Abstract

Shape-from-Focus (SFF) methods have been developed for about twenty years. They able to obtain the shape of 3D objects from a series of partially focused images. The plane to which the microscope or camera is focused intersects the 3D object in a contour line. Due to wave properties of light and due to finite resolution of the output device, the image can be considered as sharp not only on this contour line, but also in a certain interval of height—the zone of sharpness. SSFs are able to identify these focused parts to compose a fully focused 2D image and to reconstruct a 3D profile of the surface to be observed.

Highlights

  • Three-dimensional reconstruction of general surfaces has an important role in a number of fields: the morphological analysis of fracture surfaces, for example, reveals information on the mechanical properties of natural or construction materials.There are more techniques capable of producing digital three-dimensional (3D) replicas of solid surfaces

  • In addition to the mechanical tools, optical devices exist in diverse modifications [2], light section microscopy [4,5], coherence scanning interferometry [6], speckle metrology [7], stereo projection [8], photogrammetry [9], and various types of light measurement of profiles [10], to mention some of them

  • For instance, can hardly be measured by atomic force microscopes working in the nano-regions

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Summary

Introduction

Three-dimensional reconstruction of general surfaces has an important role in a number of fields: the morphological analysis of fracture surfaces, for example, reveals information on the mechanical properties of natural or construction materials. In addition to the mechanical tools, optical devices exist in diverse modifications [2], light section microscopy [4,5], coherence scanning interferometry [6], speckle metrology [7], stereo projection [8], photogrammetry [9], and various types of light measurement of profiles [10], to mention some of them. These devices are, not of universal use, with each of them having its own technical limitations [14,15]. SSeeee [[2233]] ffoorr oonnee ooff tthhee ffiirrsstt ppaappeerrss oonn tthhiiss ssuubbjjeecctt

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Multifocal Image
Discrete Two-Dimensional Fourier Transform and Inverse Transform
Identical Images
Shifted Images
Rotated Images
Multifocal Registration
Focusing Criteria
Conclusions
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