Fractional Motion Research Articles

Exploring the spatiotemporal properties of fractal rotation perception

A series of three experiments was conducted with the aim of determining the processing nature of the fractal rotation stimulus introduced by C. P. Benton, J. M. O'Brien, and W. Curran (2007). This stimulus has been proposed to be invisible to first-order sensitive mechanisms considering it is drift-balanced. Rather, motion perception would require the analysis of spatial structure (orientation) changing over time. In Experiment 1, spatiotemporal properties of fractal rotation perception have been explored, in comparison with first-order rotation perception. In Experiment 2, a motion paradigm similar to the one developed by K. Nakayama and C. W. Tyler (1981) and later used by A. E. Seiffert and P. Cavanagh (1998) has been used to characterize the motion processing mechanism responsible for fractal rotation perception. In Experiment 3, we have used a paradigm similar to N. E. Scott-Samuel and A. T. Smith (2000) to evaluate whether fractal rotation perception is analyzed by common or distinct mechanisms to those for first-order rotation perception. Results indicate that fractal rotation perception involves feature-tracking processes with mechanisms responding to global orientation-based changes of the image. Given the absence of cancellation of first-order and fractal rotation motion signals, we can therefore conclude that the first-order and fractal motion sensitive pathways are dissociable at early stages of the visual processing stream.

A SIMULATION METHOD FOR LOG-FRACTIONAL STABLE MOTION

Stoev and Taqqu1 presented a fast simulation method for the linear fractional stable motion (lfsm) process, using the fast Fourier transform. In this paper, we extend this method for fast simulation of the log-fractional stable motion (log-fsm) process. These two heavy-tailed processes, i.e. lfsm and log-fsm, can be used for modeling the modern telecommunication networks. In addition, a necessary and sufficient condition is given for the efficiency of this method. Finally, an upper bound for approximation error is presented.

SU-FF-T-147: Intra Fractional Motion in Clinical IMRT Prostate Treatments, Warrants the Use of Faster Treatment Techniques

Purpose: To estimate intrafracional motion of the prostate in a routine clinical setting and its impact on margin reduction and treatment time. Method and Materials: External beam treatment for cancer of the prostate using an IMRT technique was evaluated. Fifteen patients underwent a marker match procedure ensuring correct positioning at time of treatment. For all fields intra‐treatment images were obtained, yielding 5 to 7 images per fraction. IMRT was delivered using a dynamic sliding window technique. The obtained images were processed to remove IMRT information. The markers were detected in the image using an automated methodology. Every image was timestamped and chronologically adjacent images were backprojected to yield 3D marker coordinates. Allowing to calculate the position of the prostate during the treatment delivery at specific time instances. Using a Poisson model for the probability of movement we can determine the maximal allowable time frame within which to perform this treament. Results: The maximal treament time measured was 1460s, the shortest lasted 343s. The times were measured starting from the last image in the marker‐match procedure and includes the decision and adjustment process. Depending on the elapsed time we noticed an increase in positional confidence level from 5.8mm to 7.6mm. The delivery of the fields are of the order of 250s. Conclusion: We note a significant increase in probability of prostate movement in our treaments as time elapses. This limits the amount of margin reduction possible. There are two strategies possible to reduce this time. 1) Increase the marker match speed, or 2) increase the delivery speed. A good candidate to do this is the use of a volumetric Arc technique (VMAT) which is implemented in our department with RapidArc™. The latter is able to deliver the same or even better dose distribution in under 2 minutes (8 patients).

HDTV1080p H.264/AVC Encoder Chip Design and Performance Analysis

A H.264/AVC baseline-profile real-time encoder for HDTV-1080p at 30 fps is proposed in this paper. On the basis of the specifications and algorithm optimizations, the dedicated hardware engines and one 32-bit media embedded processor (MeP) equipped with hardware extensions are mapped into the three-stage macroblock pipelining system architecture. This paper describes the design considerations for chief components, including high throughput integer motion estimation, data reusing fractional motion estimation, and hardware friendly mode reduction for intra prediction. The 11.5 Gbps 64 Mb system-in-silicon DRAM is embedded to alleviate the external memory bandwidth. Using TSMC one-poly six-metal 0.18 mum CMOS technology, the prototype chip is implemented with 1140 k logic gates and 108.3 KB internal SRAM. The SoC core occupies 27.1 mm2 die area and consumes 1.41 W at 200 MHz execution speed in typical work conditions.

Macroblock Feature Based Complexity Reduction for H.264/AVC Motion Estimation

In H.264/AVC standard, many new techniques such as variable block size (VBS) and multiple reference frame (MRF) are used in motion estimation (ME) part to achieve superior coding performance. However, the use of new techniques will also cause great burden on computation complexity, which leads to problems in low power hardware implementation. Many software based fast ME algorithms are proposed to reduce complexity. For real-time hardwired encoder, the huge throughput of fractional motion estimation (FME) and integer motion estimation (IME) makes pipeline stage a must. In this case, IME is arranged in a single stage, which deteriorates the efficiency of many software based algorithms. Based on the hardware data flow, this paper provides a complexity reduction algorithm which speeds up ME procedure through three schemes. Firstly, the proposed algorithm executes similarity analysis to detect big mode MB and apply early termination in IME stage. Secondly, for normal MB, motion feature is extracted after IME of each frame and a 6-ring based search range adjustment scheme is introduced to remove redundant search positions. Thirdly, for MBs which have large motion feature, the pixel difference is very small due to the blur effect on video sensor. So, we use subsampling technique to reduce computation complexity for such MBs. Experimental results show that, compared with hardware friendly full search algorithm, the proposed fast ME algorithm can reduce 52.63% to 83.21% ME time with negligible video quality degradation. Furthermore, since the proposed algorithm works in a hardware friendly way, it can be embedded into 3-stage real-time hardwired video encoder to achieve low power design.

VLSI Architecture Design of Fractional Motion Estimation for H.264/AVC

The H.264/AVC Fractional Motion Estimation (FME) with rate-distortion constrained mode decision can improve the rate-distortion efficiency by 2–6 dB in peak signal-to-noise ratio. However, it comes with considerable computation complexity. Acceleration by dedicated hardware is a must for real-time applications. The main difficulty for FME hardware implementation is parallel processing under the constraint of the sequential flow and data dependency. We analyze seven inter-correlative loops extracted from FME procedure and provide decomposing methodologies to obtain efficient projection in hardware implementation. Two techniques, 4×4 block decomposition and efficiently vertical scheduling, are proposed to reuse data among the variable block size and to improve the hardware utilization. Besides, advanced architectures are designed to efficiently integrate the 6-taps 2D finite impulse response, residue generation, and 4×4 Hadamard transform into a fully pipelined architecture. This design is finally implemented and integrated into an H.264/AVC single chip encoder that supports realtime encoding of 720×480 30fps video with four reference frames at 81 MHz operation frequency with 405 K logic gates (41.9% area of the encoder).

Stochastic analysis of groundwater flow in a two‐dimensional generalized fractal field

Stochastic analysis of groundwater flow in a generalized fractal field is performed in this study. The random field is described by fractional Levy motion (fLm), which is a generalized version of traditional fractional Brownian motion (fBm) and is superior to describe a field with a high degree of variability. A truncated power variogram of the fLm is derived using the weighted superposition of mutually uncorrelated exponential variograms. When the Levy index of fLm α equals 2, the fBm is recovered. When the upper and lower cutoffs of the truncated power variogram are close, the stationary exponential model can be well approximated. First‐order perturbation analyses of flow in a two‐dimensional fLm field are performed and results are compared to those in the stationary exponential and fractal fBm fields. Since the proposed general fractal model has broader applications than the stationary and fBm models, it is versatile enough to simulate flow in different scenarios and provide more accurate modeling results.

A Virtual Simulation Environment for Lunar Rover: Framework and Key Technologies

Lunar rover development involves a large amount of validation works in realistic operational conditions, including its mechanical subsystem and on-board software. Real tests require equipped rover platform and a realistic terrain. It is very time consuming and high cost. To improve the development efficiency, a rover simulation environment called RSVE that affords real time capabilities with high fidelity has been developed. It uses fractional Brown motion (fBm) technique and statistical properties to generate lunar surface. Thus, various terrain models for simulation can be generated through changing several parameters. To simulate lunar rover evolving on natural and unstructured surface with high realism, the whole dynamics of the multi-body systems and complex interactions with soft ground is integrated in this environment. An example for path planning algorithm and controlling algorithm testing in this environment is tested. This simulation environment runs on PC or Silicon Graphics.

Short and Long Memory Fractional Ornstein–Uhlenbeck α-Stable Processes

We show that, similar to the Gaussian case, the fractional Ornstein–Uhlenbeck α-stable process obtained via the Lamperti transformation of the linear fractional stable motion is a different stationary process than the one defined as the solution of the Langevin equation driven by a linear fractional stable noise. We investigate the asymptotic dependence structure of the first process and prove that, in contrast to the second case, it is a short-memory process in the sense of the measure of dependence appropriate for processes with infinite second moment.

Approximation of Gaussian Random Fields: General Results and Optimal Wavelet Representation of the Lévy Fractional Motion

We investigate the approximation rate for certain centered Gaussian fields by a general approach. Upper estimates are proved in the context of so–called Holder operators and lower estimates follow from the eigenvalue behavior of some related self–adjoint integral operator in a suitable L2(μ)–space. In particular, we determine the approximation rate for the Levy fractional Brownian motion XH with Hurst parameter H∈(0,1), indexed by a self–similar set T⊂ℝN of Hausdorff dimension D. This rate turns out to be of order n−H/D(log n)1/2. In the case T=[0,1]N we present a concrete wavelet representation of XH leading to an approximation of XH with the optimal rate n−H/N(log n)1/2.

A Fast Algorithm and Its VLSI Architecture for Fractional Motion Estimation for H.264/MPEG-4 AVC Video Coding

This paper presents a fast algorithm and its VLSI architecture for H.264 fractional motion estimation. Motivated by the high correlation of cost between neighboring fractional pel position, the proposed algorithm efficiently explores the neighborhood position around the minimum one and thus skips other unlikely ones. Thus, the proposed search pattern and early termination under constant quantization parameter can reduce about 50% of computation complexity compared to that in reference software but only with 0.1-0.2 dB peak signal-to-noise ratio degradation and less than 2% of bit rate increase. The VLSI architecture of the proposed algorithm thus can save 40% of area cost due to only half of the processing elements and save 14% of searching time when compared with the previous design

Lossless VLSI Oriented Full Computation Reusing Algorithm for H.264/AVC Fractional Motion Estimation

Fractional Motion Estimation (FME) is an advanced feature adopted in H.264/AVC video compression standard with quarter-pixel accuracy. Although FME could gain considerably higher encoding efficiency, sub-pixel interpolation and sum of absolute transformed difference (SATD) computation, as main parts of FME, increase the computation complexity a lot. To reduce the complexity of FME, this paper proposes a full computation reusable VLSI oriented algorithm. Through exploiting the similarity among motion vectors (MVs) of partitions in the same macroblock (MB), temporary computation results can be fully reused. Furthermore, a simple and effective searching method is adopted to make the proposed method more suitable for VLSI implementation. Experiment results show that up to 80% add operations and 85% internal reference frame memory access operations are saved without any degradation in the coding quality.

A generalization of the fractal/facies model

In order to generalize the fractal/facies concept presented by Lu et al. (2002), a new stochastic fractal model for ln(K) (K = hydraulic conductivity) increment probability density functions (PDFs) is presented that produces non-Gaussian behavior at smaller measurement lags and converges to Gaussian behavior at larger lags, a property that is observed in data sets. The model is based on the classical Laplace PDF and its generalizations. In analogy with its Gaussian counterparts, the new stochastic fractal family is called fractional Laplace motion (fLam) having stationary increments called fractional Laplace noise (fLan). This fractal is different because the character of the underlying increment PDFs change dramatically with lag size, which leads to lack of self-similarity and self-affinity as they are traditionally defined. Data also appear to display this characteristic. In the larger lag size ranges, however, approximate self-affinity does hold. The basic field procedure for further testing of the fractional Laplace theory is to measure ln(K) increment distributions along transects, calculate frequency distributions from the data, and compare results to various members of the auto-correlated fLan family. The variances of the frequency distributions should also change with lag size (scale) in a prescribed manner. There are mathematical reasons, such as the geometric central limit theorem, for surmising that fLam/fLan may be more fundamental than other approaches that have been proposed for modeling ln(K) frequency distributions, such as the flexible scaling model of Painter (2001). If this turns out not to be the case, then other approaches may be comparable or preferable. (Less)

Integral representations of periodic and cyclic fractional stable motions

Stable non-Gaussian self-similar mixed moving averages can be decomposed into several components. Two of these are the periodic and cyclic fractional stable motions which are the subject of this study. We focus on the structure of their integral representations and show that the periodic fractional stable motions have, in fact, a canonical representation. We study several examples and discuss questions of uniqueness, namely how to determine whether two given integral representations of periodic or cyclic fractional stable motions give rise to the same process.

Reusable Architecture and Complexity-Controllable Algorithm for the Integer/Fractional Motion Estimation of H.264

Motion estimation is the most computational intensive part of H.264 video coding. The motion estimation of H.264 includes integer motion estimation and fractional motion estimation. In this paper, a reusable architecture for both of them is proposed. This architecture can support fractional motion estimation and fast integer motion estimation algorithms including diamond search and cross search. The complexity of the motion estimation algorithm implemented on the proposed architecture can be flexibly controlled to meet variable system requirement. Cycle allocation is used in the algorithm design so that the cycle budget can be fully utilized. Experimental results show that this architecture-algorithm co-design can support HD (1280times720) video real-time encoding at 30 frames per second with 238K logic gates and 117 Mhz operation frequency.

In Vivo Determination of Hepatic Stiffness Using Steady-State Free Precession Magnetic Resonance Elastography

The objective of this study was to introduce an magnetic resonance elastography (MRE) protocol based on fractional motion encoding and planar wave acquisition for rapid measurements of in vivo human liver stiffness. Vibrations of a remote actuator membrane were fed by a rigid rod to the patient's surface beneath the right costal arch resulting in axial shear deflections of the liver. Data acquisition was performed using a balanced steady-state free precession (bSSFP) sequence incorporating oscillating gradients for motion sensitization. Tissue vibrations of frequency fv = 51 Hz were tuned by twice the sequence repetition time (1/fv = 2TR). Twenty axial images acquired by time-resolved through-plane wave encoding were used for planar elasticity reconstruction. The MRE data acquisition was achieved within 4 breathholds of 17 seconds each. The method was applied to 12 healthy volunteers and 2 patients with diffuse liver disease (fibrosis grade 3). MRE data acquisition was successful in all volunteers and patients. The elastic moduli were measured with values between 1.99 +/- 0.16 and 5.77 +/- 0.88 kPa. Follow-up studies demonstrated the reproducibility of the method and revealed a difference of 0.74 +/- 0.47 kPa (P < 0.05) between the hepatic stiffness of 2 healthy male volunteers. bSSFP combined with fractional MRE enables rapid measurement of liver stiffness in vivo. The used actuation principle supports a 2-dimensional analysis of the strain wave field captured by axial wave images. The measured data indicate individual variations of hepatic stiffness in healthy volunteers.

Analysis and architecture design of an HDTV720p 30 frames/s H.264/AVC encoder

H.264/AVC significantly outperforms previous video coding standards with many new coding tools. However, the better performance comes at the price of the extraordinarily huge computational complexity and memory access requirement, which makes it difficult to design a hardwired encoder for real-time applications. In addition, due to the complex, sequential, and highly data-dependent characteristics of the essential algorithms in H.264/AVC, both the pipelining and the parallel processing techniques are constrained to be employed. The hardware utilization and throughput are also decreased because of the block/MB/frame-level reconstruction loops. In this paper, we describe our techniques to design the H.264/AVC video encoder for HDTV applications. On the system design level, in consideration of the characteristics of the key components and the reconstruction loops, the four-stage macroblock pipelined system architecture is first proposed with an efficient scheduling and memory hierarchy. On the module design level, the design considerations of the significant modules are addressed followed by the hardware architectures, including low-bandwidth integer motion estimation, parallel fractional motion estimation, reconfigurable intrapredictor generator, dual-buffer block-pipelined entropy coder, and deblocking filter. With these techniques, the prototype chip of the efficient H.264/AVC encoder is implemented with 922.8 K logic gates and 34.72-KB SRAM at 108-MHz operation frequency.

PLAYER'S POSITIONAL DEPENDENCE OF FRACTAL BEHAVIORS IN A SOCCER GAME

This paper describes fractal behaviors in a soccer game according to the player's position. It is quite important for us to characterize the fractal motion behaviors of the objects during the game. We obtained two-dimensional coordinates of the objects using standard video processing techniques from a computer soccer game. We calculated values of regularization dimensions of the time series to characterize their fractal behaviors. To see positional dependence, we averaged individual player's values over the same position in the same team. When a team is one-sidedly experiencing a severe attack, its defenders have higher fractal dimensions than those of the opponent's corresponding players. We propose a new measure of relative dominance in attack against the opponent team.

Performance of User Independent Echocardiographic Border Detection Algorithm: Comparison with Human Observer Variability

We evaluated a method for autonomous, user-independent automated border delineation (ABD) developed by Geiser and Wilson, by comparing the accuracy of ABD relative to manual border tracing. Short axis echocardiographic images of 84 patients from 3 clinical sites were analyzed using ABD and by manual tracing performed by two observers at each site and two observers at a core laboratory. The centerline method was used to measure the distance between each pair of computer-generated and hand-traced borders. Cardiac parameters were also measured from all sets of borders: LV area, fractional area change, antero-posterior diameter, wall motion, and wall thickening. The distance between computer-generated and hand-traced borders was slightly but significantly greater than human interobserver variability between the clinical sites and the core laboratory (0.34+/-0.25 (N = 328) vs. 0.26+/-0.16 (N = 320) cm for the endocardium at end diastole, p = 0.0001). Measurements of LV area and fractional area change were similar by ABD and manual tracing. Other cardiac parameters showed greater deviation between ABD and manually traced borders than between human observers. Autonomous ABD provides accurate measurements of LV area and area-derived indices. However measurements dependent on border point location deviate more by ABD.

Fractal Motion of Electrons with Variable Weak Memory and Nonlocality

Equations of fractal motion of electrons with variable weak memory and nonlocality are investigated. It is demonstrated that the fractal dimension of time changes by a harmonic law for stationary electron motion. The fractal nonlocality has been established for the free electron; it also changes by a harmonic law. The fractal nonlocality of the electron bound with the hydrogen atom nucleus differs radically. In this case, the fractal dimension of radial electron motion is everywhere less than unity. It can be greater than unity in regions well away from the nucleus.