Transformed Parameter Space Research Articles

Theory of complex-coordinate transformation acoustics for non-Hermitian metamaterials

Transformation acoustics (TA) has emerged as a powerful tool for designing several intriguing conceptual devices, which can manipulate acoustic waves in a flexible manner, yet their applications are limited in Hermitian materials. In this work, we propose the theory of complex-coordinate transformation acoustics (CCTA) and verify the effectiveness in realizing acoustic non-Hermitian metamaterials. Especially, we apply this theory for the first time to the design of acoustic parity–time () and antisymmetric parity–time () metamaterials and demonstrate two distinctive examples. First, we use this method to obtain the exceptional points (EPs) of the system and observe the spontaneous phase transition of the scattering matrix in the transformation parameter space. Second, by selecting the Jacobian matrix’s constitutive parameters, the -symmetric system can also be configured to approach the zero and pole of the scattering matrix, behaving as an acoustic coherent perfect absorber and equivalent laser. We envision our proposed CCTA-based paradigm to open the way for exploring the non-Hermitian physics and finding application in the design of acoustic functional devices such as absorbers and amplifiers whose material parameters are hard to realize by using the conventional transformation method.

GO-APSR: A Globally Optimal Affine Point Set Registration Method

Point set registration under affine transformation is an important problem in computer vision because not only it has many direct applications, but it is also often used as an initial step for non-rigid registration. This problem is challenging when no correspondences between the two point sets are known, and most existing methods start from an initial pose and find a local optimal transformation. This paper presents a deterministic global optimization method for affine point set registration, which is called GO-APSR. We model the two sets to be registered with Gaussian Mixture Models (GMMs) and minimize the L2 distance between the two GMMs under affine transformation. Branch-and-Bound (BnB) is employed to search the transformation parameter space, and we propose a convex quadratic function as the under-estimator of the objective function in each branch. Therefore, calculation of the lower bound in each branch is casted into a bound-constrained convex quadratic programming problem, which can be solved globally and efficiently. Experiment results verify the global optimality of the proposed method and its robustness to noise and outliers. Furthermore, it works very well in the challenging partially-overlap scenarios.

Tracking the development of seismic fracture network from The Geysers geothermal field

Underground fluid injections result in rock mass fracturing. The associated environmental hazards in a significant part stem from a possibility for linking these fractures. The resultant crevices may allow for an undesired and hazardous fluid migration. We studied the fracture linking problem on data from a part of The Geysers geothermal field in California, USA. We parameterized seismic events by the distance between hypocenter and injecting well, by the angle between the position vector of hypocentre and the maximum horizontal stress direction and by the angle of rotation required to turn the event’s double-couple mechanism into the prevailing in this area faults’ orientation. To make these parameters comparable, we transformed them to equivalent dimensions. Based on distances between events in the transformed parameter space, we divided the seismic events into clusters. The percentage of potentially linked fractures in clusters was greater at low than at high injection rate.

An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function

Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress–strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.

Performing track reconstruction at the ALICE TPC using a fast Hough Transform method

The Hough Transform algorithm is a popular image analysis method that is widely used to perform global pattern recognition in images through the identification of local patterns in a suitably chosen parameter space. The algorithm can also be used to perform track reconstruction; to estimate the trajectory of individual particles when passed through the active elements of a detector volume. This paper presents a fast reconstruction method for the Time Projection Chamber (TPC) of the ALICE experiment at LHC. The method, that combines a linear Hough Transform algorithm with a fast filling of the Hough Transform parameter space, is developed within AliceO2, the new computing framework of ALICE for RUN3.

Microstructure Feature Recognition for Materials Using Surfacelet-Based Methods for Computer-Aided Design-Material Integration

With the material processing freedoms of additive manufacturing (AM), the ability to characterize and control material microstructures is essential if part designers are to properly design parts. To integrate material information into Computer-aided design (CAD) systems, geometric features of material microstructure must be recognized and represented, which is the focus of this paper. Linear microstructure features, such as fibers or grain boundaries, can be found computationally from microstructure images using surfacelet based methods, which include the Radon or Radon-like transform followed by a wavelet transform. By finding peaks in the transform results, linear features can be recognized and characterized by length, orientation, and position. The challenge is that often a feature will be imprecisely represented in the transformed parameter space. In this paper, we demonstrate surfacelet-based methods to recognize microstructure features in parts fabricated by AM. We will provide an explicit computational method to recognize and to quantify linear geometric features from an image.

Limiting the parameter space in the Carbon Cycle Data Assimilation System (CCDAS)

Abstract. Terrestrial ecosystem models are employed to calculate the sources and sinks of carbon dioxide between land and atmosphere. These models may be heavily parameterised. Where reliable estimates are unavailable for a parameter, it remains highly uncertain; uncertainty of parameters can substantially contribute to overall model output uncertainty. This paper builds on the work of the terrestrial Carbon Cycle Data Assimilation System (CCDAS), which, here, assimilates atmospheric CO2 concentrations to optimise 19 parameters of the underlying terrestrial ecosystem model (Biosphere Energy Transfer and Hydrology scheme, BETHY). Previous experiments have shown that the identified minimum may contain non-physical parameter values. One way to combat this problem is to use constrained optimisation and so avoid the optimiser searching non-physical regions. Another technique is to use penalty terms in the cost function, which are added when the optimisation searches outside of a specified region. The use of parameter transformations is a further method of avoiding this problem, where the optimisation is carried out in a transformed parameter space, thus ensuring that the optimal parameters at the minimum are in the physical domain. We compare these different methods of achieving meaningful parameter values, finding that the parameter transformation method shows consistent results and that the other two provide no useful results.

Evaluation of similarity measures for use in the intensity‐based rigid 2D‐3D registration for patient positioning in radiotherapy

Rigid 2D-3D registration is an alternative to 3D-3D registration for cases where largely bony anatomy can be used for patient positioning in external beam radiation therapy. In this article, the authors evaluated seven similarity measures for use in the intensity-based rigid 2D-3D registration using a variation in Skerl's similarity measure evaluation protocol. The seven similarity measures are partitioned intensity uniformity, normalized mutual information (NMI), normalized cross correlation (NCC), entropy of the difference image, pattern intensity (PI), gradient correlation (GC), and gradient difference (GD). In contrast to traditional evaluation methods that rely on visual inspection or registration outcomes, the similarity measure evaluation protocol probes the transform parameter space and computes a number of similarity measure properties, which is objective and optimization method independent. The variation in protocol offers an improved property in the quantification of the capture range. The authors used this protocol to investigate the effects of the downsampling ratio, the region of interest, and the method of the digitally reconstructed radiograph (DRR) calculation [i.e., the incremental ray-tracing method implemented on a central processing unit (CPU) or the 3D texture rendering method implemented on a graphics processing unit (GPU)] on the performance of the similarity measures. The studies were carried out using both the kilovoltage (kV) and the megavoltage (MV) images of an anthropomorphic cranial phantom and the MV images of a head-and-neck cancer patient. Both the phantom and the patient studies showed the 2D-3D registration using the GPU-based DRR calculation yielded better robustness, while providing similar accuracy compared to the CPU-based calculation. The phantom study using kV imaging suggested that NCC has the best accuracy and robustness, but its slow function value change near the global maximum requires a stricter termination condition for an optimization method. The phantom study using MV imaging indicated that PI, GD, and GC have the best accuracy, while NCC and NMI have the best robustness. The clinical study using MV imaging showed that NCC and NMI have the best robustness. The authors evaluated the performance of seven similarity measures for use in 2D-3D image registration using the variation in Skerl's similarity measure evaluation protocol. The generalized methodology can be used to select the best similarity measures, determine the optimal or near optimal choice of parameter, and choose the appropriate registration strategy for the end user in his specific registration applications in medical imaging.

On the Relative and Absolute Positioning Errors in Self-Localization Systems

This paper considers the accuracy of sensor node location estimates from self-calibration in sensor networks. The total parameter space is shown to have a natural decomposition into relative and centroid transformation components. A linear representation of the transformation parameter space is shown to coincide with the nullspace of the unconstrained Fisher information matrix (FIM). The centroid transformation subspace-which includes representations of rotation, translation, and scaling-is characterized for a number of measurement models including distance, time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), and angle-difference-of-arrival (ADOA) measurements. The error decomposition may be applied to any localization algorithm in order to better understand its performance characteristics, and it may be applied to the Cramer-Rao bound (CRB) to determine performance limits in the relative and transformation domains. A geometric interpretation of the constrained CRB is provided based on the principal angles between the measurement subspace and the constraint subspace. Examples are presented to illustrate the utility of the proposed error decomposition into relative and transformation components.

AN ANTI-NOISE ALGORITHM FOR ENHANCING GLOBAL AND LOCAL CONTRAST FOR INFRARED IMAGE

Having performed discrete stationary wavelet transform (DSWT) to an infrared image and employing generalized cross validation (GCV), noise is reduced in high frequency sub-bands. These sub-bands are at finer resolution levels and the local contrast is enhanced by combining the de-noising method with non-linear operator in these sub-bands which are at coarser resolutionn levels. In order to enhance global contrast for an infrared image, the low frequency sub-band image is also enhanced employing non-incomplete Beta transform (IBT), simulated annealing algorithm (SA) and wavelet neural network (WNN). IBT is used to obtain non-linear gray transform curve. Transform parameters are determined by SA so as to obtain optimal non-linear gray transform parameters. Contrast type of an original image is determined by a new criterion. Gray transform parameters space is determined respectively according to different contrast types. A kind of WNN is proposed to approximate the IBT in the whole low frequency sub-band image. The quality of enhanced image is evaluated by an overall cost criterion. Experimental results show that the new algorithm can greatly improve the global and local contrast for an infrared image while efficiently reducing the correlative noise (CN), gauss white noise (GWN) and multiplicative noise (MN) in the infrared image.

Robust and Efficient Image Alignment Based on Relative Gradient Matching

In this paper, we present a robust image alignment algorithm based on matching of relative gradient maps. This algorithm consists of two stages; namely, a learning-based approximate pattern search and an iterative energy-minimization procedure for matching relative image gradient. The first stage finds some candidate poses of the pattern from the image through a fast nearest-neighbor search of the best match of the relative gradient features computed from training database of feature vectors, which are obtained from the synthesis of the geometrically transformed template image with the transformation parameters uniformly sampled from a given transformation parameter space. Subsequently, the candidate poses are further verified and refined by matching the relative gradient images through an iterative energy- minimization procedure. This approach based on the matching of relative gradients is robust against nonuniform illumination variations. Experimental results on both simulated and real images are shown to demonstrate superior efficiency and robustness of the proposed algorithm over the conventional normalized correlation method.

Extreme point result for robuststability of discrete systems with complex coefficients in a diamond

Robust stability of a continuous-time system with coefficients of the characteristic polynomial varying in a diamond can be considered as a 'dual' problem to Kharitonov's theorem on interval polynomials. This paper aims at developing similar results for discrete-time systems. Specifically, it shows that stability of a family of polynomials, whose complex coefficients lie in a diamond of a transformed parameter space, can be determined by simply checking four (eight) extreme polynomials. This result can be viewed as a counterpart of Kharitonov's result (strong version) for discrete-time systems.

Solution for Second Moment Reliability Index

This paper presents a general method for determination of the magnitude of the second-moment reliability index in a probabilistic design procedure. The minimum distance from the origin of a transformed parameter space to a failure surface (defined by a particular failure criterion) is deduced from consideration of the geometry of the failure surface and that of a sphere centered on the origin. The result is expressed in the original (untransformed) design parameters and is expressed in terms of the gradient of the failure surface and the means and covariances of the design parameters. The solution is shown to coincide with previous analysis for linear failure conditions and a general method for numerical solution in the case of many parameters and nonlinear failure criteria is also considered.