MOTIVATION: Rotated template matching is an efficient and versatile algorithm to analyze microscopy images, as it automates the detection of stereotypical structures, such as organelles that can appear at any orientation. Its performance however quickly degrades in noisy image data. RESULTS: We introduce Steer'n'Detect, an ImageJ plugin implementing a recently published algorithm to detect patterns of interest at any orientation with high accuracy from a single template in 2D images. Steer'n'Detect provides a faster and more robust substitute to template matching. By adapting to the statistics of the image background, it guarantees accurate results even in the presence of noise. The plugin comes with an intuitive user interface facilitating results analysis and further post-processing. AVAILABILITY AND IMPLEMENTATION: https://github.com/Biomedical-Imaging-Group/Steer-n-Detect. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: SpotCaliper is a novel wavelet-based image-analysis software providing a fast automatic detection scheme for circular patterns (spots), combined with the precise estimation of their size. It is implemented as an ImageJ plugin with a friendly user interface. The user is allowed to edit the results by modifying the measurements (in a semi-automated way), extract data for further analysis. The fine tuning of the detections includes the possibility of adjusting or removing the original detections, as well as adding further spots. RESULTS: The main advantage of the software is its ability to capture the size of spots in a fast and accurate way. AVAILABILITY AND IMPLEMENTATION: http://bigwww.epfl.ch/algorithms/spotcaliper/ CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be “dilated” by a procedure comparable to the operation of steering steerable wavelets. The fundamental aspects of the construction are the same: an admissible collection of Fourier multipliers is used to extend a tight wavelet frame, and the “scale” of the wavelets is adapted by scaling the multipliers. As an application, the proposed wavelets can be used to improve the frequency localization. Importantly, the localized frequency bands specified by this construction can be scaled efficiently using matrix multiplication.

We introduce a variational phase retrieval algorithm for the imaging of transparent objects. Our formalism is based on the transport-of-intensity equation (TIE), which relates the phase of an optical field to the variation of its intensity along the direction of propagation. TIE practically requires one to record a set of defocus images to measure the variation of intensity. We first investigate the effect of the defocus distance on the retrieved phase map. Based on our analysis, we propose a weighted phase reconstruction algorithm yielding a phase map that minimizes a convex functional. The method is nonlinear and combines different ranges of spatial frequencies - depending on the defocus value of the measurements - in a regularized fashion. The minimization task is solved iteratively via the alternating-direction method of multipliers. Our simulations outperform commonly used linear and nonlinear TIE solvers. We also illustrate and validate our method on real microscopy data of HeLa cells.

We present a variational reconstruction algorithm for the phase-retrieval problem by using the differential interference contrast microscopy. Principally, we rely on the transport-of-intensity equation that specifies the sought phase as the solution of a partial differential equation. Our approach is based on an iterative reconstruction algorithm involving the total variation regularisation which is efficiently solved via the alternating direction method of multipliers. We illustrate the applicability of the method via real data experiments. To the best of our knowledge, this work demonstrates the performance of such an iterative algorithm on real data for the first time.

BACKGROUND: Fluorescence loss in photobleaching (FLIP) is a widely used imaging technique, which provides information about protein dynamics in various cellular regions. In FLIP, a small cellular region is repeatedly illuminated by an intense laser pulse, while images are taken with reduced laser power with a time lag between the bleaches. Despite its popularity, tools are lacking for quantitative analysis of FLIP experiments. Typically, the user defines regions of interest (ROIs) for further analysis which is subjective and does not allow for comparing different cells and experimental settings. RESULTS: We present two complementary methods to detect and quantify protein transport and aggregation in living cells from FLIP image series. In the first approach, a stretched exponential (StrExp) function is fitted to fluorescence loss (FL) inside and outside the bleached region. We show by reaction-diffusion simulations, that the StrExp function can describe both, binding/barrier-limited and diffusion-limited FL kinetics. By pixel-wise regression of that function to FL kinetics of enhanced green fluorescent protein (eGFP), we determined in a user-unbiased manner from which cellular regions eGFP can be replenished in the bleached area. Spatial variation in the parameters calculated from the StrExp function allow for detecting diffusion barriers for eGFP in the nucleus and cytoplasm of living cells. Polyglutamine (polyQ) disease proteins like mutant huntingtin (mtHtt) can form large aggregates called inclusion bodies (IB's). The second method combines single particle tracking with multi-compartment modelling of FL kinetics in moving IB's to determine exchange rates of eGFP-tagged mtHtt protein (eGFP-mtHtt) between aggregates and the cytoplasm. This method is self-calibrating since it relates the FL inside and outside the bleached regions. It makes it therefore possible to compare release kinetics of eGFP-mtHtt between different cells and experiments. CONCLUSIONS: We present two complementary methods for quantitative analysis of FLIP experiments in living cells. They provide spatial maps of exchange dynamics and absolute binding parameters of fluorescent molecules to moving intracellular entities, respectively. Our methods should be of great value for quantitative studies of intracellular transport.

Edge-preserving smoothers need not be taxed by a severe computational cost. We present, in this paper, a lean algorithm that is inspired by the bi-exponential filter and preserves its structure-a pair of one-tap recursions. By a careful but simple local adaptation of the filter weights to the data, we are able to design an edge-preserving smoother that has a very low memory and computational footprint while requiring a trivial coding effort. We demonstrate that our filter (a bi-exponential edge-preserving smoother, or BEEPS) has formal links with the traditional bilateral filter. On a practical side, we observe that the BEEPS also produces images that are similar to those that would result from the bilateral filter, but at a much-reduced computational cost. The cost per pixel is constant and depends neither on the data nor on the filter parameters, not even on the degree of smoothing.

It is well known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not scale with the size or shape of the filter. These fast algorithms are generally referred to as constant-time or O(1) algorithms in the image-processing literature. Along with the spatial filter, the edge-preserving bilateral filter involves an additional range kernel. This is used to restrict the averaging to those neighborhood pixels whose intensity are similar or close to that of the pixel of interest. The range kernel operates by acting on the pixel intensities. This makes the averaging process nonlinear and computationally intensive, particularly when the spatial filter is large. In this paper, we show how the O(1) averaging algorithms can be leveraged for realizing the bilateral filter in constant time, by using trigonometric range kernels. This is done by generalizing the idea presented by Porikli, i.e., using polynomial kernels. The class of trigonometric kernels turns out to be sufficiently rich, allowing for the approximation of the standard Gaussian bilateral filter. The attractive feature of our approach is that, for a fixed number of terms, the quality of approximation achieved using trigonometric kernels is much superior to that obtained by Porikli using polynomials.

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-valued (primary) wavelet basis of L(2) (R(2)) into a complex one. The Riesz operator is also steerable in the sense that it give access to the Hilbert transform of the signal along any orientation. Having set those foundations, we specify a primary polyharmonic spline wavelet basis of L(2) (R(2)) that involves a single Mexican-hat-like mother wavelet (Laplacian of a B-spline). The important point is that our primary wavelets are quasi-isotropic: they behave like multiscale versions of the fractional Laplace operator from which they are derived, which ensures steerability. We propose to pair these real-valued basis functions with their complex Riesz counterparts to specify a multiresolution monogenic signal analysis. This yields a representation where each wavelet index is associated with a local orientation, an amplitude and a phase. We give a corresponding wavelet-domain method for estimating the underlying instantaneous frequency. We also provide a mechanism for improving the shift and rotation-invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect-reconstruction filterbanks. We illustrate the specific feature-extraction capabilities of the representation and present novel examples of wavelet-domain processing; in particular, a robust, tensor-based analysis of directional image patterns, the demodulation of interferograms, and the reconstruction of digital holograms.

We present a new, robust, computational procedure for tracking fluorescent markers in time-lapse microscopy. The algorithm is optimized for finding the time-trajectory of single particles in very noisy dynamic (two- or three-dimensional) image sequences. It proceeds in three steps. First, the images are aligned to compensate for the movement of the biological structure under investigation. Second, the particle's signature is enhanced by applying a Mexican hat filter, which we show to be the optimal detector of a Gaussian-like spot in 1/omega2 noise. Finally, the optimal trajectory of the particle is extracted by applying a dynamic programming optimization procedure. We have used this software, which is implemented as a Java plug-in for the public-domain ImageJ software, to track the movement of chromosomal loci within nuclei of budding yeast cells. Besides reducing trajectory analysis time by several 100-fold, we achieve high reproducibility and accuracy of tracking. The application of the method to yeast chromatin dynamics reveals different classes of constraints on mobility of telomeres, reflecting differences in nuclear envelope association. The generic nature of the software allows application to a variety of similar biological imaging tasks that require the extraction and quantitation of a moving particle's trajectory.

We have designed a series of computer sessions build around ImageJ (a public-domain software for image analysis), as a practical complement to a two-semester course in image processing. The students are challenged with simple practical imaging problems as they acquire hands-on practice by experimenting with image-processing operators. In the process, they also learn how to program standard image-processing algorithms in Java. This is made possible thanks to a programmer-friendly environment and a software interface that greatly facilitates the developments of plug-ins for ImageJ. Since our students have generally not acquired programming skills yet (they typically do not even know Java), we use a learning-by-example teaching strategy, with good success.