Publication

Texture mapping by successive refinement

2000
Conference Papers

Abstract

We define texture mapping as an optimization problem for which the goal of preserving the maximum amount of information in the mapped texture. We derive a solution that is optimal in the least-squares sense and that corresponds to the pseudo-inverse of a reverse transformation mapping. In practice, a first order approximation of the least-squares solution is used as an initial estimate for the mapped texture. This initial solution is refined by successive approximation to yield the least-squares optimal result. In essence, the proposed multi-pass method acts like an adaptive anti-aliasing filter.

Official source

https://infoscience.epfl.ch/entities/publication/25ebe901-638c-418f-ac69-2b38f982dabf

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2000
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/25ebe901-638c-418f-ac69-2b38f982dabf

About this result

Related concepts (32)

Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.

Texture mapping

Texture mapping is a method for mapping a texture on a . Texture here can be high frequency detail, surface texture, or color. The original technique was pioneered by Edwin Catmull in 1974. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object).

Linear least squares

Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods. The three main linear least squares formulations are: Ordinary least squares (OLS) is the most common estimator.

Related publications (32)

Texture mapping by successive refinement

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