Mathematical Principles of Object 3D Reconstruction by Shape-from-Focus Methods

Dalibor Martišek and Karel Mikulášek
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Dalibor Martišek: Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, 61669 Brno, Czech Republic
Karel Mikulášek: Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, 61669 Brno, Czech Republic

Mathematics, 2021, vol. 9, issue 18, 1-20

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.

Keywords: 3D reconstruction; shape-from-focus; optical cut; multifocal image; Fourier transform; phase correlation; focusing criteria (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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