Adaptive discrete thin plate spline smoother

The discrete thin plate spline smoother fits smooth surfaces to large data sets efficiently. It combines the favourable properties of the finite element surface fitting and thin plate splines. The efficiency of its finite element grid is improved by adaptive refinement, which adapts the precision of the solution. It reduces computational costs by refining only in sensitive regions, which are identified using error indicators. While many error indicators have been developed for the finite element method, they may not work for the discrete smoother. In this article we show three error indicators adapted from the finite element method for the discrete smoother. A numerical experiment is provided to evaluate their performance in producing efficient finite element grids. References F. L. Bookstein. Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Trans. Pat. Anal. Mach. Int. 11.6 (1989), pp. 567–585. doi: 10.1109/34.24792. C. Chen and Y. Li. A robust method of thin plate spline and its application to DEM construction. Comput. Geosci. 48 (2012), pp. 9–16. doi: 10.1016/j.cageo.2012.05.018. L. Fang. Error estimation and adaptive refinement of finite element thin plate spline. PhD thesis. The Australian National University. http://hdl.handle.net/1885/237742. L. Fang. Error indicators and adaptive refinement of the discrete thin plate spline smoother. ANZIAM J. 60 (2018), pp. 33–51. doi: 10.21914/anziamj.v60i0.14061. M. F. Hutchinson. A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines. Commun. Stat. Simul. Comput. 19.2 (1990), pp. 433–450. doi: 10.1080/0361091900881286. W. F. Mitchell. A comparison of adaptive refinement techniques for elliptic problems. ACM Trans. Math. Soft. 15.4 (1989), pp. 326–347. doi: 10.1145/76909.76912. R. F. Reiniger and C. K. Ross. A method of interpolation with application to oceanographic data. Deep Sea Res. Oceanographic Abs. 15.2 (1968), pp. 185–193. doi: 10.1016/0011-7471(68)90040-5. S. Roberts, M. Hegland, and I. Altas. Approximation of a thin plate spline smoother using continuous piecewise polynomial functions. SIAM J. Numer. Anal. 41.1 (2003), pp. 208–234. doi: 10.1137/S0036142901383296. D. Ruprecht and H. Muller. Image warping with scattered data interpolation. IEEE Comput. Graphics Appl. 15.2 (1995), pp. 37–43. doi: 10.1109/38.365004. E. G. Sewell. Analysis of a finite element method. Springer, 2012. doi: 10.1007/978-1-4684-6331-6. L. Stals. Efficient solution techniques for a finite element thin plate spline formulation. J. Sci. Comput. 63.2 (2015), pp. 374–409. doi: 10.1007/s10915-014-9898-x. O. C. Zienkiewicz and J. Z. Zhu. A simple error estimator and adaptive procedure for practical engineerng analysis. Int. J. Numer. Meth. Eng. 24.2 (1987), pp. 337–357. doi: 10.1002/nme.1620240206.

Predictive Thin Plate Spline Model for Estimation of Load Carriage at Varying Gradient and Speed

Laboratory-based experimental studies are being carried out for Indian soldiers to estimate optimal load carriage at different gradients and walking speeds. These experiments involve the recording of Cardio-respiratory responses such as Heart Rate (HR), Oxygen Consumption (VO2), Energy Expenditure (EE), Respiratory Frequency (RF), Minute Ventilation (VE), and Maximal Aerobic capacity (%VO2max). Due to limitations in the data sample size that can be obtained in laboratory-based experiments, there is a need for mathematical interpolation to obtain intermediate values in the study. Load carriage can be affected by factors that can be controlled, such as the speed of marching, and also by external factors that cannot be controlled like ambient temperature. Real-time interactions of all the factors also have an impact on the load-carrying capacity. Planning of the mission operations requires the specification of well-defined work-rest schedules and indication of total load limits, to ensure the operational effectiveness of the military personnel. In this paper, we present a Predictive 3-Dimensional Thin Plate Spline Model for efficient estimation of load. We developed a Multiple Linear Regression Model for predicting %VO2max for combinations of load and gradient. The accuracy of the model was 85 per cent and the maximum permissible loads were derived from the prediction model for the physiological limits of 50 per cent, 60 per cent, and 75 per cent of VO2max. A Thin Plate Spline based interpolation technique was used on this Multiple Linear Regression Model to generate optimal load at intermediate values for the experimental study. A similar predictive Interpolation Model was also developed for estimating load for varying walking speeds at level ground.

Shepard operator of least squares thin-plate spline type

"We obtain some new Shepard type operators based on the classical, the modi ed Shepard methods and the least squares thin-plate spline function. Given some sets of points, we compute some representative subsets of knot points following an algorithm described by J. R. McMahon in 1986."

МАПИРАЊЕ ТЕКСТУРЕ ЛИЦА ГЕНЕРИСАНЕ ПАМЕТНИМ ТЕЛЕФОНОМ НА ГЕНЕРИЧКИ МОДЕЛ ЛИЦА

Представљено је једноставно и универзално решење, које задовољава потребе корисника а ниво квалитета одговара уређају на ком се приказује, тј. паметном телефону. Основна идеја је могућност брзог креирања персонализованог анимираног аватара који би се користио на друштвеним мрежама, виртуелним конференцијама и слично. Користе се већ готови, усредњени модели главе, са добром топологијом, као и постављеним скелетом. Персонализација модела врши се помоћу текстуре, те она мора бити довољно уверљива. Текстура се добија употребом камере на мобилном телефону. Мапирање слике на модел врши се препознавањем значајних тачака лица помоћу Dlib библиотеке. Кључни алгоритам у овом раду је тзв. Thin Plate Spline алгоритам.

Intraspecific phenotype variations in olive barb Systomus sarana (Hamilton, 1822) population from different rivers is possibly linked to locomotive adaptations in caudal fin

Systomus sarana (Hamilton, 1822) [D1] is an economically important food fish species occurring throughout Indian rivers, which also has ornamental value. This study focused on morphological variations in S. sarana from five river basins across India, viz., Godavari, Mahanadi, Krishna, Middle Ganga and Lower Ganga. A truss network was constructed by interconnecting 12 landmarks to generate 65 morphometric variables extracted from digital images of specimens sampled from the study locations. Transformed truss measurements were subjected to Principal component analysis (PCA), Canonical discriminant function analysis (CDFA), Box plot and Thin plate spline (TPS) analyses. PCA identified eight truss variables with significant loadings, while CDFA designated two truss variables with potential for explaining discrimination between populations. Anterior attachment of dorsal membrane from caudal fin was identified to be the most important variable that presented variations across the river basins studied. Discriminant analysis correctly classified 70.5% of the specimens into their original populations. Thin plate spline for morphometric shape variation analysis indicated highest specimen-shape variations (warping) in Mahanadi basin. TPS-principal strain ratio on principal components (PC-1, PC-2) further revealed significant divergence among the populations in five river basins studied. Results of the study revealed variation in stocks of the species, on the basis of shape morphometry. The four significant parameters, differentiating specimens from different basins, were linked to caudal fin origin at dorsal side and the centre and possibly indicate plasticity in response to locomotive adaptations.

TERRAIN-ADAPTIVE GROUND FILTERING OF AIRBORNE LIDAR DATA BASED ON SALIENCY-AWARE THIN PLATE SPLINE

Ground filtering separates the ground and non-ground points from point clouds, which is the essential process for DEM generation, semantic segmentation, model reconstruction and so forth. Considering the topologically complex terrain environments, the segmentation results are prone to be disturbed dealing with steep slopes, buildings, bridges, cliffs, etc. from Airborne LiDAR point clouds. In this paper, a saliency-aware Thin-Plate-Spline (SATPS) interpolation method is proposed including two steps: saliency division and adaptive regularized TPS interpolation with relative variance coefficient. Firstly, the point clouds are indexed in 2D grids and segments are clustered step probing toward 8-adjacent scanning directions. Then, the saliency of each grid is calculated according to the elevation variance of adjacent segments towards each scanning direction. Subsequently, grids of high ground saliency are considered as candidates for seed point selection and then clustered by region growing. The TPS surface is interpolated for each cluster loosely fitting to the seed points involving an adaptive relative variance coefficient which is according to ground saliency and elevation deviation. And finally, the ground points are extracted around the TPS surface. Experimental results indicate that the proposed SATPS algorithm achieves better Type 1 accuracy and total accuracy than the state-of-the-art algorithms in scenes with complex terrain structures, which is practical to generate DEM products.