scholarly journals fastSW: Efficient Piecewise Linear Approximation of Quaternion-Based Orientation Sensor Signals for Motion Capturing with Wearable IMUs

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5180
Author(s):  
Florian Grützmacher ◽  
Jochen Kempfle ◽  
Kristof Van Laerhoven ◽  
Christian Haubelt
Keyword(s):  
Linear Approximation ◽  
Piecewise Linear ◽  
Approximation Error ◽  
Piecewise Linear Approximation ◽  
Approximation Technique ◽  
Angular Deviation ◽  
Unit Quaternion ◽  
Battery Capacity ◽  
Motion Capturing ◽  
Being Moved

In the past decade, inertial measurement sensors have found their way into many wearable devices where they are used in a broad range of applications, including fitness tracking, step counting, navigation, activity recognition, or motion capturing. One of their key features that is widely used in motion capturing applications is their capability of estimating the orientation of the device and, thus, the orientation of the limb it is attached to. However, tracking a human’s motion at reasonable sampling rates comes with the drawback that a substantial amount of data needs to be transmitted between devices or to an end point where all device data is fused into the overall body pose. The communication typically happens wirelessly, which severely drains battery capacity and limits the use time. In this paper, we introduce fastSW, a novel piecewise linear approximation technique that efficiently reduces the amount of data required to be transmitted between devices. It takes advantage of the fact that, during motion, not all limbs are being moved at the same time or at the same speed, and only those devices need to transmit data that actually are being moved or that exceed a certain approximation error threshold. Our technique is efficient in computation time and memory utilization on embedded platforms, with a maximum of 210 instructions on an ARM Cortex-M4 microcontroller. Furthermore, in contrast to similar techniques, our algorithm does not affect the device orientation estimates to deviate from a unit quaternion. In our experiments on a publicly available dataset, our technique is able to compress the data to 10% of its original size, while achieving an average angular deviation of approximately 2° and a maximum angular deviation below 9°.

An Automatic Selection of Segment Width for the Single Sensor Differential Thermal Analysis (SS-DTA) Based on Piecewise Linear Approximation Technique

2015 ◽  
Vol 658 ◽  
pp. 96-100 ◽  
Author(s):  
Wutipong Nieampradit ◽  
Sarawan Wongsa ◽  
Isaratat Phung-On
Keyword(s):  
Thermal Analysis ◽  
Differential Thermal Analysis ◽  
Phase Transformations ◽  
Linear Approximation ◽  
Piecewise Linear ◽  
Research Work ◽  
Piecewise Linear Approximation ◽  
Approximation Technique ◽  
Analytical Formulae ◽  
Single Sensor

Single Sensor Differential Thermal Analysis (SS-DTA) is a novel non-destructive testing technique for studying and detecting the phase transformations and structural changes in materials. It uses only one temperature sensor to measure the temperature in a particular point of interest in the material during actual and simulated thermal processing of the material. SS-DTA compares the temperature recorded in a tested specimen against a reference thermal profile which can be generated either by analytical formulae or piecewise linear approximation. The main advantage of piecewise linear approximation over the analytical formulae is that it does not need the knowledge of tested material and processing conditions to optimally estimate the parameters of reference thermal history. On the other hand, in order to apply the piecewise linear approximation technique we must specify the segment width which is normally fixed at a nominal value of 1.5 seconds. We have recently found that this nominal value might not be an optimal choice for the segment width as it does not guarantee to give the best detectability of phase transformation. Therefore, in this research work we proposed a technique to automatically select an appropriate value of the segment width. The performance of proposed method has been evaluated by investigating the phase transformations of welded stainless steel SUS 321and SUS 304. It was found that the appropriate segment width could be ranging from 1.25-1.75 seconds and by using this selection technique, we could detect the differential temperature more accurately than when using the nominal value.

A Novel Hardware Implementation for Specular Intensity of Phong Shading Used in Embedded Graphic Applications

2012 ◽  
Vol 229-231 ◽  
pp. 1146-1149
Author(s):  
Bing Chao Li ◽  
Ji Zeng Wei ◽  
Yi Song Chang ◽  
Wei Guo ◽  
Ji Zhou Sun
Keyword(s):  
Embedded System ◽  
Power Unit ◽  
Linear Approximation ◽  
Hardware Implementation ◽  
Piecewise Linear ◽  
Approximation Error ◽  
Cmos Technology ◽  
Piecewise Linear Approximation ◽  
Color Error ◽  
Visual Difference

In this paper we propose a novel hardware implementation applied in embedded system for the power computation of specular term of Phong shading. Based on piecewise linear approximation, the power unit is implemented with SMIC 0.18μm CMOS technology and can complete 50 million power computation per second with the maximum approximation error of 0.00141 when the exponent of power is 20. The area cost is 12.3K gates. The maximum RGB color error of generated graphics is only 1 resulting in no visual difference compared with graphics generated by software.

scholarly journals Approximation of the Contour of an Object in an Image Using Vector Operations

2020 ◽  
pp. 85-89
Author(s):  
P. Sabelnikov
Keyword(s):  
Linear Approximation ◽  
Extreme Values ◽  
Piecewise Linear ◽  
Approximation Error ◽  
Parallel Computations ◽  
Piecewise Linear Approximation ◽  
Contour Analysis ◽  
Straight Line ◽  
Speed Up ◽  
Identification Analysis

Introduction. One of the directions associated with identification, analysis of the shape of objects, their size, orientation, marking and other geometric characteristics is contour analysis. Various methods for contour approximation are described in the literature. The proposed method is based on a well-known method. Its essence lies in the sequential search for possible directions and end points of approximating straight line segments belonging to the contour. The number of approximation nodes should be as small as possible. The calculation is carried out only for the next point of the contour, without returning to check the criterion of approximation to all previous points. The computational complexity of the algorithm is proportional to the number of points in the contour. The purpose of the paper to propose a method of piecewise linear approximation of the contours of objects in images, which will allow to use the parallel computations at all stages of computer processing using vector operations. Results. The paper proposes an improved method for piecewise linear approximation of a closed contour of an object in an image by a polygon, the vertices of which are directly the points of this contour. Approximation criterion: the distance from each point of the approximated section of the contour to the approximating segment should not exceed the approximation error. The method is focused on parallel computing using vector operations. A method for parallel computation of integral vectors of extreme values of a sequence of numbers for the implementation of parallel computations using vector operations at all stages of approximation is also proposed. Conclusions. Methods are proposed that are implemented using vector operations and provide an opportunity to speed up the solution of contour analysis problems, as well as other similar problems in real time. The gain in computing speed is proportional to the amount of data that a vector processor can simultaneously process. The presence of developed subsystems of vector instructions in Intel and ARM processors makes it possible to use the proposed computation methods in practice. Keywords: image, object contour, piecewise linear approximation, parallel computations, vector operations.

Sign in / Sign up

Export Citation Format

Share Document