Jan Michálek

Compensation of inhomogeneous fluorescence signal distribution in 2D images acquired by confocal microscopy

In images acquired by confocal laser scanning microscopy (CLSM), regions corresponding to the same concentration of fluorophores in the specimen should be mapped to the same grayscale levels. However, in practice, due to multiple distortion effects, CLSM images of even homogeneous specimen regions suffer from irregular brightness variations, e.g., darkening of image edges and lightening of the center. The effects are yet more pronounced in images of real biological specimens. A spatially varying grayscale map complicates image postprocessing, e.g., in alignment of overlapping regions of two images and in 3D reconstructions, since measures of similarity usually assume a spatially independent grayscale map. We present a fast correction method based on estimating a spatially variable illumination gain, and multiplying acquired CLSM images by the inverse of the estimated gain. The method does not require any special calibration of reference images since the gain estimate is extracted from the CLSM image being corrected itself. The proposed approach exploits two types of morphological filters: the median filter and the upper Lipschitz cover. The presented correction method, tested on images of both artificial (homogeneous fluorescent layer) and real biological specimens, namely sections of a rat embryo and a rat brain, proved to be very fast and yielded a significant visual improvement. Microsc. Res. Tech., 2011.

Artifact-free 3D Reconstruction for Optical Projection Tomography.

Optical Projection Tomography (OPT) is a recently developed implementation of computed tomography (CT) techniques at optical frequencies. A series of 2D optical projections through a sample are generated at varying orientations, from which the 3D structure of the sample can be computationally reconstructed. OPT is especially suitable for samples from about 0.5 mm to 15 mm in size, which fills an important “imaging gap” between techniques such as confocal microscopy (useful for smaller samples) and large-sample methods such as fluorescence molecular tomography (FMT), x-ray CT or microscopic magnetic resonance imaging (μΜRI). OPT can function in both fluorescence and transmission modes.

Nonrigid registration of CLSM images of physical sections with discontinuous deformations.

When biological specimens are cut into physical sections for three-dimensional (3D) imaging by confocal laser scanning microscopy, the slices may get distorted or ruptured. For subsequent 3D reconstruction, images from different physical sections need to be spatially aligned by optimization of a function composed of a data fidelity term evaluating similarity between the reference and target images, and a regularization term enforcing transformation smoothness. A regularization term evaluating the total variation (TV), which enables the registration algorithm to account for discontinuities in slice deformation (ruptures), while enforcing smoothness on continuously deformed regions, was proposed previously. The function with TV regularization was optimized using a graph-cut (GC) based iterative solution. However, GC may generate visible registration artifacts, which impair the 3D reconstruction. We present an alternative, multilabel TV optimization algorithm, which in the examined samples prevents the artifacts produced by GC. The algorithm is slower than GC but can be sped up several times when implemented in a multiprocessor computing environment. For image pairs with uneven brightness distribution, we introduce a reformulation of the TV-based registration, in which intensity-based data terms are replaced by comparison of salient features in the reference and target images quantified by local image entropies.

Matching of irreversibly deformed images in microscopy based on piecewise monotone subgradient optimization using parallel processing

Image registration tasks are often formulated in terms of minimization of a functional consisting of a data fidelity term penalizing the mismatch between the reference and the target image, and a term enforcing smoothness of shift between neighboring pairs of pixels (a min-sum problem). For registration of neighboring physical slices of microscopy specimens with discontinuities, Janacek [1] proposed earlier an L1-distance data fidelity term and a total variation (TV) smoothness term, and used a graph-cut based iterative steepest descent algorithm for minimization. The L1-TV functional is in general non-convex, and thus a steepest descent algorithm is not guaranteed to converge to the global minimum. Schlesinger et. aI. [10] presented an equivalent transformation of max-sum problems to the problem of minimizing a dual quantity called problem power, which is - contrary to the original max-sum (min-sum) functional - convex (concave). We applied Schlesingers approach to develop an alternative, multi-label, L1-TV minimization algorithm by maximization of the dual problem. We compared experimentally results obtained by the multi-label dual solution with a graph cut based minimization. For Schlesingers subgradient algorithm we proposed a step control heuristics which considerably enhances both speed and accuracy compared with known stepsize strategies for subgradient methods. The registration algorithm is easily parallelizable, since the dynamic programming maximization of the functional along a horizontal (resp. vertical) gridline is independent of maximization along any other horizontal (resp. vertical) gridlines. We have implemented it both on Core Quad or Core Duo PCs and CUDA Graphic Processing Unit, thus significantly speeding up the computation.