Relative Distance Error Research Articles

A floating‐point multiplier based on angle representation method

SummaryThis article proposes a novel angle representation method for floating‐point number, which eliminates the need for DSP (Digital Signal Processor) resources and reduces the resource usage when performing floating‐point multiplication. Compared with the implementation of floating‐point multiplier using IP cores, the implementation of approximate multiplication based on lookup tables can achieve an average reduction of 58.2% in LUTs (look‐up tables) and an average increase of 20.4% in frequency for mantissa widths ranging from 3 to 12 bits. Additionally, it can also save an average of 23.2% in registers. Analysis of PDP (power‐delay product)/LUT to MRED (mean relative error distance)/PRED (probability of relative error distance) among other approximate multipliers shows that the proposed design extends the Pareto front. At last, simulation of a three‐level inverter is implemented to verify the effectiveness of the multiplier.

Enhancing autonomous driving through intelligent navigation: A comprehensive improvement approach

In this paper, an intelligent navigation system is developed to achieve accurate and rapid response to autonomous driving. The system is improved with three modules: target detection, distance measurement, and navigation obstacle avoidance. In the target detection module, the YOLOv7x-CM model is proposed to improve the efficiency and accuracy of target detection by introducing the CBAM attention mechanism and MPDioU loss function. In the obstacle distance measurement module, the concept of an off-center angle is introduced to optimize the traditional monocular distance measurement method. In the obstacle avoidance module, acceleration jump and steering speed constraints are introduced into the local path planning algorithm TEB, and the TEB-S algorithm is proposed. Finally, this paper evaluates the performance of the system modules using the KITTI dataset and the BDD100K dataset. It is demonstrated that YOLOv7x-CM improves the mAP @ 0.5 metrics by 5.3% and 6.8% on the KITTI dataset and the BDD100K dataset, respectively, and the FPS also increases by 35.4%. Secondly, for the optimized monocular detection method, the average relative distance error is reduced by 9 times. In addition, the proposed TEB-S algorithm has a shorter obstacle avoidance path and higher efficiency than the normal TEB algorithm.

High-Frequency Fractional Predictions and Spatial Distribution of the Magnetic Loss in a Grain-Oriented Magnetic Steel Lamination

Grain-oriented silicon steel (GO FeSi) laminations are vital components for efficient energy conversion in electromagnetic devices. While traditionally optimized for power frequencies of 50/60 Hz, the pursuit of higher frequency operation (f ≥ 200 Hz) promises enhanced power density. This paper introduces a model for estimating GO FeSi laminations’ magnetic behavior under these elevated operational frequencies. The proposed model combines the Maxwell diffusion equation and a material law derived from a fractional differential equation, capturing the viscoelastic characteristics of the magnetization process. Remarkably, the model’s dynamical contribution, characterized by only two parameters, achieves a notable 4.8% Euclidean relative distance error across the frequency spectrum from 50 Hz to 1 kHz. The paper’s initial section offers an exhaustive description of the model, featuring comprehensive comparisons between simulated and measured data. Subsequently, a methodology is presented for the localized segregation of magnetic losses into three conventional categories: hysteresis, classical, and excess, delineated across various tested frequencies. Further leveraging the model’s predictive capabilities, the study extends to investigating the very high-frequency regime, elucidating the spatial distribution of loss contributions. The application of proportional–iterative learning control facilitates the model’s adaptation to standard characterization conditions, employing sinusoidal imposed flux density. The paper deliberates on the implications of GO FeSi behavior under extreme operational conditions, offering insights and reflections essential for understanding and optimizing magnetic core performance in high-frequency applications.

A comprehensive quality assurance protocol for electromagnetic tracking in brachytherapy.

Electromagnetic tracking (EMT) systems have proven to be a valuable source of information regarding the location and geometry of applicators in patients undergoing brachytherapy (BT). As an important element of an enhanced and individualized pre-treatment verification, EMT can play a pivotal role in detecting treatment errors and uncertainties to increase patient safety. The purpose of this study is two-fold: to design, develop and test a dedicated measurement protocol for the use of EMT-enabled afterloaders in BT and to collect and compare the data acquired from three different radiation oncology centers in different clinical environments. A novel quality assurance (QA) phantom composed of a scaffold with supports to fix the field generator, different BT applicators, and reference sensors (sensor verification tools) was used to assess the precision (jitter error) and accuracy (relative distance errors and target registration error) of the EMT sensor integrated into an afterloader prototype. Measurements were repeated in different environments where EMT measurements are likely to be performed, namely an electromagnetically clean laboratory, a BT suite, an operating room, and, if available, a CT suite and an MRI suite dedicated to BT. The mean positional jitter was consistently under 0.1mm across all measurement points, with a slight trend of increased jitter at greater distances from the field generator. The mean variability of sensor positioning in the tested tandem and ring gynecological applicator was also below 0.1mm. The tracking accuracy close to the center of the measurement volume was higher than at its edges. The relative distance error at the center was 0.2-0.3mm with maximum values reaching 1.2-1.8mm, but up to 5.5mm for measurement points close to the edges. In general, similar accuracy results were obtained in the clinical environments and in all investigated institutions (median distance error 0.1-0.4mm, maximum error 1.0-2.0mm), however, errors were found to be larger in the CT suite (median distance error up to 1.0mm, maximum error up to 3.6mm). The presented quality assessment protocol for EMT systems in BT has demonstrated that EMT offers a high-accuracy determination of the applicator/implant geometry even in clinical environments. In addition to that, it has provided valuable insights into the performance of EMT-enabled afterloaders across different radiation oncology centers.

Probing the Galactic halo with RR Lyrae stars – V. Chemistry, kinematics, and dynamically tagged groups

ABSTRACT We employ a sample of 135 873 RR Lyrae stars (RRLs) with precise photometric-metallicity and distance estimates from the newly calibrated P–ϕ31–R21–[Fe/H] and Gaia G band P–R21–[Fe/H] absolute magnitude–metallicity relations of Li et al., combined with available proper motions from Gaia EDR3, and 6955 systemic radial velocities from Gaia DR3 and other sources, in order to explore the chemistry and kinematics of the halo of the Milky Way (MW). This sample is ideally suited for characterization of the inner- and outer-halo populations of the stellar halo, free from the bias associated with spectroscopically selected probes, and for estimation of their relative contributions as a function of Galactocentric distance. The results of a Gaussian mixture model analysis of these contributions are broadly consistent with other observational studies of the halo, and with expectations from recent MW simulation studies. We apply the hdbscan clustering method to the specific energies and cylindrical actions (E, Jr, Jϕ, Jz), identifying 97 dynamically tagged groups (DTGs) of RRLs, and explore their associations with recognized substructures of the MW. The precise photometric-distance determinations (relative distance errors on the order of 5 per cent or better), and the resulting high-quality determination of dynamical parameters, yield highly statistically significant (low) dispersions of [Fe/H] for the stellar members of the DTGs compared to random draws from the full sample, indicating that they share common star-formation and chemical histories, influenced by their birth environments.

Analysis of Cargo Sorting Robot Based on Multiple Photoelectric Sensors

With the rise of e-commerce, dangerous goods such as flammable and explosives carried in logistics goods have a negative impact on the development of the logistics industry and seriously threaten staff safety. Infrared is widely used in the logistics cargo security inspection system, which can detect the goods’ shape and internal temperature and analyze the type of goods through spectra. These characteristics help to determine whether it is a hazardous material. In this research, a photoelectric intelligent sorting robot based on an infrared sensor and a Charge Coupled Device (CCD) sensor is designed. The robot’s hardware system is first developed, and then its important components’ model selection is made. The cargo loading module is designed according to the size of the cargo to be sorted. The cargo information collection module comprises multi-infrared sensors and CCD sensors, and the robot’s hardware is logically connected. In the sorting process, the cargo information is required for model training, the SSD_inception network model is used for training, and the Sort_target data structure is defined to label different cargo information. In the test, the design-based robot, with the increase of measurement distance, the relative distance error of detecting cargo shows an increasing trend, but the error is within 5%. The cargo ID can be determined through the information received by multiple photoelectric level sensors, and they are placed in the designated area, thus successfully achieving the sorting of cargo.

Event-Triggered Control with Intermittent Communications over Erasure Channels for Leader–Follower Problems with the Combined-Slip Effect

In this article, we investigate the vehicle path-following problem for a vehicle-to-vehicle (V2V)–enabled leader–follower scenario and propose an integrated control policy for the following vehicle to accurately follow the leader’s path. We propose a control strategy for the follower vehicle to maintain a velocity-dependent distance relative to the leader vehicle while stabilizing its longitudinal and lateral dynamics considering the combined-slip effect and tire force saturation. In light of reducing wireless communication errors and efficient usage of battery power and resources, we propose an intermittent V2V communication in which transmissions are scheduled based on an event-triggered law. An event is triggered and a transmission is scheduled in subsequent sample time if some of the well-defined path-following error functions (relative distance error and lateral error) exceed given tolerance bounds. Considering that the V2V communication channel might be erroneous or a transmission fails due to, e.g., vehicles’ distance or low battery power, we consider data loss in the V2V channel. Our proposed control law consists of two components: a receding horizon feedback controller with state constraints based on a safe operation envelop and a feedforward controller that generates complementary control inputs when the leader’s states are successfully communicated to the follower. To mitigate the effects of data loss on the follower’s path-following performance, we design a remote estimator for the follower to predict the leader’s state using its on-board sensor equipment when an event is triggered but the corresponding state information is not received by the follower due to a packet loss. Incorporating this estimator allows the follower to apply cautionary control inputs knowing that the path-following error had exceeded a tolerance bound. We show that while the feedback controller stabilizes the follower’s dynamics, the feedforward component improves the safety margins and reduces the path-following errors even in the presence of data loss. High-fidelity simulations are performed using CarSim to validate the effectiveness of our proposed control architecture specifically in harsh maneuvers and high-slip scenarios on various road surface conditions.

Efficient and low-cost approximate multipliers for image processing applications

The image processing can be implemented in an error-tolerant mode with acceptable accuracy. In digital image processing, the adders and multipliers are the most important components. In this paper, two approximate multipliers based on an approximate 4:2 compressor and two 4-bit full adders with minimizing computational costs are proposed. The first and second proposed approximate multipliers are designed by using the proposed imprecise 4-bit full adders and 4:2 compressor, respectively. In the structure of the proposed multipliers, we have adders for the addition of two multiple-bit numbers. In the adder structure, the full adders are designed based on two modified half adders and one NAND gate. The proposed approximate 4:2 compressor and two approximate 4-bit full adders are compared from hardware and accuracy point of view such as gate count, area-delay product (ADP), error rate (ER), mean error distance (MED), mean relative error distance (MRED), and normalized error distance (NED). The efficacy of proposed multipliers in image processing applications such as image multiplication is evaluated using MATLAB. The results show the proposed approximate multipliers are comparable in terms of area, delay, and mean structural similarity index metric (MSSIM) parameter with other works.

Leader-follower formation control of Euler-Lagrange systems with limited field-of-view and saturating actuators: A case study for tractor-trailer wheeled mobile robots

In this paper, an adaptive-neural constrained controller is proposed for a group of Tractor-trailer wheeled mobile robots with limited field-of-view (FOV) constraints and saturating actuators. With an effective combination of the asymmetric Barrier Lyapunov function based control design and dynamic surface control in the proposed constrained controller, the limited FOV constraints are not transgressed the predefined and limited bounds. The risk of the actuators saturation is extremely decreased through restricting amplitudes of the output states errors. It is proved that all the output states in the closed-loop system are semi-globally uniformly ultimately bounded and the relative distance and orientation angles errors are converged in the limited and preassigned boundaries. Compared with the existing results, the proposed constrained controller not only assures that these states errors between consecutive TTWMRs are bounded, but also all the output states errors converge to a small region around zero in a fixed-time that this issue accelerates the convergence speed rate and improves the transient response performance of the perfect tracking control for all TTWMRs.

Weather-aware fuzzy adaptive cruise control: Dynamic reference signal design

This paper presents a novel Adaptive Cruise Control (ACC) system, as part of Advanced Driver Assistance Systems (ADAS), in which weather conditions are included in the ACC operations adapting to different weather conditions and road-tire friction. A controller in the main loop of the ACC generates, in real-time, a dynamic reference signal to adjust the safe distance and velocity of the vehicle, based on different weather conditions using innovative polynomial, Sine, or Gaussian functions. A slave loop minimizes the velocity error and ensures collision prevention and passenger comfort. The system considers the nonlinear behavior of the vehicles’ actuators and dynamics. Simulations with various driving scenarios, such as hard stops and frequent stop-and-go maneuvers, show that the system can achieve high safety and comfort performance in icy, snowy, rainy, or dry weather. On average, the relative distance and velocity error are less than 0.6% and 0.5%, respectively.

Toward Optimal Softcore Carry-aware Approximate Multipliers on Xilinx FPGAs

Domain-specific accelerators for signal processing, image processing, and machine learning are increasingly being implemented on SRAM-based field-programmable gate arrays (FPGAs). Owing to the inherent error tolerance of such applications, approximate arithmetic operations, in particular, the design of approximate multipliers, have become an important research problem. Truncation of lower bits is a widely used approximation approach; however, analyzing and limiting the effects of carry-propagation due to this approximation has not been explored in detail yet. In this article, an optimized carry-aware approximate radix-4 Booth multiplier design is presented that leverages the built-in slice look-up tables (LUTs) and carry-chain resources in a novel configuration. The proposed multiplier simplifies the computation of the upper and lower bits and provides significant benefits in terms of FPGA resource usage (LUTs saving 38.5%–42.9%), Power Delay Product (PDP saving 49.4%–53%), performance metric (LUTs × critical path delay (CPD) × PDP saving 68.9%–73.1%) and errors (70% improvement in mean relative error distance) compared to the latest state-of-the-art designs. Therefore, the proposed designs are an attractive choice to implement multiplication on FPGA-based accelerators.

Detection of the Milky Way Reflex Motion Caused by the Magellanic Clouds in Different Observation Accuracy

Motivated by recent studies of the perturbation of the Magellanic Clouds (MCs) on the Milky Way (MW) and the planned multi-band wide-field deep survey named Chinese Space Station Telescope (CSST), we explore the detection limit of the MW reflex motion due to the MCs infall in different observation precision using an MW-MCs-mass galaxy from magpie simulation to provide a reference for the CSST survey. By involving different errors of distance, proper motion, and radial velocity, we investigate the reflex motion characterized by the velocity shift in each velocity component. We find the strongest shifts in the tangential velocities, which align with the motion direction of the MCs. In the ideal case that distance errors dominate, we find a relative distance error of 10% can allow the reliable detection of velocity shifts in tangential velocities within 100 kpc, and a relative distance error of 30% is the minimum requirement to detect the reliable tangential velocity shifts of about 40 km s−1 within 50 kpc. Different errors of proper motions in combination with a relative distance error of 10% or 20% show an error of 0.1 mas yr−1 in proper motions can guarantee the reliable detection of velocity shifts in V l and V b up to 80–100 kpc and an error of 0.15 mas yr−1 is the minimum requirement. In the other ideal case that radial velocity errors dominate, we find a radial velocity error of 20 km s−1 can present reliable reflex motion in line-of-sight velocity up to 70 kpc, while the detection volume will be reduced to 50 kpc as the radial velocity error increases to 40 km s−1. When the radial velocity error is larger than 60 km s−1, the velocity shifts cannot be detected anymore. In addition, we find that reliable detection of reflex motion requires at least 20% of the whole sample.

Modeling the Pedestrian Flow Before Bottleneck Through Learning-Based Method

This paper proposes a learning-based approach for modeling microscopic pedestrian movement behavior before bottleneck which contains two sub models – velocity direction model and velocity magnitude model. Datasets extracted from fifteen controlled experiments were trained through CART algorithm in this approach. Fifteen original scenarios are adopted to evaluate the performance of the proposed approach from both macroscopic and microscopic aspects. Simulation results show that the trajectories and density, velocity, flow <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vs</i> . time curves and fundamental diagrams are basically consistent with those from corresponding experiments. Four evaluation metrics, final displacement error ( FDE), duration error ( DE), mean trajectory error ( MTE) and relative distance error ( RDE) are applied to quantitatively verify the precision of simulation. The mean of FDE, DE, and MTE are calculated to be 0.144 m, 0.112 s and 0.095 m respectively. With time intervals of 0.5 s, 1 s and 2 s, the mean RDE of all scenarios are respectively 0.7089, 0.4073 and 0.2515. Data from additional experiments of bottleneck scenarios and publicly available data of corridor scenarios are also introduced to prove the potential of general application of this approach. Comparisons and analysis indicate that the proposed approach has a good capability and reliability in simulating the pedestrian motion before the bottleneck. The models presented will be useful for passenger flow management and architectural design, also beneficial to understand the pedestrian movement mechanism in collective motion.

Energy efficient multiply-accumulate unit using novel recursive multiplication for error-tolerant applications

The primary requirement for multimedia applications is energy efficient design along with computational efficiency of portable devices. This work proposes an energy efficient MAC with error compensating novel approximate adder and approximate multiplier. The proposed approximate hierarchical adder (AXHA – N) has the advantage of zero carry propagation and consists of only two gate levels which deliver very high speed and very low energy consumption along with the near to zero mean error distances. The proposed approximate 4 - bit multiplier also has no carry propagation from Least Significant Bit (LSB) to Most Significant Bit (MSB), which leads to high speed with very low energy consumption and acceptable error profiles. Higher bit size multipliers can be built using the proposed modified recursive multiplication scheme. This work proposes three variants AXMAC1, AXMAC2, AXMAC3 basing on one or both of adder and multiplier being approximate. The proposed AXMAC3 with any k, has energy savings ranging from 40% to 60% for different AxL when compared to accurate with Mean Error Distance between −358 and 4305. The MED for AXMAC3 with k=8, AXL=4 is only 0.7% of the maximum possible value with 60% energy savings. The MED for AXMAC3 with k=12s, AXL=4 is only 0.8% of the maximum possible value with 57% energy savings. Mean Relative Error Distance (MRED) and Normalised Mean Error Distance (NMED) are also evaluated and presented in the paper for wholesome evaluation of AXMAC. The (Energy savings, MRED, MED) tuple 8−bit MAC for design of Adams et al., (2019) with k=8 is (26.9%, 0.1, −15048), for proposed AXMAC3 with similar configuration has (57%, 0.01, 3663).

Design and analysis of leading one/zero detector based approximate multipliers

Approximate multipliers are widely used in error-tolerant applications to improve circuit performance. For signed multiplication, previous approximate Booth multipliers usually have a large relative error with operands around “0”, while approximate leading one detector based (LOD-based) multipliers are not energy-efficient due to the extra preprocessing module. In this paper, a low relative error leading one/zero detector based approximate multiplier (LOZDAM) is proposed for signed multiplication, which dynamically truncates the operands according to the location of their most significant bits for signed complement data. Its accuracy can be configured to suit fault-tolerant applications with different accuracy requirements. A compensation strategy is proposed to reduce the calculation error of LOZDAMs at a low cost. All proposed designs are evaluated in 28nm/0.9 V/TT/25 °C CMOS. Compared with the exact design, the proposed LOZDAM6/7/8/9 with the width of Booth multiplier being 6/7/8/9-bit reduces average power by 64%/43%/33%/21%, with the mean relative error distance by 2.94%/1.46%/0.73%/0.36%, respectively. Case studies of image sharpening and serial Fast Fourier Transform system both show acceptable error and good power/area savings, which verifies the feasibility of our designs. In general, our proposed LOZD-based approximate multipliers achieve both high accuracy and low power.

High Efficient GDI-CNTFET-Based Approximate Full Adder for Next Generation of Computer Architectures

Approximate computing (AC) is an emerging technique in arithmetic circuits. In this letter, a new AC-based full adder (FA) circuit is presented with 12 transistors, 150mm]Please confirm or add details for any funding or financial support for the research of this article. -160mm]If you haven’t done so already, please make sure you have submitted a video graphical abstract (GA) for your paper, along with a caption and overlay image. The GA will be displayed on your articles abstract page on IEEE Xplore. Note that captions cannot exceed 1800 characters (including spaces). Overlay images are usually a screenshot of your video that best represents the video. This is for readers who may not have access to video-viewing software. 0.239 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}^{2}$ </tex-math></inline-formula> of area, and two errors in the outputs. In the proposed FA, the gate diffusion input (GDI) and dynamic-threshold (DT) techniques are applied using the carbon nanotube field-effect transistor (CNTFET) technology. Accuracy metrics, such as normalized mean error distance (NMED) and mean relative error distance (MRED) along with circuitry parameters of power-delay-product (PDP), energy-delay-product (EDP), and power-delay-area-product (PDAP), confirm the efficiency of the proposed FA for complex structures. The proposed FA is embedded in a ripple carry adder (RCA) by various numbers of approximate bits (NABs), and then the accuracy and circuitry parameters are extracted. Compared to the state-of-the-art designs, the high-efficient behavior of the proposed FA is proved when it is used in image processing applications.

Design of high-efficiency complex multiplier for fault-tolerant computation

In this paper, two improved structures and a truncation strategy with compensation for complex multiplication are proposed. Simulation in 28-nm CMOS for hardware performance is provided. Compared to the general complex multiplier, the two accurately improved structures realize 18.58% and 20.80% power consumption reduction, respectively. The truncation strategy with compensation reduces power consumption by 46.8% and controls Mean Relative Error Distance (MRED) at 0.54%. To verify the practicability of the proposed architecture, our designs are applied to the Fast Fourier Transform (FFT) processor to comprehensively evaluate the error characteristics and circuit performance.

Assessment of thoracic spinal curvatures in static postures using spatially tracked 3D ultrasound volumes: a proof-of-concept study

The assessment of spinal posture is a difficult endeavour given the lack of identifiable bony landmarks for placement of skin markers. Moreover, potentially significant soft tissue artefacts along the spine further affect the accuracy of marker-based approaches. The objective of this proof-of-concept study was to develop an experimental framework to assess spinal postures by using three-dimensional (3D) ultrasound (US) imaging. A phantom spine model immersed in water was scanned using 3D US in a neutral and two curved postures mimicking a forward flexion in the sagittal plane while the US probe was localised by three electromagnetic tracking sensors attached to the probe head. The obtained anatomical ‘coarse’ registrations were further refined using an automatic registration algorithm and validated by an experienced sonographer. Spinal landmarks were selected in the US images and validated against magnetic resonance imaging data of the same phantom through image registration. Their position was then related to the location of the tracking sensors identified in the acquired US volumes, enabling the localisation of landmarks in the global coordinate system of the tracking device. Results of this study show that localised 3D US enables US-based anatomical reconstructions comparable to clinical standards and the identification of spinal landmarks in different postures of the spine. The accuracy in sensor identification was 0.49 mm on average while the intra- and inter-observer reliability in sensor identification was strongly correlated with a maximum deviation of 0.8 mm. Mapping of landmarks had a small relative distance error of 0.21 mm (SD = ± 0.16) on average. This study implies that localised 3D US holds the potential for the assessment of full spinal posture by accurately and non-invasively localising vertebrae in space.

Rough discrete fracture network multi-parameter joint modeling based on improved neural spline flow

Discrete fracture network (DFN) modeling is a popular method for studying reservoir characteristics. However, on one hand of the existing DFN studies, the correlations that may exist among the multi-dimensional parameters of the fracture (dip, dip direction, trace length, aperture, and roughness) were ignored and each property was estimated independently. On the other hand, the 3D DFN models were simplified as flats without roughness. Therefore, this study proposes a simulation method for the rough discrete fracture network while considering multi-parameter joint distribution to make up for the stated deficiencies: (1) An improved deep learning model for the joint distribution estimation and joint sampling of the multi-dimensional parameters of the fracture is proposed, which is the Neural Spline Flow improved by the Multimodal Distribution (NSF-MD). The initial distribution of the Neural Spline Flow (NSF) is improved from a unimodal Gaussian to a multimodal mixed Gaussian, which enhances the fitting ability of the NSF model for the multimodal joint distribution. (2) A modeling assumption of the 3D rough fracture surface is presented to improve the conventional flat ones. In this way, a 3D rough fracture surface is generated by the NURBS tensor product of the fractal traces, and the fractal trace is simulated parametrically based on the fractal dimension. Finally, an outcrop DFN modeling application from southwest China indicates that the NSF-MD can simulate the correlations among the fracture multi-dimensional parameters and that the 3D rough discrete fracture network model (RDFN) increases the representation of the fracture roughness. The Wasserstein distance, which is an indicator quantifying the accuracy of the joint multi-parameter estimation, of the NSF-MD model was 72.4% and 81.9% better than that of the NSF model and that of the conventional method with parameters estimated independently, respectively. The relative distance error (RDE) and the global angle error (GAE) of the fractal traces were 87.9% and 88.3% more accurate than those of the conventional linear traces, respectively.

Part Affinity Fields and CoordConv for Detecting Landmarks of Lumbar Vertebrae and Sacrum in X-ray Images.

With the prevalence of degenerative diseases due to the increase in the aging population, we have encountered many spine-related disorders. Since the spine is a crucial part of the body, fast and accurate diagnosis is critically important. Generally, clinicians use X-ray images to diagnose the spine, but X-ray images are commonly occluded by the shadows of some bones, making it hard to identify the whole spine. Therefore, recently, various deep-learning-based spinal X-ray image analysis approaches have been proposed to help diagnose the spine. However, these approaches did not consider the characteristics of frequent occlusion in the X-ray image and the properties of the vertebra shape. Therefore, based on the X-ray image properties and vertebra shape, we present a novel landmark detection network specialized in lumbar X-ray images. The proposed network consists of two stages: The first step detects the centers of the lumbar vertebrae and the upper end plate of the first sacral vertebra (S1), and the second step detects the four corner points of each lumbar vertebra and two corner points of S1 from the image obtained in the first step. We used random spine cutout augmentation in the first step to robustify the network against the commonly obscured X-ray images. Furthermore, in the second step, we used CoordConv to make the network recognize the location distribution of landmarks and part affinity fields to understand the morphological features of the vertebrae, resulting in more accurate landmark detection. The proposed network was evaluated using 304 X-ray images, and it achieved 98.02% accuracy in center detection and 8.34% relative distance error in corner detection. This indicates that our network can detect spinal landmarks reliably enough to support radiologists in analyzing the lumbar X-ray images.