The use of a Riesz fractional differential-based approach for texture enhancement in image processing

Abstract: Texture enhancement is an important component of image processing, with extensive application in science and engineering. The quality of medical images, quantified using the texture of the images, plays a significant role in the routine diagnosis performed by medical practitioners. Previously, image texture enhancement was performed using classical integral order differential mask operators. Recently, first order fractional differential operators were implemented to enhance images. Experiments conclude that the use of the fractional differential not only maintains the low frequency contour features in the smooth areas of the image, but also nonlinearly enhances edges and textures corresponding to high-frequency image components. However, whilst these methods perform well in particular cases, they are not routinely useful across all applications. To this end, we applied the second order Riesz fractional differential operator to improve upon existing approaches of texture enhancement. Compared with the classical integral order differential mask operators and other fractional differential operators, our new algorithms provide higher signal to noise values, which leads to superior image quality.

Spectral approximations to the fractional integral and derivative

In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative

Rayleigh–Stokes problems have in recent years received much attention due to their importance in physics. In this article, we focus on the variable-order Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative. Implicit and explicit numerical methods are developed to solve the problem. The convergence, stability of the numerical methods and solvability of the implicit numerical method are discussed via Fourier analysis. Moreover, a numerical example is given and the results support the effectiveness of the theoretical analysis.

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D

The space and time fractional Bloch–Torrey equation (ST-FBTE) has been used to study anomalous diffusion in the human brain. Numerical methods for solving ST-FBTE in three-dimensions are computationally demanding. In this paper, we propose a computationally effective fractional alternating direction method (FADM) to overcome this problem. We consider ST-FBTE on a finite domain where the time and space derivatives are replaced by the Caputo–Djrbashian and the sequential Riesz fractional derivatives, respectively. The stability and convergence properties of the FADM are discussed. Finally, some numerical results for ST-FBTE are given to confirm our theoretical findings.

A retrospective cohort investigation of active range of motion within one week of open reduction and internal fixation of distal radius fractures

Distal radius fractures stabilized by open reduction internal fixation (ORIF) have become increasingly common. There is currently no consensus on the optimal time to commence range of motion (ROM) exercises post-ORIF. A retrospective cohort review was conducted over a five-year period to compare wrist and forearm range of motion outcomes and number of therapy sessions between patients who commenced active ROM exercises within the first seven days and from day eight onward following ORIF of distal radius fractures. One hundred and twenty-one patient cases were identified. Clinical data, active ROM at initial and discharge therapy assessments, fracture type, surgical approaches, and number of therapy sessions attended were recorded. One hundred and seven (88.4%) cases had complete datasets. The early active ROM group (n = 37) commenced ROM a mean (SD) of 4.27 (1.8) days post-ORIF. The comparator group (n = 70) commenced ROM exercises 24.3 (13.6) days post-ORIF. No significant differences were identified between groups in ROM at initial or discharge assessments, or therapy sessions attended. The results from this study indicate that patients who commenced active ROM exercises an average of 24 days after surgery achieved comparable ROM outcomes with similar number of therapy sessions to those who commenced ROM exercises within the first week.

Displacement motion prediction of a landing deck for recovery operations of rotary UAVs

This paper proposes a practical prediction procedure for vertical displacement of a Rotarywing Unmanned Aerial Vehicle (RUAV) landing deck in the presence of stochastic sea state disturbances. A proper time series model tending to capture characteristics of the dynamic relationship between an observer and a landing deck is constructed, with model orders determined by a novel principle based on Bayes Information Criterion (BIC) and coefficients identified using the Forgetting Factor Recursive Least Square (FFRLS) method. In addition, a fast-converging online multi-step predictor is developed, which can be implemented more rapidly than the Auto-Regressive (AR) predictor as it requires less memory allocations when updating coefficients. Simulation results demonstrate that the proposed prediction approach exhibits satisfactory prediction performance, making it suitable for integration into ship-helicopter approach and landing guidance systems in consideration of computational capacity of the flight computer.

Motion capture and the future of virtual production

Motion capture continues to be adopted across a range of creative fields including, animation, games, visual effects, dance, live theatre and the visual arts. This panel will discuss and showcase the use of motion capture across these creative fields and consider the future of virtual production in the creative industries.

The development of a kinematic model to quantify in-shoe foot motion

A multi-segment foot model was used to develop an accurate and reliable kinematic model to describe in-shoe foot kinematics during gait.

Buzz in motion pictures : what is buzz and how can marketing create it?

In the movie industry, the extraordinarily successful theatrical performance of certain films is largely attributed to buzz. Despite longstanding commentary about the role of buzz in successful movie marketing and the belief that it accelerates new product diffusion, limited scholarly evidence exists to support these assertions. This is primarily due to the lack of conceptual distinction of buzz from word-of-mouth, which is often used as the main basis for conceptualising buzz. However, word-of-mouth does not fully explain the buzz surrounding films such as 'Gone With The Wind', 'The Dark Knight' and 'Avatar'. Informed by valuable insights from key experts who have launched some of the most successful movies in box office history, as well as a range of moviegoers, this thesis developed a deeper understanding of what buzz is and how it is created. This thesis concludes that buzz is not the same as word-of-mouth.

The effect of organ motion of radiotherapy plans

Organ motion as a result of respiration is an important field of research for medical physics. Knowledge of magnitude and direction of this motion is necessary to allow for more accurate radiotherapy treatment planning. This will result in higher doses to the tumour whilst sparing healthy tissue. This project involved human trials, where the radiation therapy patient's kidneys were CT scanned under three different conditions; whilst free breathing (FB), breath-hold at normal tidal inspiration (BHIN), and breath-hold at normal tidal expiration (BHEX). The magnitude of motion was measured by recording the outline of the kidney from a Beam's Eye View (BEV). The centre of mass of this 2D shape was calculated for each set using "ImageJ" software and the magnitude of movement determined from the change in the centroid's coordinates between the BHIN and BHEX scans. The movement ranged from, for the left and right kidneys, 4-46mm and 2-44mm in the superior/inferior (axial) plane, 1-21mm and 2- 16mm in the anterior/posterior (coronal) plane, and 0-6mm and 0-8mm in the lateral/medial (sagittal) plane. From exhale to inhale, the kidneys tended to move inferiorly, anteriorly and laterally. A standard radiotherapy plan, designed to treat the para-aortics with opposed lateral fields was performed on the free breathing (planning) CT set. The field size and arrangement was set up using the same parameters for each subject. The prescription was to deliver 45 Gray in 25 fractions. This field arrangement and prescription was then copied over to the breath hold CT sets, and the dosimetric differences were compared using Dose Volume Histograms (DVH). The point of comparison for the three sets was recorded as the percentage volume of kidney receiving less than or equal to 10 Gray. The QUASAR respiratory motion phantom was used with the range of motion determined from the human study. The phantom was imaged, planned and treated with a linear accelerator with dose determined by film. The effect of the motion was measured by the change in the penumbra of the film and compared to the penumbra from the treatment planning system.

Made by motion, Series one

“Made by Motion” is a collaboration between digital artist Paul Van Opdenbosch and performer and choreographer Elise May; a series of studies on captured motion data used to generating experimental visual forms that reverberate in space and time. The project investigates the invisible forces generated by and influencing the movement of a dancer. Along with how the forces can be captured and applied to generating visual outcomes that surpass simple data visualisation, projecting the intent of the performer’s movements. The source or ‘seed’ comes from using an Xsens MVN - Inertial Motion Capture system to capture spontaneous dance movements, with the visual generation conducted through a customised dynamics simulation. In this first series the visual investigation focused on manipulating the movement date at the instance of capture, capture been the recording of three-dimensional movement as ‘seen’ by the hardware and ‘understood’ through the calibration of software. By repositioning the capture hardware on the body we can effectively change how the same sequence of movements is ‘seen’ by the motion capture system thus generating a different visual result from effetely identical movement. The outcomes from the experiments clearly demonstrates the effectiveness of using motion capture hardware as a creative tool to manipulate the perception of the capture subject, in this case been a sequence of dance movements. The creative work exhibited is a cross-section of the experiments conducted in practice with the first animated work (Movement A - Control) using the motion capture hardware in its default ‘normal’ configuration. Following this is the lower body moved to the upper body (Lb-Ub), right arm moved onto the left arm (Ra-La), right leg moved onto the left leg (Rl-Ll) and finally the left leg moved onto a object that is then held in the left hand (Ll-Pf (Lh)).

Experimental arts practice incorporating motion capture

My practice-led research explores and maps workflows for generating experimental creative work involving inertia based motion capture technology. Motion capture has often been used as a way to bridge animation and dance resulting in abstracted visuals outcomes. In early works this process was largely done by rotoscoping, reference footage and mechanical forms of motion capture. With the evolution of technology, optical and inertial forms of motion capture are now more accessible and able to accurately capture a larger range of complex movements. Made by Motion is a collaboration between digital artist Paul Van Opdenbosch and performer and choreographer Elise May; a series of studies on captured motion data used to generate experimental visual forms that reverberate in space and time. The project investigates the invisible forces generated by and influencing the movement of a dancer. Along with how the forces can be captured and applied to generating visual outcomes that surpass simple data visualisation, projecting the intent of the performer’s movements. The source or ‘seed’ comes from using an Xsens MVN – Inertial Motion Capture system to capture spontaneous dance movements, with the visual generation conducted through a customised dynamics simulation. In my presentation I will be displaying and discussing a selected creative works from the project along with the process and considerations behind the work.

Lattice-free descriptions of collective motion with crowding and adhesion

Cell-to-cell adhesion is an important aspect of malignant spreading that is often observed in images from the experimental cell biology literature. Since cell-to-cell adhesion plays an important role in controlling the movement of individual malignant cells, it is likely that cell-to-cell adhesion also influences the spatial spreading of populations of such cells. Therefore, it is important for us to develop biologically realistic simulation tools that can mimic the key features of such collective spreading processes to improve our understanding of how cell-to-cell adhesion influences the spreading of cell populations. Previous models of collective cell spreading with adhesion have used lattice-based random walk frameworks which may lead to unrealistic results, since the agents in the random walk simulations always move across an artificial underlying lattice structure. This is particularly problematic in high-density regions where it is clear that agents in the random walk align along the underlying lattice, whereas no such regular alignment is ever observed experimentally. To address these limitations, we present a lattice-free model of collective cell migration that explicitly incorporates crowding and adhesion. We derive a partial differential equation description of the discrete process and show that averaged simulation results compare very well with numerical solutions of the partial differential equation.

The Tarim picrite-basalt-rhyolite suite, a Permian flood basalt from Northwest China with contrasting rhyolites produced by fractional crystallization and anatexis

We report major and trace element composition, Sr–Nd isotopic and seismological data for a picrite–basalt–rhyolite suite from the northern Tarim uplift (NTU), northwest China. The samples were recovered from 13 boreholes at depths between 5,166 and 6,333 m. The picritic samples have high MgO (14.5–16.8 wt%, volatiles included) enriched in incompatible element and have high 87Sr/86Sr and low 143Nd/144Nd isotopic ratios (εNd (t) = −5.3; Sri = 0.707), resembling the Karoo high-Ti picrites. All the basaltic samples are enriched in TiO2 (2.1–3.2 wt%, volatiles free), have high FeOt abundances (11.27–15.75 wt%, volatiles free), are enriched in incompatible elements and have high Sr and low Nd isotopic ratios (Sri = 0.7049–0.7065; εNd (t) = −4.1 to −0.4). High Nb/La ratios (0.91–1.34) of basalts attest that they are mantle-derived magma with negligible crustal contamination. The rhyolite samples can be subdivided into two coeval groups with overlapping U–Pb zircon ages between 291 ± 4 and 272 ± 2 Ma. Group 1 rhyolites are enriched in Nb and Ta, have similar Nb/La, Nb/U, and Sr–Nd isotopic compositions to the associated basalts, implying that they are formed by fractional crystallization of the basalts. Group 2 rhyolites are depleted in Nb and Ta, have low Nb/La ratios, and have very high Sr and low Nd isotopic ratios, implying that crustal materials have been extensively, if not exclusively, involved in their source. The picrite–basalt–rhyolite suite from the NTU, together with Permian volcanic rocks from elsewhere Tarim basin, constitute a Large Igneous Province (LIP) that is characterized by large areal extent, rapid eruption, OIB-type chemical composition, and eruption of high temperature picritic magma. The Early Permian magmatism, which covered an area >300,000 km2, is therefore named the Tarim Flood Basalt.