Close-range photogrammetry is widely used for numerically and graphically representing historical buildings for documentation. Such data can be later used as the base for conservation and restoration processes. The highest precision in point determination in photogrammetry can be achieved using a metric camera, although it is expensive. Recently, many studies have used SLR non-metric cameras, which have the advantage of a self-calibration method and furthermore, are cheaper than the metric camera. In most cases, for close-range photogrammetry applications that use an SLR digital camera, the object is close to the camera (less than 50 m), requiring a wide-angle setting. In our study, the precision achieved is based on a compact camera (Lumix TZ-10) used in building restitution. We experimented with the two extremes in close-range photogrammetry: close object, less than 15 m between the camera lens and to building faç ade; and distant object, up to 200 m between camera lens and building. In both cases, the precision achieved was suitable for the restitution of the historical buildings: under 1 cm for near objects using a 25-mm wide-angle lens and 3 cm for the distant object using a 280-mm telescopic lens. We achieved remarkable precision in the case of the tele lens, where it is unusual to use the focal length for building restitution in close-range photogrammetry. Nevertheless, a tele lens becomes necessary when it is not possible to place the camera near the object, as in the case of the northern faç ade of the Alhambra in Granada, Spain.

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a b s t r a c tThis work is devoted to a generalization of the framework presented in Beam and Warming (2000) [6], where a multiresolution analysis scheme with supercompact multiwavelets was presented. The approach considers uniform partitions of a nested grid hierarchy in the framework of Harten's multi-scale representations. In this paper we study the non-uniform case. The non-uniform analysis is well adapted to more realistic contexts and makes it possible to improve the approximation.

We consider four-point subdivision schemes of the formwith any M that is originally defined as a positive-valued function for positive arguments and is extended to the whole of R 2 by setting M(x, y) :For these schemes, we study analytic properties, such as convexity preservation, convergence, smoothness of the limit function, stability and approximation order, in terms of simple and easily verifiable conditions on M. Fourth-order approximation on intervals of strict convexity is also investigated. All the results known for the most frequently used schemes, the PPH scheme and the power-p schemes, are included as special cases or improved, and extended to more general situations. The various statements are illustrated by two examples and tested by numerial experiments.Communicated by Charles Micchelli.A. Guessab

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