Improved Accuracy of Area Objects in a Geographic Information System Based on Helmert’s Variance Component Estimation Method

Tong, Xiaohua; Shi, Wenzhong; Liu, Dajie

doi:10.1061/(asce)0733-9453(2009)135:1(19)

Cited by 7 publications

(3 citation statements)

References 13 publications

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“…The coordinates of a key point on the original polyline are denoted as ( x , y ), and we define their expected values using the expectation operator E (Tong et al., 2009). The expectation operator E can be expressed as:

({, \begin{matrix} E ()(, x) goodbreak= x goodbreak+ v_{x} \\ E ()(, y) goodbreak= y goodbreak+ v_{y} \end{matrix})

where

()(,, v_{x}, v_{y})

are the residuals of the coordinates of the point on the lines to be simplified.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Line simplification with sidedness relationship consistency using the constrained total least squares method

Jin,

Zhou,

Song

et al. 2024

Transactions in GIS

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The simplification of lines plays a crucial role in map generalization and multiscale representation; however, addressing inconsistent sidedness relationships between the simplified lines and their neighboring features poses a persistent challenge. In order to preserve correct and consistent sidedness relationships following simplification, this study introduces a novel line simplification method. This method incorporates topological constraints pertaining to left–right sidedness relationships, formulated as an optimization procedure based on the proposed partial total least squares method with constraints. The primary objective is to minimize the positional difference between the line features before and after simplification, with the sidedness relationship represented as an inequality constraint. Moreover, an optimization algorithm is derived to address the simplification problem effectively while adhering to the specified constraints. The proposed method is then applied to simplify the lines within three distinct datasets. Experimental results validate the efficacy of the proposed method in maintaining sidedness consistency across all tested datasets. In comparison to the Douglas–Peucker (DP) method, the proposed method exhibits minimal vertical displacement variance in the line feature points post‐simplification. Additionally, it achieves a smaller overall positional difference between the simplified and original lines compared to the DP method. These findings underscore the superior performance of the proposed method in maintaining sidedness relationships and minimizing positional differences during the line simplification process.

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({, \begin{matrix} E ()(, x) goodbreak= x goodbreak+ v_{x} \\ E ()(, y) goodbreak= y goodbreak+ v_{y} \end{matrix})

where

()(,, v_{x}, v_{y})

are the residuals of the coordinates of the point on the lines to be simplified.…”

Section: Methodsmentioning

confidence: 99%

“…The coordinates of a key point on the original polyline are denoted as (x, y), and we define their expected values using the expectation operator E (Tong et al, 2009). The expectation operator E can be expressed as:…”

Section: Establishmentofthelinearfittingmodelmentioning

confidence: 99%

Line simplification with sidedness relationship consistency using the constrained total least squares method

Jin,

Zhou,

Song

et al. 2024

Transactions in GIS

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show abstract

“…In this paper, an approach for redetermining the weights of measures more accurately is adopted based on Helmert's variance component estimation method. A detailed discussion of weight determinations is presented by Tong et al (2009).…”

Section: A Probability-based Matching Methods By Integrating Multiple mentioning

confidence: 99%

A probability-based multi-measure feature matching method in map conflation

Tong

Shi

Deng

2009

International Journal of Remote Sensing

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This paper presents a probability-based multi-measure feature matching method in map conflation. Feature matching is used to determine the corresponding features in different datasets that represent analogous entities in the real world. In the proposed method, a total matching probability is computed by the weighted average of multiple measures, including positional measure, shape measure, directional measure and topological measure. The matching strategies for point features, linear features and areal features are also provided. The proposed method is implemented in a prototype for matching features from two different data sources, and is compared with traditional methods. The results demonstrate not only the practicability of using the proposed method to resolve feature matching issues in map conflation, but also its advantages compared with traditional methods in terms of matching effects.

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An Improved Weighted Total Least Squares Method with Applications in Linear Fitting and Coordinate Transformation

Tong

Jin

2011

J. Surv. Eng.

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Improved Accuracy of Area Objects in a Geographic Information System Based on Helmert’s Variance Component Estimation Method

Cited by 7 publications

References 13 publications

Line simplification with sidedness relationship consistency using the constrained total least squares method

Line simplification with sidedness relationship consistency using the constrained total least squares method

A probability-based multi-measure feature matching method in map conflation

An Improved Weighted Total Least Squares Method with Applications in Linear Fitting and Coordinate Transformation

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