOTHNESS CONSTRAINT IS CAST IN THE FORM OF ENERGY MINIMIZATION. RESULTS OF APPLYING OUR ALGORITHM TO PAIRS OF REAL IMAGES ARE INCLUDED. IN ADDITION TO OUR OWN

1,175 citations

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TL;DR: In this article, a technique for modeling arbitrary discontinuities in finite elements is presented, in which both the signed distance function and its derivatives are considered, and a standard displacement Galerkin method is used for developing the discrete equations.

Abstract: A technique for modelling arbitrary discontinuities in finite elements is presented. Both discontinuities in the function and its derivatives are considered. Methods for intersecting and branching discontinuities are given. In all cases, the discontinuous approximation is constructed in terms of a signed distance functions, so level sets can be used to update the position of the discontinuities. A standard displacement Galerkin method is used for developing the discrete equations. Examples of the following applications are given: crack growth, a journal bearing, a non-bonded circular inclusion and a jointed rock mass. Copyright © 2001 John Wiley & Sons, Ltd.

1,091 citations

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TL;DR: In this article, a small well-exposed normal fault zone at Kilve, Somerset, U.K., is described, which consists of 34 individual offset and linked fault segments, and a simple model is presented which assumes different displacement gradients inside and outside the influence of relay structures.

Abstract: A fault zone is produced by the displacement and linkage of component segments, and hence these are important to the understanding of fault zone-development. A small well-exposed normal fault zone at Kilve, Somerset, U.K., is described, which consists of 34 individual offset and linked fault segments. Antithetic faults appear to be associated with bending at relay ramps and foot wall uplift. A simple model is presented which assumes different displacement gradients inside and outside the influence of relay structures. High displacement gradients at the tips of offset fault segments produce lower r/dMAX ratios than those of isolated faults (where r = distance between the fault tip and point of maximum displacement, and dMAX = maximum displacement). Relay structures form between offset normal fault segments, producing inclined zones (relay ramps) whose geometry can be related to the displacement gradients at the fault tips. Linkage points between segments are marked by fault displacement minima, causing further complexity in displacement—distance data.

802 citations