Minimum Distance Function Research Articles

Distance Determination Method for Normally Distributed Obstacle Avoidance of Mobile Robots in Stochastic Environments

Obstacle avoidance methods require knowledge of the distance between a mobile robot and obstacles in the environment. However, in stochastic environments, distance determination is difficult because objects have position uncertainty. The purpose of this paper is to determine the distance between a robot and obstacles represented by probability distributions. Distance determination for obstacle avoidance should consider position uncertainty, computational cost and collision probability. The proposed method considers all of these conditions, unlike conventional methods. It determines the obstacle region using the collision probability density threshold. Furthermore, it defines a minimum distance function to the boundary of the obstacle region with a Lagrange multiplier method. Finally, it computes the distance numerically. Simulations were executed in order to compare the performance of the distance determination methods. Our method demonstrated a faster and more accurate performance than conventional methods. It may help overcome position uncertainty issues pertaining to obstacle avoidance, such as low accuracy sensors, environments with poor visibility or unpredictable obstacle motion.

Minimum Distance Lasso for robust high-dimensional regression

We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. Likelihood-based estimators lack resilience against outliers and model misspecification, a critical issue when dealing with high-dimensional noisy data. Our method, Minimum Distance Lasso (MD-Lasso), combines minimum distance functionals customarily used in nonparametric estimation for robustness, with $\ell_{1}$-regularization. MD-Lasso is governed by a scaling parameter capping the influence of outliers: the loss is locally convex and close to quadratic for small squared residuals, and flattens for squared residuals larger than the scaling parameter. As the parameter approaches infinity the estimator becomes equivalent to least-squares Lasso. MD-Lasso is able to maintain the robustness of minimum distance functionals in sparse high-dimensional regression. The estimator achieves maximum breakdown point and enjoys consistency with fast convergence rates under mild conditions on the model error distribution. These hold for any solution in a convexity region around the true parameter and in certain cases for every solution. We provide an alternative set of results that do not require the solutions to lie within the convexity region but where the $\ell_{2}$-norm of the feasible solutions is constrained within a safety radius. Thanks to this constraint, a first-order optimization method is able to produce local optima that are consistent. A connection is established with re-weighted least-squares that intuitively explains MD-Lasso robustness. The merits of our method are demonstrated through simulation and eQTL analysis.

Internal Ballistic Code for Solid Rocket Motors using Minimum Distance Function for Grain Burnback

A computer code has been developed for internal ballistic performance evaluation of solid rocket motors, using minimum distance function (MDF) approach for prediction of geometry evolution. This method can handle any complex geometry without the need to define different geometrical shapes and their evolution as used in several existing analytical geometry evolution-based methodologies. The code is validated with both experimental results published in literature, as well as for solid rocket motors of tactical and strategic missiles and a very good match is obtained with static test results. The output of the code gives p-t (pressure-time) curve as well as the detailed parameters of the flow along the axial direction, and geometries in the form of mesh file, which can be further used as input to codes for CFD analysis. Defence Science Journal, Vol. 65, No. 3, May 2015, pp.181-188, DOI: http://dx.doi.org/10.14429/dsj.65.8304

Fast recognition of overlapping fruit based on maximum optimisation for apple harvesting robot

In order to improve the recognition speed and accuracy, this study aimed at overlapping apples proposes a positioning method based on the maximum optimisation, for fitting of overlapping circles. Owing to the diversity of apple growth posture, the overlap and shade between the apples will influence the recognition efficiency of apple harvesting robot vision system. Firstly, using the K-means method to segment the captured overlapping apple image under the L*a*b* colour space, lead to the overlapping apple target, and carries on the morphological processing, extracting the outline of the overlapping apple. And then to calculate the minimum distance between the pixels in the circle and the edge of outline, to obtain the minimum distance function, and find the local maximum in these functions, that is the centres of two circles. Finally, the radius is determined by the minimum distance between centres to the edge of the outline and to realise the positioning of overlapping apple, in order to verify the validity of maximum recognition method for the overlapping apples, and comparing with corrosion method and the Hough transform method, using two overlapping images captured by different apple varieties to repeat experiments. The experimental results show that, for the recognition speed and accuracy, the maximum optimisation method is optimal.

Footpoint distance as a measure of distance computation between curves and surfaces

In automotive domain, CAD models and its assemblies are validated for conformance to certain design requirements. Most of these design requirements can be modeled as geometric queries, such as distance to edge, planarity, gap, interference and parallelism. Traditionally these queries are made in discrete domain, such as a faceted model, inducing approximation. Thus, there is a need for modeling and solving these queries in the continuous domain without discretizing the original geometry. In particular, this work presents an approach for distance queries of curves and surfaces, typically represented using NURBS.Typical distance problems that have been solved for curves/surfaces are the minimum distance and the Hausdorff distance. However, the focus in the current work is on computing corresponding portions (patches) between surfaces (or between a curve and a set of surfaces) that satisfy a distance query. Initially, it was shown that the footpoint of the bisector function between two curves can be used as a distance measure between them, establishing points of correspondence. Curve portions that are in correspondence are identified using the antipodal points. It is also identified that the minimum distance in a corresponding pair is bound by the respective antipodal points. Using the established footpoint distance function, the distance between two surfaces was approached. For a query distance, sets of points satisfying the distance measure are identified. The boundary of the surface patch that satisfies the distance is computed using the α-shape in the parametric space of the surface. Islands contributing to the distance query are also then computed. A similar approach is then employed for the distance between a curve and a set of surfaces. Initially, the minimum footpoint distance function for a curve to a surface is computed and repeated for all other surfaces. A lower envelope then gives the portions of the curves where the distance is more than the query.

A Novel Autocalibration of 3-Axis MEMS Accelerometers Based on Improved PSO Algorithm

This paper presents a novel procedure to calibrate the strap-down 3-axis MEMS accelerometers for UAV navigat-ion. Firstly, we establish an explicit calibration model with the measurement values of accelerometers, where the calibration is realized via geometric transformations. Secondly, the transfor-mation parameters are calculated through particle swarm optimization (PSO). For the problem of slower convergence rates near the global optimum, the classical PSO algorithm is improved. Based on the numerical optimization idea, the steepest descent method is introduced to PSO. The parameters are searched in the rough by adopting PSO and the precision ones are found by using steepest descent method. Then, the optimal transformation is achieved by the minimum distance function based on this improved PSO(IPSO) algorithm. Finally, the calibration procedure is tested by comparing the attitude produced by the 3-axis accelerometers with that measured by a turntable. The results show that the IPSO algorithm can significantly improve the performance of the classical PSO algorithm, and the maximum attitude error is reduced to 6% of that before calibration. In addition, the proposed procedure does not rely on prior knowledge of the accelerometers and any equipment. So, it is suitable for calibration in field. Such a method is especially useful in UAV applications.

An Automatic and Robust Algorithm of Reestablishment of Digital Dental Occlusion

In the field of craniomaxillofacial (CMF) surgery, surgical planning can be performed on composite 3-D models that are generated by merging a computerized tomography scan with digital dental models. Digital dental models can be generated by scanning the surfaces of plaster dental models or dental impressions with a high-resolution laser scanner. During the planning process, one of the essential steps is to reestablish the dental occlusion. Unfortunately, this task is time-consuming and often inaccurate. This paper presents a new approach to automatically and efficiently reestablish dental occlusion. It includes two steps. The first step is to initially position the models based on dental curves and a point matching technique. The second step is to reposition the models to the final desired occlusion based on iterative surface-based minimum distance mapping with collision constraints. With linearization of rotation matrix, the alignment is modeled by solving quadratic programming. The simulation was completed on 12 sets of digital dental models. Two sets of dental models were partially edentulous, and another two sets have first premolar extractions for orthodontic treatment. Two validation methods were applied to the articulated models. The results show that using our method, the dental models can be successfully articulated with a small degree of deviations from the occlusion achieved with the gold-standard method.

Automated digital dental articulation.

Articulating digital dental models is often inaccurate and very time-consuming. This paper presents an automated approach to efficiently articulate digital dental models to maximum intercuspation (MI). There are two steps in our method. The first step is to position the models to an initial position based on dental curves and a point matching algorithm. The second step is to finally position the models to the MI position based on our novel approach of using iterative surface-based minimum distance mapping with collision constraints. Finally, our method was validated using 12 sets of digital dental models. The results showed that using our method the digital dental models can be accurately and effectively articulated to MI position.

An overdetermined geodetic boundary value problem approach to telluroid and quasi-geoid computations

In this paper an overdetermined Geodetic Boundary Value Problem (GBVP) approach for telluroid and quasi-geoid computations is presented. The presented GBVP approach can solve the problem of potential value computation on the surface of the Earth, which when applied to a mapping scheme, e.g., here minimum distance mapping, provides a point-wise approach to telluroid computation. Besides, we have succeeded in reducing the number of equations and unknowns of the minimum distance telluroid mapping by one. The sufficient condition of minimum distance telluroid mapping is also recapitulated. Since the introduced GBVP approach has the advantage of implementing various gravity observables simultaneously as input boundary data, it can be regarded as a data fusion technique that exploits all available gravity data. The developed GBVP is used for the computation of the quasi-geoid within a test area in Southwest Finland.

SU-FF-T-23: Analysis of Dosimetric Quantities Associated with Partial Breast Brachytherapy

Purpose: Radiation dose to the heart and lung are a concern in accelerated partial breast irradiation (APBI). This work presents an analysis of the metrics inherent to high dose rate APBI using a brachytherapy source. Method and Materials: Five patients receiving APBI brachytherapy, and 4 patients, who were simulated in both supine and prone position for XRT, were contoured. Dose to the heart and lung were calculated for all potential dwell locations within the contoured breast for a range of potential dwell times. Summary volume and dose metrics were calculated for heart and lung as function of minimum distance (dmin) to the normal structures. The distribution of minimum distances was then compared for the prone and supine patients. Results: Dose metrics such as the D10cc were patient specific and not well suited to parameterization. Volume metrics such as V10Gy tend to have similar behavior and may be characterized as a function of dmin. The characterization provides a measure of the normal tissue dose parameters that are achievable as a function of dmin. While prone position shift the distribution of lung to breast distances towards greater value, the distribution of heart to breast distances is shifted to smaller distances. Conclusion: Characteristic curves of the achievable volume metrics as a function of minimum distance from implant to normal structures are presented. These curves may be helpful in the decision to use APBI brachytherapy based on the location of the cavity. The choice of treatment position affects the distribution of breast tissue, though the effect on distance to heart and lung differs.

Neutron transfers at low-energy collisions of nonspherical nuclei

A semiclassical model is used to analyze the evolution of the valence-neutron wave function at a collision between a spherical 48Ca nucleus and a deformed 248Cm nucleus with near-Coulomb-barrier energies. The probabilities of neutron transfers are determined as a function of minimum internuclear distance.

Solid Rocket Motor Internal Ballistics Simulation Using Three-Dimensional Grain Burnback

Internal ballistics simulations of solid rocket motors have been conducted with the propellant grain's 3-D burning surface geometry described by a new minimum distance function approach and the internal flowfield represented by 1-D, time-dependent, single-phase compressible flow equations. The combustion model includes erosive burning and unsteady, dynamic burning corresponding to transient energy storage in the heated surface layer of the propellant. The integrated internal ballistics code (Rocballist) is used to investigate the role of these two burning rate augmenting mechanisms in solid rocket motor performance. Two tactical motors are used as test cases. Results indicate that dynamic burning can be the dominant factor in producing a short-duration ignition pressure spike in low-L* motors, particularly if the L/D ratio is not too large and the port cross section is nonrestrictive (e.g., center perforated grain). However, when L/D is large and the port cross section is noncircular in the aft section (aft fins/slots), erosive burning can take over in dominating the burning rate to the extent that an otherwise progressive pressure-time trace becomes regressive/neutral. That is, erosive burning can effectively prolong the initial pressure spike in some star-aft motors. The results also show that with sufficiently accurate models of dynamic burning and erosive burning, it is reasonable to expect reliable internal ballistics predictions with suitable simplified flowfield models, thereby realizing significant reductions in computation time compared with 3-D, multiphase reacting flow simulations.

Solid Propellant Grain Design and Burnback Simulation Using a Minimum Distance Function

DOI: 10.2514/1.22937 A fast computational method for simulating the evolution of the burning surface of a complex, three-dimensional solid rocket motor propellant grain has been developed using a signed minimum distance function. The minimum distance function is calculated using stereo-lithography surface information from a computer-aided-design file and propellant surface burnback is simulated by manipulation of the initial minimum distance function. Variable time steppingandmultiplespatialgridsfurtherreducecomputationtimerequirements. Resultsindicatethatthismethod gives adequate accuracy with acceptable computation time for time scales of the full motor burn. The resulting code (Rocgrain) allows for motor grain design by user-friendly commercial computer-aided-design programs and for coupling with internal flow codes. This enables a single geometric tool to be used for describing the propellant grain geometry for both grain design and internal flowfield analysis. The Rocgrain code can be coupled with a variety of flowfield codes ranging in complexity from simple zero-dimensional to more sophisticated computational fluid dynamics analysis (e.g., nonlinear acoustic instability).

Minimum distance mapping using three-dimensional optical coherence tomography for glaucoma diagnosis

Objective imaging of the optic nerve structure has become central to the management of patients with glaucoma. There is an urgent need in diagnosis and staging for reliable objective precursors and markers. Three-dimensional ultrahigh-resolution frequency domain optical coherence tomography (3D UHR OCT) holds particular promise in this respect since it enables volumetric assessment of intraretinal layers including tomographic data for the retinal nerve fiber layer (RNFL) and optic nerve head. The integrated analysis of this information and the resolution advantage has enabled the development of more informative indices of axonal damage in glaucoma compared with measurements of RNFL thickness and cup-to-disc ratio provided by commercial OCT devices. The potential for UHR OCT in enabling the combined analysis of tomographic and volumetric data on retinal structure is explored. A novel parameter was developed; the three-dimensional minimal distance as the optical correlate of true retinal nerve fiber layer thickness around the optic nerve head region. For the purposes of this pilot study, we present data from a normal subject and from two patients with characteristic optic nerve and retinal nerve fiber layer changes secondary to glaucoma.

Upper bounds on the rate of LDPC codes as a function of minimum distance

New upper bounds on the rate of low-density parity-check (LDPC) codes as a function of the minimum distance of the code are derived. The bounds apply to regular LDPC codes, and sometimes also to right-regular LDPC codes. Their derivation is based on combinatorial arguments and linear programming. The new bounds improve upon the previous bounds due to Burshtein et al. It is proved that at least for high rates, regular LDPC codes with full-rank parity-check matrices have worse relative minimum distance than the one guaranteed by the Gilbert-Varshamov bound.

Multi-sensor image registration using multi-resolution shape analysis

Multi-sensor image registration has been widely used in remote sensing and medical image field, but registration performance is degenerated when heterogeneous images are involved. An image registration method based on multi-resolution shape analysis is proposed in this paper, to deal with the problem that the shape of similar objects is always invariant. The contours of shapes are first detected as visual features using an extended contour search algorithm in order to reduce effects of noise, and the multi-resolution shape descriptor is constructed through Fourier curvature representation of the contour’s chain code. Then a minimum distance function is used to judge the similarity between two contours. To avoid the effect of different resolution and intensity distribution, suitable resolution of each image is selected by maximizing the consistency of its pyramid shapes. Finally, the transformation parameters are estimated based on the matched control-point pairs which are the centers of gravity of the closed contours. Multi-sensor Landsat TM imagery and infrared imagery have been used as experimental data for comparison with the classical contour-based registration. Our results have been shown to be superior to the classical ones.

Autolabeling 3D tracks using neural networks

Motion capturing systems based on monochrome video have problems assigning measured 3D marker positions to the anatomically defined positions or labels of the markers applied to the test subject. This task is usually called “labelling” and is paramount to the reconstruction of 3D trajectories from a set of video frames from multiple cameras––the tracking procedure. Labelling means sorting a set of 3D vectors by their spatial positions. Neural networks can be made to “learn” from examples of marker positions in a given marker set, i.e. previously manually tracked video sequences. Trained neural networks are able to calculate a set of sorted approximate marker positions from an unsorted set of exact marker positions. The set of sorted exact positions can be found by pairing up both sets of marker positions via a minimum distance function. The neural network is trained only once and can then be applied to any number of individuals. The algorithm is designed for cyclic motions like for locomotion analysis.

Robust joint estimation of location and scale parameters in ranked set samples

A robust estimator is developed for the location and scale parameters of a location-scale family. The estimator is defined as the minimizer of a minimum distance function that measures the distance between the ranked set sample empirical cumulative distribution function and a possibly misspecified target model. We show that the estimator is asymptotically normal, robust, and has high efficiency with respect to its competitors in literature. It is also shown that the location estimator is consistent within the class of all symmetric distributions whereas the scale estimator is Fisher consistent at the true target model. The paper also considers an optimal allocation procedure that does not introduce any bias due to judgment error classification. It is shown that this allocation procedure is equivalent to Neyman allocation. A numerical efficiency comparison is provided.

Efficient determination of multiple regularization parameters in a generalizedL-curve framework

The selection of multiple regularization parameters is considered in a generalizedL-curve framework. Multiple-dimensional extensions of the L-curve for selectingmultiple regularization parameters are introduced, and a minimum distancefunction (MDF) is developed for approximating the regularization parameterscorresponding to the generalized corner of the L-hypersurface. For thesingle-parameter (i.e. L-curve) case, it is shown through a model that theregularization parameters minimizing the MDF essentially maximize the curvatureof the L-curve. Furthermore, for both the single-and multiple-parameter cases theMDF approach leads to a simple fixed-point iterative algorithm for computingregularization parameters. Examples indicate that the algorithm convergesrapidly thereby making the problem of computing parameters according tothe generalized corner of the L-hypersurface computationally tractable.

Molodensky potential telluroid based on a minimum-distance map. Case study: the quasi-geoid of East Germany in the World Geodetic Datum 2000

A potential-type Molodensky telluroid based upon a minimum-distance mapping is derived. With respect to a reference potential of Somigliana–Pizzetti type which relates to the World Geodetic Datum 2000, it is shown that a point-wise minimum-distance mapping of the topographical surface of the Earth onto the telluroid surface, constrained to the gauge W(P)=u(p), leads to a system of four nonlinear normal equations. These normal equations are solved by a fast Newton–Raphson iteration.