Elasticity of Space-Time: Basis of Newton’s 2nd Law of Motion

In this paper we derive Newton’s 2nd Law of Motion from the constitutive equation of elasticity of a space-time continuum in four dimensions. This we do by introducing a four-dimensional material continuum with a Minkowskian metric, in analogy with Einstein’s general theory of relativity. The four-continuum is deformable in both space and time. The physics of the deformation is embedded in a variational principle, which is a form-invariant extension of its classical mechanical counterpart in three dimensions, but with the acceleration term absent. General dynamic equations of elasticity in four dimensions are thereby derived. When the constraint of temporal inextensibility (universal time) is introduced, these equations yield readily the dynamic equations of elasticity in three dimensions. The presence of the inertia term in these equations, is a direct consequence of the temporal curvature induced by the deformation of the four-continuum. Newton’s law of motion for rigid bodies follows when the additional constraint of spatial inextensibility is introduced.     

Development and implementation of a NURBS curve motion interpolator

This paper deals with the issues of development and implementation of a real-time NURBS interpolator for a six-axis robot. Using an open-architecture controller system as a testbed, a real-time NURBS curve interpolator was developed, implemented and tested. Sample runs were conducted with the resulting trajectories measured in real-time during robot motion. The resulting trajectories are analyzed, discussed and compared with those from a commonly used point-to-point approximation technique. The real-time NURBS curve interpolator's feasibility, advantages and related issues are also discussed.     

A region-based selective optical flow back-projection for genuine motion vector estimation

Motion vector plays one significant feature in moving object segmentation. However, the motion vector in this application is required to represent the actual motion displacement, rather than regions of visually significant similarity. In this paper, region-based selective optical flow back-projection (RSOFB) which back-projects optical flows in a region to restore the region's motion vector from gradient-based optical flows, is proposed to obtain genuine motion displacement. The back-projection is performed based on minimizing the projection mean square errors of the motion vector on gradient directions. As optical flows of various magnitudes and directions provide various degrees of reliability in the genuine motion restoration, the optical flows to be used in the RSOFB are optimally selected based on their sensitivity to noises and their tendency in causing motion estimation errors. In this paper a deterministic solution is also derived for performing the minimization and obtaining the genuine motion magnitude and motion direction.     

Air entrainment in fresh concrete with PFA

The results of a study into the influence of PFA on air entrainment in fresh concrete are discussed It is shown that the required dosage of AEA to produce an air content of 5.5 ± 0.5% in a PFA modified concrete mix is two-six times that required in the corresponding neat OPC concrete mix. The dosage of a vinsol based air entraining agent (AEA) required appears to be directly related to the PFA content of the mix. Similar direct relationships were obtained with a range of different PFAs. The dosage of an AEA based on the salt of a fatty acid appears to be sensitive to both PFA and OPC contents. For the type of PFA used, the variability of measured air content or the amount of air retained after continued agitation both indicated that vinsol based AEAs show the highest variability whilst fatty acid based AEAs show low variability. The between batch variability of air content was significantly improved by the addition of PFA regardless of the AEA used.     

Convex relaxation for a 3D spatiotemporal segmentation model using the primal-dual method

A method based on 3D videos is proposed for multi-target segmentation and tracking with a moving viewing system. A spatiotemporal energy functional is built up to perform motion segmentation and estimation simultaneously. To overcome the limitation of the local minimum problem with the level set method, a convex relaxation method is applied to the 3D spatiotemporal segmentation model. The relaxed convex model is independent of the initial condition. A primal-dual algorithm is used to improve computational efficiency. Several indoor experiments show the validity of the proposed method.     

Motion-based method for estimating time required to attach self-adhesive insulators

A self-adhesive insulator is a component of a home appliance that is used to suppress vibration or prevent humidity affecting the internal parts of the appliance. There is a wide range of types and designs available, allowing them to be applied to areas having different shapes. At the design stage, once an insulator design has been developed sufficiently to identify its dimensions and features, the attaching time and baseline cost must be estimated with reasonable accuracy to enable a comparison of vendor quotes. However, the current estimation method is not sufficiently accurate in terms of the baseline cost. This paper presents a motion-based time-estimating scheme with which the time required for the attachment of such insulators can be calculated more accurately. The scheme has been developed by analyzing the motions needed to attach 350 insulators and then designating representative motions and their time values. For this purpose, a modular arrangement of predetermined time standards (MODAPTS) is adopted. Motion-based time-estimation method is useful in terms of simplicity and accuracy. It enables design engineers to estimate the time required for the attachment based only on a drawing of the insulator and a few MODAPTS rules. Estimates made with this method should vary from the actual value by no more than 9.5%.     

Single frame correction of motion artifacts in PMD-based time of flight cameras

One of the leading time of flight imaging technologies for depth sensing is based on Photonic Mixer Devices (PMD). In PMD sensors each pixel samples the correlation between emitted and received light signals. Current PMD cameras compute eight correlation samples per pixel in four sequential stages to obtain depth with invariance to signal amplitude and offset variations. With motion, PMD pixels capture different depths at each stage. As a result, correlation samples are not coherent with a single depth, producing artifacts. We propose to detect and remove motion artifacts from a single frame taken by a PMD camera. The algorithm we propose is very fast, simple and can be easily included in camera hardware. We recover depth of each pixel by exploiting consistency of the correlation samples and local neighbors of the pixel. In addition, our method obtains the motion flow of occluding contours in the image from a single frame. The system has been validated in real scenes using a commercial low-cost PMD camera and high speed dynamics. In all cases our method produces accurate results and it highly reduces motion artifacts.     

gHRV: Heart rate variability analysis made easy

In this paper, the gHRV software tool is presented. It is a simple, free and portable tool developed in python for analysing heart rate variability. It includes a graphical user interface and it can import files in multiple formats, analyse time intervals in the signal, test statistical significance and export the results.     

3D soft-tissue tracking using spatial-color joint probability distribution and thin-plate spline model

Visual tracking techniques based on stereo endoscope are developed to measure tissue motion in robot-assisted minimally invasive surgery. However, accurate 3D tracking of tissue surfaces remains challenging due to complicated deformation, poor imaging conditions, specular reflections and other dynamic effects during surgery. This study employs a robust and efficient 3D tracking scheme with two independent recursive processes, namely kernel-based inter-frame motion estimation and model-based intra-frame 3D matching. In the first process, target region is represented in joint spatial-color space for robust estimation. By defining a probabilistic similarity measure, a mean-shift-based iterative algorithm is derived for location of the target region in a new image. In the second process, the thin-plate spline model is used to fit the 3D shape of tissue surfaces around the target region. An iterative algorithm based on an efficient second-order minimization technique is derived to compute optimal model parameters. The two processes can be computed in parallel. Their outputs are combined to recover 3D information about the target region. The performance of the proposed method is validated using phantom heart videos and in vivo videos acquired by the daVinci^®${\mathrm{daVinci}}^{\circledR }$ surgical robotic platform and a synthesized data set with known ground truth.