In this paper, we present a method for simultaneously tracking thousands of targets in biological image sequences, which is of major importance in modern biology. The complexity and inherent randomness of the problem lead us to propose a unified probabilistic framework for tracking biological particles in microscope images. The framework includes realistic models of particle motion and existence and of fluorescence image features. For the track extraction process per se, the very cluttered conditions motivate the adoption of a multiframe approach that enforces tracking decision robustness to poor imaging conditions and to random target movements. We tackle the large-scale nature of the problem by adapting the multiple hypothesis tracking algorithm to the proposed framework, resulting in a method with a favorable tradeoff between the model complexity and the computational cost of the tracking procedure. When compared to the state-of-the-art tracking techniques for bioimaging, the proposed algorithm is shown to be the only method providing high-quality results despite the critically poor imaging conditions and the dense target presence. We thus demonstrate the benefits of advanced Bayesian tracking techniques for the accurate computational modeling of dynamical biological processes, which is promising for further developments in this domain.

We introduce a complete parameterization of the family of two-dimensional steerable wavelets that are polar-separable in the Fourier domain under the constraint of self-reversibility. These wavelets are constructed by multiorder generalized Riesz transformation of a primary isotropic bandpass pyramid. The backbone of the transform (pyramid) is characterized by a radial frequency profile function $h(\omega)$, while the directional wavelet components at each scale are encoded by an $M \times (2N+1)$ shaping matrix ${\bf U}$, where $M$ is the number of wavelet channels and $N$ the order of the Riesz transform. We provide general conditions on $h(\omega)$ and ${\bf U}$ for the underlying wavelet system to form a tight frame of $L_2(\mathbb{R}^2)$ (with a redundancy factor $4/3M$). The proposed framework ensures that the wavelets are steerable and provides new degrees of freedom (shaping matrix ${\bf U}$) that can be exploited for designing specific wavelet systems. It encompasses many known transforms as particular cases: Simoncelli's steerable pyramid, Marr gradient and Hessian wavelets, monogenic wavelets, and $N$th-order Riesz and circular harmonic wavelets. We take advantage of the framework to construct new generalized spheroidal prolate wavelets, whose angular selectivity is maximized, as well as signal-adapted detectors based on principal component analysis. We also introduce a curvelet-like steerable wavelet system. Finally, we illustrate the advantages of some of the designs for signal denoising, feature extraction, pattern analysis, and source separation.

We present a new fast active-contour model (a.k.a. snake) for image segmentation in 3D microscopy. We introduce a parametric design that relies on exponential B-spline bases and allows us to build snakes that are able to reproduce ellipsoids. We design our bases to have the shortest-possible support, subject to some constraints. Thus, computational efficiency is maximized. The proposed 3D snake can approximate blob-like objects with good accuracy and can perfectly reproduce spheres and ellipsoids, irrespective of their position and orientation. The optimization process is remarkably fast due to the use of Gauss' theorem within our energy computation scheme. Our technique yields successful segmentation results, even for challenging data where object contours are not well defined. This is due to our parametric approach that allows one to favor prior shapes. In addition, this paper provides a software that gives full control over the snakes via an intuitive manipulation of few control points.

We introduce a systematic and practical design for steerable wavelet frames in 3D. Our steerable wavelets are obtained by applying a 3D version of the generalized Riesz transform to a primary isotropic wavelet frame. The novel transform is self-reversible (tight frame) and its elementary constituents (Riesz wavelets) can be efficiently rotated in any 3D direction by forming appropriate linear combinations. Moreover, the basis functions at a given location can be linearly combined to design custom (and adaptive) steerable wavelets. The features of the proposed method are illustrated with the processing and analysis of 3D biomedical data. In particular, we show how those wavelets can be used to characterize directional patterns and to detect edges by means of a 3D monogenic analysis. We also propose a new inverse-problem formalism along with an optimization algorithm for reconstructing 3D images from a sparse set of wavelet-domain edges. The scheme results in high-quality image reconstructions which demonstrate the feature-reduction ability of the steerable wavelets as well as their potential for solving inverse problems.

We present a functional framework for the design of tight steerable wavelet frames in any number of dimensions. The 2-D version of the method can be viewed as a generalization of Simoncelli's steerable pyramid that gives access to a larger palette of steerable wavelets via a suitable parametrization. The backbone of our construction is a primal isotropic wavelet frame that provides the multiresolution decomposition of the signal. The steerable wavelets are obtained by applying a one-to-many mapping (Nth-order generalized Riesz transform) to the primal ones. The shaping of the steerable wavelets is controlled by an M×M unitary matrix (where M is the number of wavelet channels) that can be selected arbitrarily; this allows for a much wider range of solutions than the traditional equiangular configuration (steerable pyramid). We give a complete functional description of these generalized wavelet transforms and derive their steering equations. We describe some concrete examples of transforms, including some built around a Mallat-type multiresolution analysis of L(2)(R(d)), and provide a fast Fourier transform-based decomposition algorithm. We also propose a principal-component-based method for signal-adapted wavelet design. Finally, we present some illustrative examples together with a comparison of the denoising performance of various brands of steerable transforms. The results are in favor of an optimized wavelet design (equalized principal component analysis), which consistently performs best.

This paper presents a new method to accelerate the automatic tracking of multiple articulated objects in video sequences. The tracking method exploits the physics modeling of the articulated objects. The physics approach has numerous advantages such as the capability to let multiple models interact when tracking simultaneously multiple objects. Solving the tracking problem is generally done with an iterative scheme involving the computation of numerous forces, which usually turns out to be time consuming. This paper tackles the computational cost bottleneck by introducing a multi scale decomposition of the force maps. At each step of the tracking optimization scheme the multiple force maps are efficiently combined using a quadtree structure to recover the resulting forces. We demonstrate through multiple experiments that our results are both exact and drastically faster than the standard computation scheme.

In this paper we present a new procedure for tracking bi-directional objects in kymographs. The proposed technique is based on a novel adaptive and directional band-pass filtering method which allows us to separate particles which move in opposite directions. The filtering method exploits the curvelet analysis of the kymograph image to automatically adapt to the objects trails characteristics and select oriented features. The separation of bi-directional objects in separated images allows us to reliably detect and track fluorescent particles in fluorescence image sequences, despite numerous crossroad points in the kymograph space. The new abilities provided by the proposed technique are highlighted by the analysis of biological images which were previously impossible to analyze reliably.

Particle detection and tracking methods generally assume a simplistic image model that is rarely valid when imaging biological processes in fluorescence microscopy. The tracking task may become nearly impossible when complex biological structures are visible and interfere with the signal of interest. To address this limitation we have adapted a source separation technique based on sparsity principles to the characteristics of fluorescent biological images. Since it allows the discrimination of objects with different morphologies, we present an approach to detect and track particles that exploits its results. The tracking algorithm resolves particles that temporarily aggregate by exploiting the proposed model of image. We prove in a real case the ability of the method to track numerous particles in a complex and dynamic background, something which was not feasible until now, hence offering new tools to document interactions between cellular compartments.

Multiple hypothesis tracking (MHT) is a preferred technique for solving the data association problem in modern multiple targets tracking systems. However its computational cost is generally considered prohibitive for tracking numerous objects in cluttered environments due to numerous targets and spurious measurements. We present in this paper a new MHT formulation in which target perceivability is modeled whereby automatic early track termination and false measurements exclusion reduce the problem complexity and improve the method robustness to clutter. Moreover we propose a MHT implementation exploiting the tree structure of the potential tracks to take full advantages of parallel computing technologies. We provide experimental results showing that both the track model and algorithmic design make the algorithm fast and robust even in highly complex situations such as tracking numerous particles in fluorescent microscopy images.

We present a new feature-aided tracking algorithm dedicated to the task of tracking multiple and closely-spaced biological particles. We propose a new function to score associations, based on kinetic models, and enriched with an additional feature. This feature is based on adaptive profiles and the physical properties of the acquisition system. A key property is that this feature definition allows to resolve the challenging task of tracking particles that appear fused. Results on simulations show improved performances over existing methods both on tracking and on the resolution of fused particles.

Tracking nano-metric particles in a biological environment is a very difficult task because of the low signal intensity and the high mobility of these small objects. The task becomes nearly impossible for classical tracking procedures when the targets are labeled with a marker that is not strictly specific, because in this case dynamic structures in the cell are also visible. To address this limitation, we propose to use a source separation technique based on sparsity principles which allows the discrimination of objects with different morphologies. We prove in a real case that tracking in the source separated images allows to track particles that interact with other sources, something which was not feasible until now. This capability opens up new perspectives for the analysis documenting intricate interactions between cellular compartments.

In this paper, we propose a new method to reconstruct high resolution images from structured illumination microscopy. It consists of estimating the illumination pattern parameters with a multiscale analysis in the Fourier domain and filtering the significative features with a statistical test. Our method is fast and automatic, aiming at being computationally effective for in vivo biomedical applications.