Directional Statistics and Shape Analysis-英文文献.pdfVIP

Directional Statistics and Shap e Analysis by KV Mardia Department of Statistics University of Leeds Leeds LS JT UK Abstract There have b een various developments in shap e analysis in the last decade We describ e here some relationships of shap e analysis with directional statistics For shap e rotations are to b e integrated out or to b e optimized over whilst they are the basis for directional statistics However various concepts are connected In particular certain distributions of directional statistics have emerged in shap e analysis such a distribution is Complex Bingham Distribution This pap er rst gives some background to shap e analysis and then it go es on to directional distributions and their applications to shap e analysis Note that the idea of using tangent space for analysis is common to b oth manifold as well Intro duction Consider shap es of congurations of p oints in Euclidean space There are various contexts in m which k lab elled p oints or landmarks x x k in IR are given and interest is in the shap e of x x k Example The microscopic fossil Globorotalia truncatulinoides is shap ed rather like a snail For each of such fossils three landmarks are given in Fig Do the triangles given by these landmarks tend to b e almost equilateral Insert Fig Example Given a set of a mouse vertebrae b ones T with six landmarks see Fig the question arises for comparison purp oses what is the sample mean shap e How to measure its variation Insert Fig Example Given unlab elle