Limited Number Of Control Points Research Articles

GLS‐PIA: n‐Dimensional Spherical B‐Spline Curve Fitting based on Geodesic Least Square with Adaptive Knot Placement

AbstractDue to the widespread applications of curves on n‐dimensional spheres, fitting curves on n‐dimensional spheres has received increasing attention in recent years. However, due to the non‐Euclidean nature of spheres, curve fitting methods on n‐dimensional spheres often struggle to balance fitting accuracy and curve fairness. In this paper, we propose a new fitting framework, GLS‐PIA, for parameterized point sets on n‐dimensional spheres to address the challenge. Meanwhile, we provide the proof of the method. Firstly, we propose a progressive iterative approximation method based on geodesic least squares which can directly optimize the geodesic least squares loss on the n‐sphere, improving the accuracy of the fitting. Additionally, we use an error allocation method based on contribution coefficients to ensure the fairness of the fitting curve. Secondly, we propose an adaptive knot placement method based on geodesic difference to estimate a more reasonable distribution of control points in the parameter domain, placing more control points in areas with greater detail. This enables B‐spline curves to capture more details with a limited number of control points. Experimental results demonstrate that our framework achieves outstanding performance, especially in handling imbalanced data points. (In this paper, “sphere” refers to n‐sphere (n ≥ 2) unless otherwise specified.)

Multizone sound field reproduction using pressure matching with sparse equivalent source

Multizone sound field reproduction aims to create different acoustic environments in multiple spatial zones, allowing listeners to enjoy their individual sounds without being disturbed by sound from other zones. The conventional pressure matching method is used in practice to reproduce the desired sound field by minimizing the sound field error with a limited number of control points, whose reproduction performance decreases above the cutoff frequency. In this paper, a multizone sound field reproduction method based on a sparse equivalent source method is proposed to reproduce the sound field in the whole target region. The acoustic transfer function of each loudspeaker and the desired sound field are represented by the sparse equivalent sources. The whole target region is controlled by interpolating fine virtual control points within the region of the uncontrolled points, and the acoustic transfer functions between the virtual control points and the loudspeaker array are interpolated by the sparse equivalent sources. An optimization reproduction model with the objective of reproducing a desired sound field in the bright zone and constraining the acoustic energy in the dark zone is formulated to find the sparse loudspeaker weights. The simulation results and experimental results show that the proposed method achieves better performance than the conventional pressure matching method in free field and reverberant environments.

Multichannel room response equalization with a broadened control region using a linearly constrained approach and sensor interpolation

This paper describes a room response equalization technique based on an underdetermined multichannel inverse filtering (UMIF) and linearly constrained minimum variance (LCMV) approach. Not limited to the local control at the neighborhood of the measured control points, the proposed UMIF-LCMV system is capable of widening the effective equalization area of the reproduced sound field, with a large number of interpolated control points. Specifically, a constrained optimization problem is formulated to minimize the matching error at the interpolated control points while seeking precise matching at the measured control points. In practical implementation, only the frequency responses (FRs) associated with a limited number of control points need to be measured, whereas the FRs for the interpolated points are established by using a plane wave decomposition-based sensor interpolation technique. A two-stage procedure is developed to trim down plane wave components by using the least absolute shrinkage and selection operator (LASSO) algorithm and to obtain the complex amplitudes of the principal components. Simulations and objective and subjective experiments are conducted for a system comprising a linear loudspeaker array and a linear microphone array. The results have confirmed the efficacy of the proposed system in widening the effective listening area with only limited discrete measurements.

Seismic horizon extraction with dynamic programming

Horizon picking is a fundamental and crucial step for seismic interpretation, but it remains a time-consuming task. Although various automatic methods have been developed to extract horizons in seismic images, most of them may fail to pick horizons across discontinuities such as faults and noise. To obtain more accurate horizons, we have developed a dynamic programming algorithm to efficiently refine manually or automatically extracted horizons so that they can more accurately track reflectors across discontinuities, follow consistent phases, and reveal more geologic details. In this method, we first compute an initial horizon using an automatic method, manual picking, or interpolation with several control points. The initial horizon may not be accurate, and it only needs to follow the general trend of the target horizon. Then, we extract a subvolume of amplitudes centered at the initial horizon and meanwhile flatten the subvolume according to the initial horizon. Finally, we use the dynamic programming to efficiently pick the globally optimal path that passes through the global maximum or minimum amplitudes in the subvolume. As a result, we are able to refine the initial horizon to a more accurate horizon that follows consistent amplitude peaks, troughs, or zero crossings. Because our method does not strictly depend on the initial horizon, we prefer to directly interpolate an initial horizon from a limited number of control points, which is computationally more efficient than automatically or manually picking an initial horizon. In addition, our method is convenient to interactively implement to update the horizon while editing or moving the control points. More importantly, these control points are not required to be exactly placed on the target horizon, which makes the human interaction highly convenient and efficient. We develop our method with multiple 2D and 3D field examples that are complicated by noise, faults, and salt bodies.

Optimization of RFM’s Structure Based on PSO Algorithm and Figure Condition Analysis

Rational function model (RFM) faces difficulty in extracting accurate geometric information from remotely sensed images, which is mainly due to the problems of overparameterization and ill-posedness. These problems can be addressed via variable selection methods, in which an optimum subset of rational polynomial coefficients is identified via an optimization algorithm, usually metaheuristic methods [e.g., genetic algorithm and particle swarm optimization (PSO)]. In this letter, we propose a PSO-based method that benefits from a novel cost function. The proposed cost function applies a figure condition analysis, where the sum of estimated errors for the entire image’s pixels is regarded as the cost value. The main advantages of the proposed method, in comparison to its alternatives of the same type, are as follows: 1) in contrast to other metaheuristic-based methods, it can be applied even with a limited number of control points (CPs); 2) since the proposed cost function is a global and continuous one, it yields an appealing RFM from the generalization capability viewpoint (i.e., it leads to satisfying positional accuracies for the entire image, even for those pixels far from CP); and 3) the method is much more stable, which means that it gives very similar results in successive runs. Our experiments, conducted over four real data sets, demonstrate that the proposed method addresses the aforementioned problems, namely, overparameterization and ill-posedness. In addition, it outperforms the typical PSO-based method by 37% on average and also achieves RFM’s structures that are more reliable and more stable than those identified by its alternative.

Dynamic lip animation from a limited number of control points: Towards an effective audiovisual spoken communication

In audiovisual speech communication, the lower part of the face (mainly lips and jaw) actively participates during speech production. Modeling well lip motion and deformation in audiovisual speech synthesis is important to achieve realism and effective communication. This is essential for challenged population as hard-of-hearing people or new language learners. In this scope, we propose a technique that allows for animation of a human face with realistic lips using a limited number of control points. We have used an articulograph that provides high temporal and spatial precision, allowing tracking the positions of small electromagnetic sensors, even when occluded, which is often the case when tracking the lip movement. In our work, the control point data are first acquired, then fitted to a 3D face model of a human speaker, i.e., each control point is associated with a region of the face by minimizing the distance between the control points and the surface of the face model. Finally, we apply an interpolation scheme of the displacement field between the control points. This displacement field describes the deformation of a surface. In the case of the face, this method is well adapted to animating the region of the face that is highly correlated with speech, specifically the lips and the lower part of the face, even with a very limited number of control points.

Assessing the geometric accuracy of UAV-based orthophotos

Attempt has been made in this research to investigate geometric quality of an Unmanned Aerial Photograph from Trimble UX5 Aerial imaging solution for map generation and compilation despite the limited number of control points used and the mode of establishment of the control points. Two important criteria are pivotal to Geometric quality assessment of an Aerial photograph; Geometric accuracy and Object-definition property but this research bothers on the geometric accuracy. In remote sensing and photogrammetric operations, the geometric quality of the imagery basically depends on the relation between pixel size and the map scale, contrast information, atmosphere and the sun elevation, the printing technology, screen resolution and the visual acuity. The Unmanned Aircraft System (UAS) deliverables which are the orthophoto and the digital surface model (DSM) show that UAS (Trimble UX5) can be used for compilation of large scale maps in partly accessible or inaccessible areas according to the map accuracy analysis of the National Standard for Spatial Data Accuracy (NSSDA, 1998). The horizontal accuracy of 3.207m (RMSE: 1.85m) and vertical accuracy of 0.884m (RMSE: 0.45m) were obtained which fall within the allowable misclosure, hence, suitable for Cadastral map compilation.Keywords: Geometric Accuracy, Object-definition, Image, Map generation, Map compilation, Geometric quality

A Virtual Subarray Architecture for Imaging Radar

In this paper, an architecture for imaging systems employing a smart subarray design to reduce the number of control points as much as possible is proposed. The radar consists of two linear arrays, orthogonally orientated to achieve the same response of a full planar rectangular array, while the feeds are realized by means of properly designed subarrays, that cancel out the grating lobes of the array factor. In the proposed architecture, the role of the subarrays is interchanged: The subarray that cancels out the grating lobes of the vertical array is used as the element of the horizontal array, and vice-versa, so that there is no feed overlapping. A synthesis strategy for the optimization of subarray and array excitations, based on generalized alternate projections, is also presented and validated by means of a number of simulations. The proposed radar is compared with other existing radar architectures, showing good performances with a very limited number of control points.

Fast design of local N‐gram‐specific absorption rate–optimized radiofrequency pulses for parallel transmit systems

Designing multidimensional radiofrequency pulses for clinical application must take into account the local specific absorption rate (SAR) as controlling the global SAR does not guarantee suppression of hot spots. The maximum peak SAR, averaged over an N grams cube (local NgSAR), must be kept under certain safety limits. Computing the SAR over a three-dimensional domain can require several minutes and implementing this computation in a radiofrequency pulse design algorithm could slow down prohibitively the numerical process. In this article, a fast optimization algorithm is designed acting on a limited number of control points, which are strategically selected locations from the entire domain. The selection is performed by comparing the largest eigenvalues and the corresponding eigenvectors of the matrices which locally describe the tissue's amount of heating. The computation complexity is dramatically reduced. An additional critical step to accelerate the computations is to apply a multi shift conjugate gradient algorithm. Two transmit array setups are studied: a two channel 3 T birdcage body coil and a 12-channel 7 T transverse electromagnetic (TEM) head coil. In comparison with minimum power radiofrequency pulses, it is shown that a reduction of 36.5% and 35%, respectively, in the local NgSAR can be achieved within short, clinically feasible, computation times.

A Coarse-to-Fine Subpixel Registration Method to Recover Local Perspective Deformation in the Application of Image Super-Resolution

In this paper, a coarse-to-fine framework is proposed to register accurately the local regions of interest (ROIs) of images with independent perspective motions by estimating their deformation parameters. A coarse registration approach based on control points (CPs) is presented to obtain the initial perspective parameters. This approach exploits two constraints to solve the problem with a very limited number of CPs. One is named the point-point-line topology constraint, and the other is named the color and intensity distribution of segment constraint. Both of the constraints describe the consistency between the reference and sensed images. To obtain a finer registration, we have converted the perspective deformation into affine deformations in local image patches so that affine refinements can be used readily. Then, the local affine parameters that have been refined are utilized to recover precise perspective parameters of a ROI. Moreover, the location and dimension selections of local image patches are discussed by mathematical demonstrations to avoid the aperture effect. Experiments on simulated data and real-world sequences demonstrate the accuracy and the robustness of the proposed method. The experimental results of image super-resolution are also provided, which show a possible practical application of our method.

Shape “Break-and-Repair” Strategy and Its Application to Automated Medical Image Segmentation

In three-dimensional medical imaging, segmentation of specific anatomy structure is often a preprocessing step for computer-aided detection/diagnosis (CAD) purposes, and its performance has a significant impact on diagnosis of diseases as well as objective quantitative assessment of therapeutic efficacy. However, the existence of various diseases, image noise or artifacts, and individual anatomical variety generally impose a challenge for accurate segmentation of specific structures. To address these problems, a shape analysis strategy termed "break-and-repair" is presented in this study to facilitate automated medical image segmentation. Similar to surface approximation using a limited number of control points, the basic idea is to remove problematic regions and then estimate a smooth and complete surface shape by representing the remaining regions with high fidelity as an implicit function. The innovation of this shape analysis strategy is the capability of solving challenging medical image segmentation problems in a unified framework, regardless of the variability of anatomical structures in question. In our implementation, principal curvature analysis is used to identify and remove the problematic regions and radial basis function (RBF) based implicit surface fitting is used to achieve a closed (or complete) surface boundary. The feasibility and performance of this strategy are demonstrated by applying it to automated segmentation of two completely different anatomical structures depicted on CT examinations, namely human lungs and pulmonary nodules. Our quantitative experiments on a large number of clinical CT examinations collected from different sources demonstrate the accuracy, robustness, and generality of the shape "break-and-repair" strategy in medical image segmentation.

A Facial Expression Parameterization by Elastic Surface Model

We introduce a novel parameterization of facial expressions by using elastic surface model. The elastic surface model has been used as a deformation tool especially for nonrigid organic objects. The parameter of expressions is either retrieved from existing articulated face models or obtained indirectly by manipulating facial muscles. The obtained parameter can be applied on target face models dissimilar to the source model to create novel expressions. Due to the limited number of control points, the animation data created using the parameterization require less storage size without affecting the range of deformation it provides. The proposed method can be utilized in many ways: (1) creating a novel facial expression from scratch, (2) parameterizing existing articulation data, (3) parameterizing indirectly by muscle construction, and (4) providing a new animation data format which requires less storage.