Approximation of a Thin Plate Spline Smoother Using Continuous Piecewise Polynomial Functions

Roberts, Stephen; Hegland, Markus; Altas, Irfan

doi:10.1137/s0036142901383296

Cited by 30 publications

(53 citation statements)

References 15 publications

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“…For example, Roberts et al [54] presented a finite element TPS-based smoother, which combines the favorable properties of finite element surface fitting with the ones of thin plate splines. This method can deal with very large data sets consisting of tens of millions of predictor and response observations.…”

Section: Discussionmentioning

confidence: 99%

A Thin Plate Spline-Based Feature-Preserving Method for Reducing Elevation Points Derived from LiDAR

Chen

Yan

et al. 2015

Remote Sensing

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Light detection and ranging (LiDAR) technique is currently one of the most important tools for collecting elevation points with a high density in the context of digital elevation model (DEM) construction. However, the high density data always leads to serious time and memory consumption problems in data processing. In this paper, we have developed a thin plate spline (TPS)-based feature-preserving (TPS-F) method for LiDAR-derived ground data reduction by selecting a certain amount of significant terrain points and by extracting geomorphological features from the raw dataset to maintain the accuracy of constructed DEMs as high as possible, while maximally keeping terrain features. We employed four study sites with different topographies (i.e., flat, undulating, hilly and mountainous terrains) to analyze the performance of TPS-F for LiDAR data reduction in the context of DEM construction. These results were compared with those of the TPS-based algorithm without features (TPS-W) and two classical data selection methods including maximum z-tolerance (Max-Z) and the random method. Results show that irrespective of terrain characteristic, the OPEN ACCESS Remote Sens. 2015, 7 11345 two versions of TPS-based approaches (i.e., TPS-F and TPS-W) are always more accurate than the classical methods in terms of error range and root means square error. Moreover, in terms of streamline matching rate (SMR), TPS-F has a better ability of preserving geomorphological features, especially for the mountainous terrain. For example, the average SMR of TPS-F is 89.2% in the mountainous area, while those of TPS-W, max-Z and the random method are 56.6%, 34.7% and 35.3%, respectively.

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Section: Discussionmentioning

confidence: 99%

A Thin Plate Spline-Based Feature-Preserving Method for Reducing Elevation Points Derived from LiDAR

Chen

Yan

et al. 2015

Remote Sensing

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“…We compare the error bound (2.5) with the Krawczyk method, the LU decomposition method, the block component verification method and the function verifylss of INTLAB using examples from CUTEr [6], optimal surface fitting [3,10], mixed finite element discretization of Stokes equations [1] and image restoration [5,15].…”

Section: From (24) We Obtainmentioning

confidence: 99%

“…In section 3, we discuss how to compute an upper bound of α efficiently and accurately by taking all possible effects of rounding errors into account. In section 4, we compare our verification method with the Krawczyk method [13], the LU decomposition method [8], verifylss function of INTLAB, and a block component verification method proposed in [2] using examples from CUTEr [6], optimal surface fitting [3,10], mixed finite element discretization of Stokes equations [1] and image restoration [5,15]. Therefore, we find that Hz = 0 with z = (x, 0).…”

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confidence: 99%

Validated Solutions of Saddle Point Linear Systems

Kimura¹,

Chen²

2009

SIAM J. Matrix Anal. & Appl.

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“…The fitted surface should have these same properties to be an accurate virtual representation. The aim of this paper is to compare the effectiveness of constructing virtual leaves through the use of discrete smoothing D 2 -splines [1], the thin plate spline finite element method [17], and the radial basis function Clough-Tocher method [14,15].…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Techniques for the Reconstruction of Leaf Surfaces from Scanned Data

Kempthorne¹,

Turner²,

Belward³

2014

SIAM J. Sci. Comput.

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The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modeling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D 2 -splines [R. Arcangéli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, New York, 2004], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, SIAM J. Numer. Anal., 1 (2003), pp. 208-234], and the radial basis function Clough-Tocher method [M. N. Oqielat, I. W. Turner, and J. A. Belward, Appl. Math. Model., 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D 2 -splines produce reconstructed leaf surfaces which better represent the original physical leaf. 1. Introduction. The application of pesticides, herbicides, and fertilizers is important in agriculture. They provide improved growing conditions for the plants to which they are applied. Recently, studies have been undertaken to model the adhesion and movement of these solutions on the plants [3, 6, 16, 20]. Realistic virtual plant models are developed to model the behavior of these solutions accurately. This fundamental research of leaf surface construction from scattered data is of importance in the context of the larger framework in which the current work resides, where droplet impaction, retention, and deposited droplet behavior are investigated [4].Many known species of plants are able to be distinguished from their leaves alone [18, p. 108]. For this reason, the plant model for a particular species should have a foliage structure appropriate to that species. Furthermore, if the plant model is to be used in future studies for modeling droplet motion on the surface or some other biological process, then a realistic representation of the plant under consideration will provide more reliable results. This can occur only if an accurate and realistic model of the foliage for the particular species is used, as the foliage of the plant performs many vital functions, such as photosynthesis and transpiration [18]. Accurate representations of a leaf surface have been previously considered by Loch and coworkers [11,12], and then this work was developed further by Oqielat and coworkers [14,15,16], using

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Approximation of a Thin Plate Spline Smoother Using Continuous Piecewise Polynomial Functions

Cited by 30 publications

References 15 publications

A Thin Plate Spline-Based Feature-Preserving Method for Reducing Elevation Points Derived from LiDAR

A Thin Plate Spline-Based Feature-Preserving Method for Reducing Elevation Points Derived from LiDAR

Validated Solutions of Saddle Point Linear Systems

A Comparison of Techniques for the Reconstruction of Leaf Surfaces from Scanned Data

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