Kernel density estimation on the rotation group and its application to crystallographic texture analysis

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Kernel density estimation on the rotation group and its application to crystallographic texture analysis

We are concerned with kernel density estimation on the rotation group SO(3). We prove asymptotically optimal convergence rates for the minimax risk of the mean integrated squared error for different function classes including bandlimited functions, functions with bounded Sobolev norm and functions with polynomial decaying Fourier coefficients and give optimal kernel functions. Furthermore, we c...

متن کامل

Fast Estimation of Nonparametric Kernel Density Through PDDP, and its Application in Texture Synthesis

In thiswork, anewalgorithm isproposed for fast estimationofnonparametricmultivariate kernel density, based on principal direction divisive partitioning (PDDP) of the data space.The goal of the proposed algorithm is to use the finite support property of kernels for fast estimation of density. Compared to earlier approaches, this work explains the need of using boundaries (for partitioning the sp...

متن کامل

Kernel Density Estimation: Theory and Application in Discriminant Analysis

Nowadays, one can find a huge set of methods to estimate the density function of a random variable nonparametrically. Since the first version of the most elementary nonparametric density estimator (the histogram) researchers produced a vast amount of ideas especially corresponding to the issue of choosing the bandwidth parameter in a kernel density estimator model. To focus not only on a descri...

متن کامل

Density Estimation on the rotation group using Diffusive wavelets

This paper considers the problem of estimating probability density functions on the rotation group SO(3). Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel. Expressions are derived for their Mean Integrated Squared Errors. The performance of the estimators is studied numerically and compared with the performance of an exi...

متن کامل

Nonparametric density estimation on the rotation group . Supervisors :

In many applications, the collected data takes values in a manifold rather than in an Euclidian space. Numerous examples of such datasets can be found in the fields of robotics, satellite control attitude, chemistry, crystallography [1]. In statistics, many applications have lead to the study of datasets on spheres or oriented frames [2] as well as on special matrix manifolds (Grassmann and Sti...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Multivariate Analysis

سال: 2013

ISSN: 0047-259X

DOI: 10.1016/j.jmva.2013.03.014