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Summary:In this paper, I present an interesting processing method of microscopic images. High-pass type filters are generally used for image focusing. They enhance the high spatial frequencies. They are, however, efficient only in cases when the picture is not sharp because of the low contrast on high frequencies (for example in a TV picture). These filters, are not appropriate if the lack of sharpness has been caused by other factors. In this case, it is not possible to construct a three-dimensional model of the observed object. Better results and a three-dimensional model can be obtained by applying the following theory. As part of this paper, an original program based on this theory is described.

A three-dimensional absolute profile parameter was used to characterize the height irregularities of the fracture surfaces of cement pastes. The dependence of these irregularities on porosity was studied and its non-linear character was proved. An analytical form for the detected non-linearity was suggested and then experimentally tested. The surface irregularities manifest scale-invariance properties.

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This paper deals with 3D reconstructions of series of partially focussed images. Some of these methods are known in case of images which were acquired in small field of view (by confocal microscope or CCD camera, e.g.). In this case, recorded images do not differ in any geometrical transformation from each other. In case of larger samples (oversized for microscope or CCD camera), it is necessary to use wider viewing field (standard cameras, e.g.), and taken images primarily differ in scaling but may also differ in shifting and rotation too. These images cannot be used for reconstruction directly; they must be registered; that is, we must determine all transformations which the images differ and eliminate their effects. There are several ways to do this. This paper deals with the registration based on phase correlation. After this registration, it is necessary to identify the sharp parts and to compose a 2D and 3D model. Present methods are very sensitive to noise and their results are not satisfactory in many cases. We introduce a new method for 3D reconstruction which is significantly better.