1 Citation (Scopus)

Abstract

Shape analysis is useful for a wide variety of disciplines and has many applications. One of the many approaches to shape analysis focuses on shapes that are represented by predefined landmarks on an object. Some landmarks may be measured with greater precision, exhibit more natural variation, or be more important than others to an analysis. This article introduces a method for including this information when estimating mapping relations or assessing the degree of similarity between two objects that are represented by a set of two-dimensional landmarks. Weighted bidimensional regression combines aspects of weighted least squares regression and bidimensional regression as a way to weight variables that are represented by a set of two-dimensional spatial coordinates. One possible weighting scheme is suggested, and the effect of weighting is demonstrated through a face-matching application. Results indicate that appropriate weighting increases the ability to correctly match two faces and that weighting has the largest effect when used with a projective transformation.

Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalGeographical Analysis
Volume43
Issue number1
DOIs
StatePublished - Jan 1 2011

Fingerprint

shape analysis
weighting
regression
effect
ability
analysis
method

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Earth-Surface Processes

Cite this

Weighted Bidimensional Regression. / Schmid, Kendra K; Marx, David B.; Samal, Ashok K.

In: Geographical Analysis, Vol. 43, No. 1, 01.01.2011, p. 1-13.

Research output: Contribution to journalArticle

Schmid, Kendra K ; Marx, David B. ; Samal, Ashok K. / Weighted Bidimensional Regression. In: Geographical Analysis. 2011 ; Vol. 43, No. 1. pp. 1-13.
@article{81f48cbaf41e4aa5919d3094ae307842,
title = "Weighted Bidimensional Regression",
abstract = "Shape analysis is useful for a wide variety of disciplines and has many applications. One of the many approaches to shape analysis focuses on shapes that are represented by predefined landmarks on an object. Some landmarks may be measured with greater precision, exhibit more natural variation, or be more important than others to an analysis. This article introduces a method for including this information when estimating mapping relations or assessing the degree of similarity between two objects that are represented by a set of two-dimensional landmarks. Weighted bidimensional regression combines aspects of weighted least squares regression and bidimensional regression as a way to weight variables that are represented by a set of two-dimensional spatial coordinates. One possible weighting scheme is suggested, and the effect of weighting is demonstrated through a face-matching application. Results indicate that appropriate weighting increases the ability to correctly match two faces and that weighting has the largest effect when used with a projective transformation.",
author = "Schmid, {Kendra K} and Marx, {David B.} and Samal, {Ashok K}",
year = "2011",
month = "1",
day = "1",
doi = "10.1111/j.1538-4632.2010.00805.x",
language = "English (US)",
volume = "43",
pages = "1--13",
journal = "Geographical Analysis",
issn = "0016-7363",
publisher = "Wiley-Blackwell",
number = "1",

}

TY - JOUR

T1 - Weighted Bidimensional Regression

AU - Schmid, Kendra K

AU - Marx, David B.

AU - Samal, Ashok K

PY - 2011/1/1

Y1 - 2011/1/1

N2 - Shape analysis is useful for a wide variety of disciplines and has many applications. One of the many approaches to shape analysis focuses on shapes that are represented by predefined landmarks on an object. Some landmarks may be measured with greater precision, exhibit more natural variation, or be more important than others to an analysis. This article introduces a method for including this information when estimating mapping relations or assessing the degree of similarity between two objects that are represented by a set of two-dimensional landmarks. Weighted bidimensional regression combines aspects of weighted least squares regression and bidimensional regression as a way to weight variables that are represented by a set of two-dimensional spatial coordinates. One possible weighting scheme is suggested, and the effect of weighting is demonstrated through a face-matching application. Results indicate that appropriate weighting increases the ability to correctly match two faces and that weighting has the largest effect when used with a projective transformation.

AB - Shape analysis is useful for a wide variety of disciplines and has many applications. One of the many approaches to shape analysis focuses on shapes that are represented by predefined landmarks on an object. Some landmarks may be measured with greater precision, exhibit more natural variation, or be more important than others to an analysis. This article introduces a method for including this information when estimating mapping relations or assessing the degree of similarity between two objects that are represented by a set of two-dimensional landmarks. Weighted bidimensional regression combines aspects of weighted least squares regression and bidimensional regression as a way to weight variables that are represented by a set of two-dimensional spatial coordinates. One possible weighting scheme is suggested, and the effect of weighting is demonstrated through a face-matching application. Results indicate that appropriate weighting increases the ability to correctly match two faces and that weighting has the largest effect when used with a projective transformation.

UR - http://www.scopus.com/inward/record.url?scp=78650779865&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650779865&partnerID=8YFLogxK

U2 - 10.1111/j.1538-4632.2010.00805.x

DO - 10.1111/j.1538-4632.2010.00805.x

M3 - Article

AN - SCOPUS:78650779865

VL - 43

SP - 1

EP - 13

JO - Geographical Analysis

JF - Geographical Analysis

SN - 0016-7363

IS - 1

ER -