Non-parametric deconvolution using Bézier curves for quantification of cerebral perfusion in dynamic susceptibility contrast MRI

Objective Deconvolution is an ill-posed inverse problem that tends to yield non-physiological residue functions R(t) in dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI). In this study, the use of Bézier curves is proposed for obtaining physiologically reasonable residue functions in perfusion MRI. Materials and methods Cubic Bézier curves were employed, ensuring R(0) = 1, bounded-input, bounded-output stability and a non-negative monotonically decreasing solution, resulting in 5 parameters to be optimized. Bézier deconvolution (BzD), implemented in a Bayesian framework, was tested by simulation under realistic conditions, including effects of arterial delay and dispersion. BzD was also applied to DSC-MRI data from a healthy volunteer. Results Bézier deconvolution showed robustness to different underlying residue function shapes. Accurate perfusion estimates were observed, except for boxcar residue functions at low signal-to-noise ratio. BzD involving corrections for delay, dispersion, and delay with dispersion generally returned accurate results, except for some degree of cerebral blood flow (CBF) overestimation at low levels of each effect. Maps of mean transit time and delay were markedly different between BzD and block-circulant singular value decomposition (oSVD) deconvolution. Discussion A novel DSC-MRI deconvolution method based on Bézier curves was implemented and evaluated. BzD produced physiologically plausible impulse response, without spurious oscillations, with generally less CBF underestimation than oSVD.

Path Planning for Bulldozers with Curvature Constraints

There is presently no solution to the problem of an autonomous bulldozer pushing mounds of material to desired goal locations in the presence of obstacles whilst obeying the kinematic constraints of the bulldozer. Past work has solved some aspects of this problem, but not all. This research presents the first complete, practical solution to the problem. It works by creating a fixed RRT in advance, and then during operation connecting pushing poses into this RRT using Bezier curves. The RRT algorithm leverages a novel data structure for performing nearest neighbour comparisons for Ackermann-steering vehicles; termed the Distmetree. The resulting pushing states are searched using greedy heuristic search to find a solution and the final path is smoothed with cubic Bezier curves. The mode of operation chosen for best performance also constructs bidirectional RRTs to reach difficult to access pushing poses. The final mode of the algorithm was tested in simulation and proven to be able to solve a wide variety of maps in a few minutes while obeying bulldozer kinematic constraints. The algorithm, whilst not optimal, is complete which is the more desirable property in industry, and the solutions it produces are both feasible and reasonable.

Path Planning for Bulldozers with Curvature Constraints

There is presently no solution to the problem of an autonomous bulldozer pushing mounds of material to desired goal locations in the presence of obstacles whilst obeying the kinematic constraints of the bulldozer. Past work has solved some aspects of this problem, but not all. This research presents the first complete, practical solution to the problem. It works by creating a fixed RRT in advance, and then during operation connecting pushing poses into this RRT using Bezier curves. The RRT algorithm leverages a novel data structure for performing nearest neighbour comparisons for Ackermann-steering vehicles; termed the Distmetree. The resulting pushing states are searched using greedy heuristic search to find a solution and the final path is smoothed with cubic Bezier curves. The mode of operation chosen for best performance also constructs bidirectional RRTs to reach difficult to access pushing poses. The final mode of the algorithm was tested in simulation and proven to be able to solve a wide variety of maps in a few minutes while obeying bulldozer kinematic constraints. The algorithm, whilst not optimal, is complete which is the more desirable property in industry, and the solutions it produces are both feasible and reasonable.

Steganographic method based on hidden messages embedding into Bezier curves of SVG images

The description of the steganographic method for embedding the digital watermark into image vector files of the SVG format is given. Vector images in SVG format can include elements based on Bezier curves. The proposed steganographic method is based on the splitting of cubic Bezier curves. Embedding hidden information involves splitting cubic Bezier curves according to the digital watermark given as numerical sequence. Algorithms of direct and reverse steganographic transformation are considered for proving the authenticity and integrity of a digital vector image. The StegoSVG library has been developed to implement forward and reverse steganographic transformations. The developed desktop application that implements the method is briefly described.

Planar Typical Bézier Curves Made Simple

Recently, He et al. derived several remarkable properties of the so-called typical Bézier curves, a subset of constrained Bézier curves introduced by Mineur et al. In particular, He et al. proved that such curves display at most one curvature extremum, give an explicit formula of the parameter at the extremum, and show that subdividing a curve at this point furnishes two new typical curves. We recall that typical curves amount to segments of a special family of sinusoidal spirals, curves already studied by Maclaurin in the early 18th century and whose properties are well-known. These sinusoidal spirals display only one curvature extremum (i.e., vertex), whose parameter is simply that corresponding to the axis of symmetry. Subdividing a segment at an arbitrary point, not necessarily the vertex, always yields two segments of the same spiral, hence two typical curves.

Geometric modeling of some engineering GBT-Bézier surfaces with shape parameters and their applications

This study is based on some $C^{1}$ C 1 , $C^{2}$ C 2 , and $C^{3}$ C 3 continuous computer-based surfaces that are modeled by using generalized blended trigonometric Bézier (shortly, GBT-Bézier) curves with shape parameters. Initially, generalized blended trigonometric Bernstein-like (shortly, GBTB) basis functions with two shape parameters are derived in explicit expression which satisfied the basic geometric features of the traditional Bernstein basis functions. Moreover, the GBT-Bézier curves and tensor product GBT-Bézier surfaces with two shape parameters are also presented. All geometric features of the proposed GBT-Bézier curves and surfaces are similar to the traditional Bézier curves and surfaces, but the shape-adjustment is the additional feature that the traditional Bézier curves and surfaces do not hold. Finally, a class of some complex computer-based engineering surfaces via GBT-Bézier curves with shape parameters is presented. In addition, two adjacent GBT-Bézier surfaces segments are connected by higher $C^{2}$ C 2 and $C^{3}$ C 3 continuity constraints than the existing only $C^{1}$ C 1 shape adjustable Bézier surfaces. Some practical examples are provided to show the efficiency of the proposed scheme and to prove it as another powerful way for the construction and modeling of various complex composite computer-based engineering surfaces using higher-order continuities.