Showing papers by "Trevor Hastie published in 1991"

Statistical Models in S

Abstract: The interactive data analysis and graphics language S (Becker, Chambers and Wilks, 1988) has become a popular environment for both data analysts and research statisticians. A common complaint, however, has concerned the lack of statistical modeling tools, such as those provided by GLIM© or GENSTAT©.

The II P method for estimating multivariate functions from noisy data

Abstract: The Π method for estimating an underlying smooth function of M variables, (x l , …, xm ), using noisy data is based on approximating it by a sum of products of the form Π m φ m (x m ). The problem is then reduced to estimating the univariate functions in the products. A convergent algorithm is described. The method keeps tight control on the degrees of freedom used in the fit. Many examples are given. The quality of fit given by the Π method is excellent. Usually, only a few products are enough to fit even fairly complicated functions. The coding into products of univariate functions allows a relatively understandable interpretation of the multivariate fit.

A model for signature verification

Abstract: The authors propose a statistical model for signature verification by computer. The model recognizes that repeated signatures by the owner are similar but not identical. The model consists of a template signature for each individual, and several factors which allow for variations in each rendition of this template. These variations include the speed of writing, as well as slowly varying affine transformations size as size, rotation and shear. The estimated template represents the mean of a sample of signatures from an individual, and the variations in the factors can be used to establish several measures of variance. These quantitative measures are essential for reliable signature verification. >

3-D curve matching using splines

Abstract: A machine vision algorithm to find the longest common subcurve of two 3-D curves is presented. The curves are represented by splines fitted through sequences of sample points extracted from dense range data. The approximated 3-D curves are transformed into 1-D numerical strings of rotation and translation invariant shape signatures, based on a multiresolution representation of the curvature and torsion values of the space curves. The shape signature strings are matched using an efficient hashing technique that finds longest matching substrings. The results of the string matching stage are later verified by a robust, least-squares, 3-D curve matching technique, which also recovers the Euclidean transformation between the curves being matched. This algorithm is of average complexity O(n) where n is the number of the sample points on the two curves. The algorithm has applications in assembly and object recognition tasks. Results of assembly experiments are included.