Analysis of landmark data using multidimensional regression
Kendra K. Schmid · Lincoln (University of Nebraska) · 2007
Shape analysis is useful for a wide variety of disciplines and has many applications. There are many different approaches to shape analysis, one of which focuses on the analysis of shapes that are represented by predefined landmarks on the object. This dissertation consists of three papers written on the analysis of landmark data. The first paper introduces Tridimensional Regression, a technique that can be used for mapping images and shapes that are represented by sets of three-dimensional landmark coordinates. The degree of similarity between shapes can be quantified using the tridimensional coefficient of determination ( R2). An experiment was conducted to evaluate the effectiveness of this technique to correctly match the image of a face with another image of the same face. These results were compared to the R 2 values obtained when only two dimensions are used, and show using three dimensions increases the ability to correctly discriminate between faces. In many shape or image matching applications, it is only feasible to obtain two-dimensional data for analysis. Some landmarks may be measured with greater precision than others, or some landmarks may be more important to the analysis than others. The second paper presents a method for dealing with these situations. Weighted Bidimensional Regression is introduced as a method for including this important information in the analysis of two-dimensional landmark data. One possible weighting scheme is suggested, and the effect of weighting on the ability to correctly match two faces is investigated. Results indicate that appropriate weighting increases the ability to correctly match two faces, and that weighting has the largest effect when used with the projective transformation. The third paper analyzes the role of face geometry in determining how attractive a face is perceived to be. Adherence to Neoclassical Canons, the Golden Ratio, and face symmetry are investigated as predictors of attractiveness. These measures are used to develop a model for predicting the attractiveness of a given face and to determine which features are most related to attractiveness.