Fractional Motion Research Articles

Variable Block Size Fractional Motion Estimation Hardware Architecture for VVC and HEVC Standards

The ever-increasing growth in digital video consumption motivates the research and development of new video coding standards to improve coding efficiency. Among the several new tools that the Versatile Video Coding (VVC) standard introduced lies the Quadtree Plus Multi-Type Tree (QT+MTT), which improves upon the quadtree of High Efficiency Video Coding (HEVC) in terms of coding efficiency. Nevertheless, such improvements come at the cost of increased complexity. Hence, to meet the real-time and energy efficiency requirements, embedded devices must adopt techniques to effectively reduce the VVC complexity, including customized hardware accelerators. This work presents a low-energy hardware architecture design for the Fractional Motion Estimation (FME), one of the most critical steps of HEVC and VVC encoders. The proposed architecture supports the Switchable Interpolation Filter (SIF) of VVC and was synthesized to enable Variable Block Size (VBS) from 8×8 up to 128×128 sized blocks so that it can perform the FME of most partitions of the QT+MTT from VVC. The results show increases of at most 4.52% in area and 10.79% in total power for the extra hardware needed to support VBS, and up to 9.15% and 15.72%, in area and power, respectively, for supporting up to 128×128 block sizes.

Rate-Distortion Optimization-Based Learned Fractional Interpolation Filter Design for HEVC

Fractional motion compensation (FMC) has been widely adopted in modern video coding standards such as high-efficiency video coding (HEVC). The fractional pixels in FMC are generated by the interpolation filters, and the coefficients of the filters are designed using a Fourier decomposition of the discrete cosine transform (DCT) in HEVC. To overcome the compression deficiency caused by these handcrafted filters, deep learning-based interpolation filter approaches have been introduced recently. In this paper, we analyze the drawbacks of the mean square error (MSE) only loss function which is widely adopted in existing learned-based approaches, and introduce the rate-distortion optimization (RDO) theory into network training to formulate a joint loss function to overcome this issue. Then, a new training scheme is proposed for the detailed implementation of the joint loss function. Besides the calculated MSE loss, the residual will be sent into a rate estimation model which includes three stages: transform/quantization/rate modeling, and the output rate cost will be used as the second part of the loss function. Finally, we propose a novel network structure that utilizes the deformable convolution layer and the residual dense block to enhance the feature extraction and transmission ability to adapt to complex video contents. The proposed RDO-based interpolation filter (RDOIF) has been integrated into HEVC reference software HM-16.7, and extensive experiments are conducted to verify the efficiency of the proposed method. Experimental results show that the proposed RDOIF method achieves 3.1%, 2.4%, and 1.4% BD-rate reduction on average under the low-delay-P, low-delay-B, and random access configurations, respectively. When implemented in the versatile video coding (VVC) test model VTM-10.0, the proposed method can achieve 2.3%, 1.2%, and 0.5% BD-rate savings on average under the low-delay-P, low-delay-B, and random access configurations, respectively.

A motion model-guided 4D dose reconstruction for pencil beam scanned proton therapy

Objective. 4D dose reconstruction in proton therapy with pencil beam scanning (PBS) typically relies on a single pre-treatment 4DCT (p4DCT). However, breathing motion during the fractionated treatment can vary considerably in both amplitude and frequency. We present a novel 4D dose reconstruction method combining delivery log files with patient-specific motion models, to account for the dosimetric effect of intra- and inter-fractional breathing variability. Approach. Correlation between an external breathing surrogate and anatomical deformations of the p4DCT is established using principal component analysis. Using motion trajectories of a surface marker acquired during the dose delivery by an optical tracking system, deformable motion fields are retrospectively reconstructed and used to generate time-resolved synthetic 4DCTs (‘5DCTs’) by warping a reference CT. For three abdominal/thoracic patients, treated with respiratory gating and rescanning, example fraction doses were reconstructed using the resulting 5DCTs and delivery log files. The motion model was validated beforehand using leave-one-out cross-validation (LOOCV) with subsequent 4D dose evaluations. Moreover, besides fractional motion, fractional anatomical changes were incorporated as proof of concept. Main results. For motion model validation, the comparison of 4D dose distributions for the original 4DCT and predicted LOOCV resulted in 3%/3 mm gamma pass rates above 96.2%. Prospective gating simulations on the p4DCT can overestimate the target dose coverage V95% by up to 2.1% compared to 4D dose reconstruction based on observed surrogate trajectories. Nevertheless, for the studied clinical cases treated with respiratory-gating and rescanning, an acceptable target coverage was maintained with V95% remaining above 98.8% for all studied fractions. For these gated treatments, larger dosimetric differences occurred due to CT changes than due to breathing variations. Significance. To gain a better estimate of the delivered dose, a retrospective 4D dose reconstruction workflow based on motion data acquired during PBS proton treatments was implemented and validated, thus considering both intra- and inter-fractional motion and anatomy changes.

Ultra-High Definition AV1 FME Interpolation Architectures Exploring Approximate Computing

Modern video encoders like the AOMedia Video 1 (AV1) implement several complex tools to allow the required high level of compression efficiency. The Fractional Motion Estimation (FME) is one of these complex tools, and AV1 FME defines 42 different interpolation filters. To handle such complexity, hardware acceleration using approximate computing has become an interesting alternative to be explored. This paper presents three optimized approximate architectures for the AV1 FME interpolation filters. The architectures reach real time interpolation for UHD 4K videos at 30 frames per second in a low cost, low power, and memory-efficient design. The architectures were synthesized for a 40nm TSMC standard-cells technology reaching power gains up to 83%, when compared to a precise architecture, and up to 20% when compared to a previously published approximated solution. The area gains were also expressive: up to 83% and 40%, respectively. The architectures also allow a memory bandwidth reduction of up to 59.5%, in comparison with the state-of-the-art solutions. The approximations implied small coding efficiency degradation of 0.54% and 1.25% in BD-BR. The presented architectures have the best results found in the literature when considering the trade-off among hardware cost, power dissipation, processing rate, memory bandwidth, and coding efficiency.

Fractal Operators and Fractional Dynamics with 1/2 Order in Biological Systems

This paper reports the new advances in biological fractal dynamics. The following contents are included: (1) physical (or functional) fractal spaces abstracted from biological materials, biological structures and biological motions; (2) fractal operators on fractal spaces; (3) 1/2-order fractional dynamics controlled by fractal operators; and (4) the origin of 1/2-order. Based on the new progress, we can make a judgment that all the two-bifurcation physical functional fractal motions in the living body can be attributed to the fractional dynamics with 1/2-order.

FastInter360: A Fast Inter Mode Decision for HEVC 360 Video Coding

This paper presents FastInter360, a fast inter mode decision algorithm for accelerating the encoding of ERP 360 videos. The development of FastInter360 involves an in-depth and comprehensive set of evaluations performed to understand the differences in the encoder’s behavior when encoding 360 and conventional videos. These evaluations showed that due to the texture distortions resulting from projection, the encoder presents a specific behavior when encoding 360 videos, making it more likely to use a recurrent set of encoding modes when processing 360 videos. Besides, the coding efficiency is less sensible to approximations in some encoding steps depending on the frame region. FastInter360 is then proposed to reduce the encoding complexity by exploiting these differences. FastInter360 comprises three algorithms that accelerate the encoding by performing early decision by SKIP mode, reducing integer motion estimation search range, and adjusting fractional motion estimation precision. Furthermore, each of these algorithms behaves according to distortion intensity, performing greater complexity reduction in more distorted regions. When employed altogether, these algorithms compose FastInter360, which is able to achieve an average complexity reduction of 22.84% with a coding efficiency loss of 0.652% BD-BR, on average, making FastInter360 competitive with literature works.

Derivation and Application of Some Fractional Black–Scholes Equations Driven by Fractional G-Brownian Motion

Derivation and Application of Some Fractional Black–Scholes Equations Driven by Fractional G-Brownian Motion

Hysteretic Implications for Graded Bed Load Sediment Transport in Symmetrical Hydrograph Flows

Differential parametric values associated with bed load sediment transport, that result at the same discharge levels on the rising and falling limbs of a flood hydrograph, are usually defined as bed load hysteresis. This hysteresis in bed load sediment transport rates is of considerable interest in the field of fluvial hydraulics. Within this study, a series of well-defined, symmetrical hydrograph flows are generated over a graded, mobile sediment bed to fully examine the hysteresis of the resulting bed load sediment transport in terms of the threshold of motion, and differential bed load transport rates and bed load yields during the hydrographs. The experiments are conducted in a titling flume without sediment supply specified at the upstream inlet, thereby representing typical river reach conditions immediately downstream of a dam that are exclusively subject to net in-channel bed degradation from sediment transport initiated during flood events. Our results show that the fractional bed load transport of defined fine, medium and coarse size classes within the graded sediment bed generally display clockwise, no/mixed and counter-clockwise hysteresis patterns, respectively, with clockwise hysteresis most commonly found for the coarse size class mobilised by hydrographs with long durations. By contrast, counter-clockwise hysteresis is usually observed for fine size class transported by hydrographs with short durations. Accordingly, the corresponding reference stresses for each size class vary between different hydrographs and are primarily controlled by the hydrograph flashiness (i.e. unsteadiness) and magnitude (i.e. total water work). Moreover, it is shown that the hysteresis effect, particularly for those size classes and hydrograph combinations that result in clockwise and counter-clockwise behaviour, should be fully accounted for when reproducing bed load transport rates using separate-limb based method. Finally, we investigate the relative fractions of the overall bed load yields generated during the rising and falling limbs of all symmetrical hydrographs (i.e. the bed load yield ratio), which are found to be primarily dependent on bed load transport hysteresis. Finally, the relationship between the bed load yield ratio and the ratio of reference stresses for the fractional sediment motion of each size class on both limbs is found to follow a power law.

Models of monitoring of self-like traffic of information and communication networks for attack detection systems

Autoregressive, fractal and multifractal models of network self-similar traffic are con-sidered, which allow to form an adequate reference model (template) of "normal" traffic and to detect traffic anomalies in attack detection and prevention systems. Models of fractal Brownian motion and fractal Gaussian noise were considered as models of fractal motions, because they have self-similarity and long-term dependence properties that correspond to the properties of experimental data, as well as the possibility of their analytical interpretation. When evaluating and identifying processes for the implementation of autoregressive models use adaptive filters-approximators, among which there are neural network and neuro-wavelet. The following were used as multifractal models: a multifractal wavelet model with a beta distribution and a hybrid multifractal wavelet model in which the beta distribution is used on a coarse scale and the dis-tribution of point masses on an accurate scale By modeling as a result of adaptation and learning of models, autocorrelation functions, spectra and variances of model signals qualitatively correspond to the graphs of the experimental signal. In addition, the qualitative and numerical values of the characteristics of the model signals generally correspond to the characteristics of the experimental signal. In this case, beta multifractal wavelet models have a smaller error of determination of characteristics than hybrid multifractal wavelet models, and the relative root mean square error of approximation of the experimental signal using a neural network adaptive filter approximator does not exceed 0.046. Statistical verification by non-parametric criterion of signs allowed to establish the adequacy of experimental and model signals with a significance level of 0.01. Further research should be aimed at developing and using predictive models of self-similar traffic in attack detection and prevention systems, which will increase the efficiency of attack detection.

Analytical and Numerical Connections between Fractional Fickian and Intravoxel Incoherent Motion Models of Diffusion MRI

Impaired tissue perfusion underlies many chronic disease states and aging. Diffusion-weighted imaging (DWI) is a noninvasive MRI technique that has been widely used to characterize tissue perfusion. Parametric models based on DWI measurements can characterize microvascular perfusion modulated by functional and microstructural alterations in the skeletal muscle. The intravoxel incoherent motion (IVIM) model uses a biexponential form to quantify the incoherent motion of water molecules in the microvasculature at low b-values of DWI measurements. The fractional Fickian diffusion (FFD) model is a parsimonious representation of anomalous superdiffusion that uses the stretched exponential form and can be used to quantify the microvascular volume of skeletal muscle. Both models are established measures of perfusion based on DWI, and the prognostic value of model parameters for identifying pathophysiological processes has been studied. Although the mathematical properties of individual models have been previously reported, quantitative connections between IVIM and FFD models have not been examined. This work provides a mathematical framework for obtaining a direct, one-way transformation of the parameters of the stretched exponential model to those of the biexponential model. Numerical simulations are implemented, and the results corroborate analytical results. Additionally, analysis of in vivo DWI measurements in skeletal muscle using both biexponential and stretched exponential models is shown and compared with analytical and numerical models. These results demonstrate the difficulty of model selection based on goodness of fit to experimental data. This analysis provides a framework for better interpreting and harmonizing perfusion parameters from experimental results using these two different models.

Adaptive fractional motion and disparity estimation skipping in MV-HEVC

MV-HEVC can efficiently compress multiview video data captured from different viewpoints. To achieve high coding efficiency, it consists of not only inter coding but also interview coding. The inter coding includes a motion estimation (ME) process that reduces temporal redundancies between consecutive frames, and the interview coding performs a disparity estimation (DE) that reduces interview redundancies between neighboring views. As a result, MV-HEVC needs high encoding complexity to perform both ME and DE. In order to reduce the complexity, this paper proposes an adaptive fractional ME and DE skipping method in a partitioned inter prediction unit (PU) mode, based on a result of a 2 N × 2 N inter PU coding. Experimental results show that the proposed method efficiently reduces the encoding complexity with negligible coding loss, compared to conventional methods.

Slices of the Anomalous Phase Cube Depict Regions of Sub- and Super-Diffusion in the Fractional Diffusion Equation

Fractional-order time and space derivatives are one way to augment the classical diffusion equation so that it accounts for the non-Gaussian processes often observed in heterogeneous materials. Two-dimensional phase diagrams—plots whose axes represent the fractional derivative order—typically display: (i) points corresponding to distinct diffusion propagators (Gaussian, Cauchy), (ii) lines along which specific stochastic models apply (Lévy process, subordinated Brownian motion), and (iii) regions of super- and sub-diffusion where the mean squared displacement grows faster or slower than a linear function of diffusion time (i.e., anomalous diffusion). Three-dimensional phase cubes are a convenient way to classify models of anomalous diffusion (continuous time random walk, fractional motion, fractal derivative). Specifically, each type of fractional derivative when combined with an assumed power law behavior in the diffusion coefficient renders a characteristic picture of the underlying particle motion. The corresponding phase diagrams, like pages in a sketch book, provide a portfolio of representations of anomalous diffusion. The anomalous diffusion phase cube employs lines of super-diffusion (Lévy process), sub-diffusion (subordinated Brownian motion), and quasi-Gaussian behavior to stitch together equivalent regions.

Local asymptotic self-similarity for heavy-tailed harmonizable fractional Lévy motions

In this work we characterize the local asymptotic self-similarity of harmonizable fractional Levy motions in the heavy tailed case. The corresponding tangent process is shown to be the harmonizable fractional stable motion. In addition, we provide sufficient conditions for existence of harmonizable fractional Levy motions.

Motion equations and non-Noether symmetries of Lagrangian systems with conformable fractional derivative

In this paper, we present the fractional motion equations and fractional non-Noether symmetries of Lagrangian systems with the conformable fractional derivatives. The exchanging relationship between isochronous variation and fractional derivative, and the fractional Hamilton?s principle of the holonomic conservative and non-conservative systems under the conformable fractional derivative are proposed. Then the fractional motion equations of these systems based on the Hamil?ton?s principle are established. The fractional Euler operator, the definition of fractional non-Noether symmetries, non-Noether theorem, and Hojman?s conserved quantities for the Lagrangian systems are obtained with conformable fractional derivative. An example is given to illustrate the results.

Hardware Implementation for the HEVC Fractional Motion Estimation Targeting Real-Time and Low-Energy

This paper presents an energy-aware and high-throughput hardware design for the Fractional Motion Estimation (FME) compliant with the High Efficiency Video Coding (HEVC) standard. An extensive software evaluation was performed to guide the hardware design. The adopted strategy mainly consists in using only the four squareshaped Prediction Unit (PU) sizes rather than using all 24 possible PU sizes in the Motion Estimation (ME). This approach reduces about 59% the total encoding time and, as a penalty, it leads to an increase of only 4% in the bit rate for the same image quality. Together with this simplification, a multiplierless approach, algebraic optimizations and low-power techniques were applied to the hardware design to reduce the hardware-resource usage and the energy consumption, maintaining a high processing rate. The architecture was described in VHDL and the synthesis results for ASIC 45nm Nangate standard cells demonstrate that the developed architecture is able to process Ultra-High Definition (UHD) 2160p videos at 60 frames per second (fps), with the lowest power consumption and the lowest hardware-resource usage among the related works.

RETRACTED: FPGA-Based Motion Estimation Algorithm Optimization

The new international video compression standards (HEVC) are referred to as video motion detection and efficient physical education video encoding. HEVC is determined by calculating the increasing complexity of video compression efficiency of the remarkable possible. Motion estimation is the most complicated arithmetic unit video encoder. Integer motion estimation and HEVC 70%, accounted for, and the video encoder's complexity calculates fractional motion estimation. High-Level Synthesis (HLS) tools algorithms have been successfully used in digital signal processing on FPGA. According to the actual requirements of the project, it is set as sports video management, target detection, video acquisition and target tracking. In order to adapt the smoothing time, the hardware configure ration consists of two parts: the intermediate results of the final optical flow vector and the optical flow calculating module generates the derivative calculation to adapt the smoothing time. Run built processor, software. FPGA chip, designed for directing data flow management and hardware components. Recommend using a first interpolation HEVC FPGA implementation scores and Vivado HLS motion estimation. The sports video target detection and tracking system designed in this paper analyzes the scene to be detected, further analyzes the moving target trajectory, and tracks the target according to the trajectory.

Anisotropy of Anomalous Diffusion Improves the Accuracy of Differentiating and Grading Alzheimer's Disease Using Novel Fractional Motion Model.

Background and Purpose: Recent evidence shows that the fractional motion (FM) model may be a more appropriate model for describing the complex diffusion process of water in brain tissue and has shown to be beneficial in clinical applications of Alzheimer's disease (AD). However, the FM model averaged the anomalous diffusion parameter values, which omitted the impacts of anisotropy. This study aimed to investigate the potential feasibility of anisotropy of anomalous diffusion using the FM model for distinguishing and grading AD patients.Methods: Twenty-four patients with AD and 11 matched healthy controls were recruited, diffusion MRI was obtained from all participants and analyzed using the FM model. Generalized fractional anisotropy (gFA), an anisotropy metric, was introduced and the gFA values of FM-related parameters, Noah exponent (α) and the Hurst exponent (H), were calculated and compared between the healthy group and AD group and between the mild AD group and moderate AD group. The receiver-operating characteristic (ROC) analysis and the multivariate logistic regression analysis were used to assess the diagnostic performances of the anisotropy values and the directionally averaged values.Results: The gFA(α) and gFA(H) values of the moderate AD group were higher than those of the mild AD group in left hippocampus. The gFA(α) value of the moderate AD group was significantly higher than that of the healthy control group in both the left and right hippocampus. The gFA(ADC) values of the moderate AD group were significantly lower than those of the mild AD group and healthy control group in the right hippocampus. Compared with the gFA(α), gFA(H), α, and H, the ROC analysis showed larger areas under the curves for combination of α + gFA(α) and the combination of H + gFA(H) in differentiating the mild AD and moderate AD groups, and larger area under the curves for combination of α + gFA(α) in differentiating the healthy controls and AD groups.Conclusion: The anisotropy of anomalous diffusion could significantly differentiate and grade patients with AD, and the diagnostic performance was improved when the anisotropy metric was combined with commonly used directionally averaged values. The utility of anisotropic anomalous diffusion may provide novel insights to profoundly understand the neuropathology of AD.

Fast motion estimation algorithm for HEVC video codec

Subject of Research. The paper considers motion estimation as the most difficult and resource-consuming process in the high efficiency video coding standard. A fast algorithm is proposed that skips the fractional-pixel motion estimation. Method. The fractional-pixel motion estimation, including the half-pixel and quarter-pixel motion estimation, is used as a refinement process for integer-pixel motion estimation to provide better coding efficiency. The proposed algorithm involves skipping the fractional motion estimation for prediction blocks if the block with 2N × 2N dimension, which contains more information than the other block sizes, is encoded with integer motion estimation. The decision can also be made in reference frames, so that motion estimation at half- and/or quarter-pixel levels can be skipped to reduce encoding time. Main Results. The proposed algorithm is implemented in HM-16.20 reference software. Several test sequences recommended by the International Telecommunication Union (ITU) are used to evaluate its effectiveness. Experimental results show that the proposed fast algorithm reduces the encoding time by an average of 64 % with a performance loss of less than 1 %. Practical Relevance. The proposed fast algorithm provides a reduction in coding time with a slight loss in performance. It can replace an existing unit in the H.265 standard speed up the video compression process.

Generalized Unsteady MHD Natural Convective Flow of Jeffery Model with ramped wall velocity and Newtonian heating; A Caputo-Fabrizio Approach

This theoretical investigation aims to highlight the unsteady freely convective fractional motion of a Jeffery fluid near an infinite vertical plate. The additional effects of ramped velocity condition, Newtonian heating, magnetohydrodynamics (MHD), and nonlinear radiative heat flux are also examined. A system of fractional order partial differential equations is established by choosing Caputo-Fabrizio fractional derivative as a foundation. Laplace transformation followed by an adequate choice of unit-less parameters is executed to solve the subsequent ordinary differential equations. Stehfest’s and Zakian’s numerical algorithms are invoked to find and justify the inverse Laplace transform of velocity and shear stress. Temperature and velocity gradients are evaluated at the wall to effectively probe the rate of heat transfer and shear stress. In this regard, numerical computations of Nusselt number and shear stress for several inputs of connected parameters are tabulated. Furthermore, graphical elucidations of velocity and temperature profiles are provided to observe the rise and fall subjected to variation in several parameters. Additionally, the velocity profile for both ramped boundary condition and constant boundary condition is analyzed to get a deep insight into the physical phenomenon of the considered problem. Finally, a comparative analysis between Jeffery fluid and second grade fluid is carried out for both factional and ordinary cases, and it is determined that Jeffery fluids exhibit rapid motion in both cases.

Identification and Classification of Alzheimer's Disease Patients Using Novel Fractional Motion Model.

Most diffusion magnetic resonance imaging (dMRI) techniques use the mono-exponential model to describe the diffusion process of water in the brain. However, the observed dMRI signal decay curve deviates from the mono-exponential form. To solve this problem, the fractional motion (FM) model has been developed, which is regarded as a more appropriate model for describing the complex diffusion process in brain tissue. It is still unclear in the identification and classification of Alzheimer’s disease (AD) patients using the FM model. The purpose of this study was to investigate the potential feasibility of FM model for differentiating AD patients from healthy controls and grading patients with AD. Twenty-four patients with AD and 11 healthy controls were included. The left and right hippocampus were selected as regions of interest (ROIs). The apparent diffusion coefficient (ADC) values and FM-related parameters, including the Noah exponent (α), the Hurst exponent (H), and the memory parameter (μ=H−1/α), were calculated and compared between AD patients and healthy controls and between mild AD and moderate AD patients using a two-sample t-test. The correlations between FM-related parameters α, H, μ, and ADC values and the cognitive functions assessed by mini-mental state examination (MMSE) and Montreal cognitive assessment (MoCA) scales were investigated using Pearson partial correlation analysis in patients with AD. The receiver-operating characteristic analysis was used to assess the differential performance. We found that the FM-related parameter α could be used to distinguish AD patients from healthy controls (P < 0.05) with greater sensitivity and specificity (left ROI, 0.917 and 0.636; right ROI, 0.917 and 0.727) and grade AD patients (P < 0.05) showed higher sensitivity and specificity (right ROI, 0.917, 0.75). The α was found to be positively correlated with MMSE (P < 0.05) and MoCA (P < 0.05) scores in patients with AD, indicating that the α values in the bilateral hippocampus were a potential MRI-based biomarker of disease severity in AD patients. This novel diffusion model may be useful for further understanding neuropathologic changes in patients with AD.