Multifocal image processing

Abstract

Abstract. In this paper, we present a processing method for digital images from an optical microscope. High-pass type filters are generally used for image focusing. They enhance the high spatial frequencies. These filters are not appropriate if the lack of sharpness is caused by other factors. On the other hand, the (un)sharpness can be taken as an advantage and can be used for studies of the spatial distribution of structures in the observed scene. In many cases, it is possible to construct a threedimensional model of the observed object by analyzing image sharpness. Interesting two-dimensional images and a three-dimensional model can be obtained by applying the theory for multifocal image processing described in this paper. We improve the quality of the results compared to the previous methods using the Fourier transform for the analysis of local sharpness in the images.

Registration of Partially Focused Images for 2D and 3D Reconstruction of Oversized Samples

“…The entire process of 2D and 3D processing of the series of the partially focused images acquired in central projection thus proceeds as follows: Preprocessing: registration of partially focused images using elementary mathematics (see Figure 6 on the left) simple but usually not precise enough method; or registration using the method proposed in Sections 2.2 – 2.7 in this paper. 2D reconstruction: Identification of sharp parts in separated images and composition of a new whole sharp 2D image (see [ 3 , 4 ]). 3D reconstruction: Height is assigned to all the image points (see [ 1 , 2 , 4 , 10 ]).…”

“…This is an integral transform that transforms a function of one or more variables (in spatial domain) to another function (in frequency domain) of the same number of variables [ 3 , 13 , 14 ]. Since the Fourier transform of a function is in general a function with a complex image and since a digital image is a function of two spatial variables, we will deal here for simplicity with functions f : ℝ 2 → ℂ .…”

“…There are two principal problems in this 2D and 3D reconstruction. The work [ 3 ] deals with methods that detect focused and blurred parts in images taken in nonconfocal mode and are able to assign the corresponding focus plane for each surface point. In this way, construction of 3D stair-approximation of the studied surface is possible (see Figure 2 ).…”

“…In the case of the confocal microscope, we can assume that the field of view is small and the used projection is parallel. The paper [ 4 ] and many other works [ 3 , 5 – 11 ] presume this projection property. In parallel projection, all images are provided in the field of view with the same size.…”

“…This goal has already been met in [ 2 ]; for the result of this new reconstruction see Figure 3 . Some other works [ 3 , 8 , 10 ] also deal with this problem.…”