Smoothing

About: Smoothing is a research topic. Over the lifetime, 36305 publications have been published within this topic receiving 942408 citations.

Smoothing Noisy Data with Spline Functions Estimating the Correct Degree of Smoothing by the Method of Generalized Cross-Validation*

Abstract: Smoothing splines are well known to provide nice curves which smooth discrete, noisy data. We obtain a practical, effective method for estimating the optimum amount of smoothing from the data. Deri...

Shape and motion from image streams under orthography: a factorization method

Abstract: Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step. An image stream can be represented by the 2FxP measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3. Based on this observation, the factorization method uses the singular-value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a partially filled-in measurement matrix that may result from occlusions or tracking failures. The method gives accurate results, and does not introduce smoothing in either shape or motion. We demonstrate this with a series of experiments on laboratory and outdoor image streams, with and without occlusions.

Applied Nonparametric Regression

Abstract: Preface Part I. Regression Smoothing: 1. Introduction 2. Basic idea of smoothing 3. Smoothing techniques Part II. The Kernel Method: 4. How close is the smooth to the true curve? 5. Choosing the smoothing parameter 6. Data sets with outliers 7. Smoothing with correlated data 8. Looking for special features (qualitative smoothing) 9. Incorporating parametric components and alternatives Part III. Smoothing in High Dimensions: 10. Investigating multiple regression by additive models Appendices References List of symbols and notation.

A transformation for ordering multispectral data in terms of image quality with implications for noise removal

Abstract: A transformation known as the maximum noise fraction (MNF) transformation, which always produces new components ordered by image quality, is presented. It can be shown that this transformation is equivalent to principal components transformations when the noise variance is the same in all bands and that it reduces to a multiple linear regression when noise is in one band only. Noise can be effectively removed from multispectral data by transforming to the MNF space, smoothing or rejecting the most noisy components, and then retransforming to the original space. In this way, more intense smoothing can be applied to the MNF components with high noise and low signal content than could be applied to each band of the original data. The MNF transformation requires knowledge of both the signal and noise covariance matrices. Except when the noise is in one band only, the noise covariance matrix needs to be estimated. One procedure for doing this is discussed and examples of cleaned images are presented. >