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Weighted Bidimensional Regression
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DOI：10.1111/j.1538-4632.2010.00805.x.png)
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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.
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