Automated visual-tracking of cell populations in vitro using time-lapse phase contrast microscopy enables quantitative, systematic and high-throughput measurements of cell behaviors. These measurements include the spatiotemporal quantification of cell migration, mitosis, apoptosis, and the reconstruction of cell lineages. The combination of low signal-to-noise ratio of phase contrast microscopy images, high and varying densities of the cell cultures, topological complexities of cell shapes, and wide range of cell behaviors poses many challenges to existing tracking techniques. This paper presents a fully-automated multi-target tracking system that can efficiently cope with these challenges while simultaneously tracking and analyzing thousands of cells observed using time-lapse phase contrast microscopy. The system combines bottom-up and top-down image analysis by integrating multiple collaborative modules, which exploit a fast geometric active contour tracker in conjunction with adaptive interacting multiple models (IMM) motion filtering and spatiotemporal trajectory optimization. The system, which was tested using a variety of cell populations, achieved tracking accuracy in the range of 86.9%-92.5%.

Abstract—In this paper, we propose a natural framework that allows any region-based segmentation energy to be re-formulated in a local way. We consider local rather than global image statistics and evolve a contour based on local information. Localized contours are capable of segmenting objects with heterogeneous feature profiles that would be difficult to capture correctly using a standard global method. The presented technique is versatile enough to be used with any global region-based active contour energy and instill in it the benefits of localization. We describe this framework and demonstrate the localization of three well-known energies in order to illustrate how our framework can be applied to any energy. We then compare each localized energy to its global counterpart to show the improvements that can be achieved. Next, an in-depth study of the behaviors of these energies in response to the degree of localization is given. Finally, we show results on challenging images to illustrate the robust and accurate segmentations that are possible with this new class of active contour models. Index Terms—Active contours, level set methods, curve evolution, image segmentation, partial differential equations, multiregion segmentation. I.

We present a novel variational approach for simultaneous segmentation of two images of the same object taken from different viewpoints. Due to noise, clutter and occlusions, neither of the images contains sufficient information for correct object-background partitioning. The evolving object contour in each image provides a dynamic prior for the segmentation of the other object view. We call this process mutual segmentation. The foundation of the proposed method is a unified level-set framework for region and edge based segmentation, associated with a shape similarity term. The suggested shape term incorporates the semantic knowledge gained in the segmentation process of the image pair, accounting for excess or deficient parts in the estimated object shape. Transformations, including planar projectivities, between the object views are accommodated by a registration process held concurrently with the segmentation. The proposed segmentation algorithm is demonstrated on a variety of image pairs. The Homography between each of the image pairs is estimated and its accuracy is evaluated.

This paper shows that adding 3D depth information to RGB colour images improves segmentation of pigmented and non-pigmented skin lesion. A regionbased active contour segmentation approach using a statistical model based on the level-set framework is presented. We consider what kinds of properties (e.g., colour, depth, texture) are most discriminative. The experiments show that our proposed method integrating chromatic and geometric information produces segmentation results for pigmented lesions close to dermatologists and more consistent and accurate results for non-pigmented lesions. 1

Abstract. Tracking is usually interpreted as finding an object in single consecutive frames. Regularization is done by enforcing temporal smoothness of appearance, shape and motion. We propose a tracker, by interpreting the task of tracking as segmentation of a volume in 3D. Inherently temporal and spatial regularization is unified in a single regularization term. Segmentation is done by a variational approach using anisotropic weighted Total Variation (TV) regularization. The proposed convex energy is solved globally optimal by a fast primal-dual algorithm. Any image feature can be used in the segmentation cue of the proposed Mumford-Shah like data term. As a proof of concept we show experiments using a simple color-based appearance model. As demonstrated in the experiments, our tracking approach is able to handle large variations in shape and size, as well as partial and complete occlusions. 1

Physical simulation on surfaces and various applications in geometry processing are based on partial differential equations on surfaces. The implicit representation of these eventually evolving surfaces in terms of level set methods leads to effective and flexible numerical tools. This paper addresses the computational problem of how to solve partial differential equations on level sets with an underlying very high-resolution discrete grid. These highresolution grids are represented in a very efficient format, which stores only grid points in a thin narrow band. Reaction diffusion equations on a fixed surface and the evolution of a surface under curvature motion are considered as model problems. The proposed methods are based on a semi implicit finite element discretization directly on these thin narrow bands and allow for large time steps. To ensure this, suitable transparent boundary conditions are introduced on the boundary of the narrow band and the time discretization is based on a nested iteration scheme. Methods are provided to assemble finite element matrices and to apply matrix vector operators in a manner that do not incur additional overhead and give fast, cache-coherent access to very large data sets. 1

Abstract. The simulation of physical processes on interfaces and a variety of applications in geometry processing and geometric modeling are based on the solution of partial differential equations on curved and evolving surfaces. Frequently, an implicit level set type representation of these surfaces is the most effective and computationally advantageous approach. This paper addresses the computational problem of how to solve partial differential equations on highly resolved level sets with an underlying very high-resolution discrete grid. These high-resolution grids are represented in a very efficient Dynamic Tubular Grid encoding format for a narrow band. A reaction diffusion model on a fixed surface and surface evolution driven by a nonlinear geometric diffusion approach, by isotropic, or truly anisotropic curvature motion are investigated as characteristic model problems. The proposed methods are based on semi-implicit finite element discretizations directly on these narrow bands, require only standard numerical quadrature and allow for large time steps. To combine large time steps with a very thin and thus storage inexpensive narrow band, suitable transparent boundary conditions on the boundary of the narrow band and a nested iteration scheme in each time step are investigated. This nested iteration scheme enables the discrete interfaces to move in a single time step significantly beyond the domain of the narrow band of the previous time step. Furthermore, algorithmic tools are provided to assemble finite element matrices and to apply matrix vector operators via fast, cache-coherent access to the Dynamic Tubular Grid encoded data structure. The consistency of the presented approach is evaluated and various numerical examples show its application potential. Key words. level set methods, narrow band approach, partial differential equations on surfaces, curvature motion AMS subject classifications. 65D18, 65D10, 65M50 65M60 65N30, 65N50, 68P05, 68P20

In this paper we propose an efficient unsupervised texture segmentation method. We introduce the extension of a state-of-the-art segmentation algorithm, which is exclusively based on color cues, by incorporating texture information. We further show how to use covariance matrices of low level features for texture description which can be efficiently calculated based on integral images. Furthermore, a multi-scale extension allows to provide accurate texture segmentation results. An experimental evaluation on a synthetic texture database and images of the Berkeley image database demonstrate the improved performance of the algorithm. 1.

An active contour based tracking framework is described that generates and integrates dynamic shape information without having to learn a priori shape constraints. This dynamic shape information is combined with dynamic photometric foreground model matching and background mismatching. Boundary based optical flow is also used to estimate the location of the object in each new frame, incorporating Procrustes shape alignment. Promising results under complex deformations of shape, varied levels of noise, and closeto-complete occlusion in complex textured backgrounds are presented. 1

Many image analysis or image processing algorithms are based on the solution of an optimization problem. To address the image analysis problem usually requires the following steps 1) Formulation of the problem: What information is given and what information do I want to obtain. Frequently the given information will be a volume of image intensities. The information to obtain can be a segmentation, a deformation field (as for registration), etc. 2) Mathematical formulation of the problem: Deterministic formulation versus probabilistic modeling. 3) Choice of optimization method: How to solve the optimization problem formulated in step 2. Frequently a variety of optimization methods are applicable. Choosing the right one can have a huge impact in terms of algorithm robustness (i.e., some form of stochastic search may be useful to avoid local minima) and in terms of solution speed. 1 Motivational Example: Least-squares To illustrate the concept of optimal estimation and probabilistic modeling versus a deterministic formulation let’s consider a least squares problem. Assume y = Ax + η, ηi ∼ N (0, σ), where A is a m × n matrix (m ≥ n), y is the measurement vector and η is a vector of Gaussian random variables with standard deviation σ. The goal is to estimate the unknown vector x given the measurements y and the noise model. The conditional probability of observing a measurement yi given the real value ˆyi = (Ax)i is p(yi|ˆyi) = 1 √ 2πσ e − (y i −ˆy i) 2σ 2. Assuming the measurement noise is uncorrelated, we can write the joint conditional probability as p(y | ˆy) = � p(yi|ˆyi). Our optimization problem is to find the values ˆy (and ultimately ˆx) that best explain the measurements y. This can be accomplished by maximum likelihood (ML) estimation, i.e., This is equivalent to solving i ˆx = argmax