Model-Based 2.5-D Deconvolution for Extended Depth of Field in Brightfield Microscopy

Abstract

Abstract-Due to the limited depth of field of brightfield microscopes, it is usually impossible to image thick specimens entirely in focus. By optically sectioning the specimen, the in-focus information at the specimen's surface can be acquired over a range of images. Commonly based on a high-pass criterion, extendeddepth-of-field methods aim at combining the in-focus information from these images into a single image of the texture on the specimen's surface. The topography provided by such methods is usually limited to a map of selected in-focus pixel positions and is inherently discretized along the axial direction, which limits its use for quantitative evaluation. In this paper, we propose a method that jointly estimates the texture and topography of a specimen from a series of brightfield optical sections; it is based on an image formation model that is described by the convolution of a thick specimen model with the microscope's point spread function. The problem is stated as a least-squares minimization where the texture and topography are updated alternately. This method also acts as a deconvolution when the in-focus PSF has a blurring effect, or when the true in-focus position falls in between two optical sections. Comparisons to state-of-the-art algorithms and experimental results demonstrate the potential of the proposed approach.Index Terms-Biomedical image processing, deconvolution, inverse problems, optical transfer functions.

A focus fusion framework with anisotropic depth map smoothing

“…A representative of segmentation-based techniques is the method of Agarwala et al [13]. In particular to evaluate our depth map estimation, we additionaly compare our results to the depth-from-defocus method of Aguet et al [44]. Based on deconvolution, they explicitly model the physical image acquisition process and jointly estimate the sharp image and the depth map.…”

Physically inspired depth-from-defocus

“…However, in the general case of non-constant depth map, the radius changes with the depth of each surface point. Thus, to estimate the intensity of an image point x, Aguet et al [1] weight each neighbouring point u(y) corresponding to its circle of confusion, where a point having a large circle of confusion will get a small weight and vice versa. To achieve this, they introduce a 3-D PSF h : Ω 3 ⊂ R 3 → R 0+ as an approximation of H d :…”

“…In this model, the weight not only depends on the distance of two points like convolution but also on the actual depth value. To take into account the wave character of light, Aguet et al [1] choose a Gaussian PSF instead of a pillbox as already proposed in [28]. Then the standard deviation of the Gaussian replaces the radius of the pillbox.…”

“…A simultaneous multifocus image fusion and denoising approach is proposed by Ludusan and Lavialle in [21]. Embedding the image formation model into a suitable energy functional, and posing depth-from-defocus as a variational minimisation problem is most related to our work [13,19,1]. While the first two approaches suggest Csiszár's information divergence as fidelity term, Aguet et al penalise deviations from the model assumption in a quadratic way.…”

“…Instead of assuming a locally equifocal surface [13] which implies a shift-invariant PSF, Jin et al [19] refrain from such a restriction and embed a shift-variant PSF in their model. Interpreting a shift-variant PSF as a 4-D function and a shift-invariant as a 2-D one, the approach of Aguet et al [1], can be seen as a compromise between both. They propose the use of a 3-D PSF consisting of 2-D normalised Gaussians with varying standard deviation.…”