Topic

# Transformation (function)

About: Transformation (function) is a research topic. Over the lifetime, 18195 publications have been published within this topic receiving 283231 citations. The topic is also known as: transformations.

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TL;DR: In this paper, a framework for efficient IV estimators of random effects models with information in levels which can accommodate predetermined variables is presented. But the authors do not consider models with predetermined variables that have constant correlation with the effects.

Abstract: This article develops a framework for efficient IV estimators of random effects models with information in levels which can accommodate predetermined variables Our formulation clarifies the relationship between the existing estimators and the role of transformations in panel data models We characterize the valid transformations for relevant models and show that optimal estimators are invariant to the transformation used to remove individual effects We present an alternative transformation for models with predetermined instruments which preserves the orthogonality among the errors Finally, we consider models with predetermined variables that have constant correlation with the effects and illustrate their importance with simulations

14,232 citations

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TL;DR: In this article, Lindley et al. make the less restrictive assumption that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the y's.

Abstract: [Read at a RESEARCH METHODS MEETING of the SOCIETY, April 8th, 1964, Professor D. V. LINDLEY in the Chair] SUMMARY In the analysis of data it is often assumed that observations Yl, Y2, *-, Yn are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters 0. In this paper we make the less restrictive assumption that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the y's. Inferences about the transformation and about the parameters of the linear model are made by computing the likelihood function and the relevant posterior distribution. The contributions of normality, homoscedasticity and additivity to the transformation are separated. The relation of the present methods to earlier procedures for finding transformations is discussed. The methods are illustrated with examples.

11,432 citations

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TL;DR: In this article, the authors introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision, and study their application in computer vision.

Abstract: : This reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision. In computer vision, a fundamental problem is to appropriately decompose the domain R of a function g (x,y) of two variables. This problem starts by describing the physical situation which produces images: assume that a three-dimensional world is observed by an eye or camera from some point P and that g1(rho) represents the intensity of the light in this world approaching the point sub 1 from a direction rho. If one has a lens at P focusing this light on a retina or a film-in both cases a plane domain R in which we may introduce coordinates x, y then let g(x,y) be the strength of the light signal striking R at a point with coordinates (x,y); g(x,y) is essentially the same as sub 1 (rho) -possibly after a simple transformation given by the geometry of the imaging syste. The function g(x,y) defined on the plane domain R will be called an image. What sort of function is g? The light reflected off the surfaces Si of various solid objects O sub i visible from P will strike the domain R in various open subsets R sub i. When one object O1 is partially in front of another object O2 as seen from P, but some of object O2 appears as the background to the sides of O1, then the open sets R1 and R2 will have a common boundary (the 'edge' of object O1 in the image defined on R) and one usually expects the image g(x,y) to be discontinuous along this boundary. (JHD)

5,241 citations

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TL;DR: A new approach is proposed which works on range data directly and registers successive views with enough overlapping area to get an accurate transformation between views and is performed by minimizing a functional which does not require point-to-point matches.

Abstract: We study the problem of creating a complete model of a physical object. Although this may be possible using intensity images, we here use images which directly provide access to three dimensional information. The first problem that we need to solve is to find the transformation between the different views. Previous approaches either assume this transformation to be known (which is extremely difficult for a complete model), or compute it with feature matching (which is not accurate enough for integration). In this paper, we propose a new approach which works on range data directly and registers successive views with enough overlapping area to get an accurate transformation between views. This is performed by minimizing a functional which does not require point-to-point matches. We give the details of the registration method and modelling procedure and illustrate them on real range images of complex objects.

2,626 citations

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TL;DR: In this paper, a simple procedure is derived which determines a best rotation of a given vector set into a second vector set by minimizing the weighted sum of squared deviations, which is generalized for any given metric constraint on the transformation.

Abstract: A simple procedure is derived which determines a best rotation of a given vector set into a second vector set by minimizing the weighted sum of squared deviations. The method is generalized for any given metric constraint on the transformation.

2,546 citations