Abstract not found

The dynamic dictionary problem is considered: provide an algorithm for storing a dynamic set, allowing the operations insert, delete, and lookup. A dynamic perfect hashing strategy is given: a randomized algorithm for the dynamic dictionary problem that takes O(1) worst-case time for lookups and O(1) amortized expected time for insertions and deletions; it uses space proportional to the size of the set stored. Furthermore, lower bounds for the time complexity of a class of deterministic algorithms for the dictionary problem are proved. This class encompasses realistic hashing-based schemes that use linear space. Such algorithms have amortized worst-case time complexity \Omega(log n) for a sequence of n insertions and

Inflammatory disease is initiated by leukocytes (white blood cells) rolling along the inner surface Hning of small blood vessels called postcapillary venules. Studying the number and velocity of rolling leukocytes is essential to understanding and successfully treating inflammatory diseases. Potential inhibitors of leukocyte recruitment can be screened by leukocyte rolling assays and successful inhibitors validated by intravital microscopy. In this paper we present an active contour or snake-based technique to automatically track the movement of the leukocytes. The novelty of the proposed method Hes in the energy functional that constrains the shape and size of the active contour. This paper introduces a significant enhancement over existing gradientbased snakes in the form of a modified gradient vector flow. Using the gradient vector flow, we can track leukocytes rolling at high speeds that are not amenable to tracking with the existing edge-based techniques. We also propose a new energy based implicit sampling method of the points on the active contour that replaces the computationally expensive explicit method. To enhance the performance of this shape and size constrained snake model we have coupled it with Kalman f'fiter, so that during coasting (when the leukocytes are completely occluded or obscured), the tracker may infer the location of the center of the leukocyte. Finally we have compared the performance of the proposed snake tracker with that of the correlation and centroid-based trackers. The proposed snake tracker results in superior performance measures such as reduced error in locating the leukocyte under tracking and improvements in the percentage of frames successfully tracked. For screening and drug validation, the tracker shows promise as an automat...

Abstract—We propose a cell detection and tracking solution using image-level sets computed via threshold decomposition. In contrast to existing methods where manual initialization is required to track individual cells, the proposed approach can automatically identify and track multiple cells by exploiting the shape and intensity characteristics of the cells. The capture of the cell boundary is considered as an evolution of a closed curve that maximizes image gradient along the curve enclosing a homogeneous region. An energy functional dependent upon the gradient magnitude along the cell boundary, the region homogeneity within the cell boundary and the spatial overlap of the detected cells is minimized using a variational approach. For tracking between frames, this energy functional is modified considering the spatial and shape consistency of a cell as it moves in the video sequence. The integrated energy functional complements shape-based segmentation with a spatial consistency based tracking technique. We demonstrate that an acceptable, expedient solution of the energy functional is possible through a search of the image-level lines: boundaries of connected components within the level sets obtained by threshold decomposition. The level set analysis can also capture multiple cells in a single frame rather than iteratively computing a single active contour for each individual cell. Results of cell detection using the energy functional approach and the level set approach are presented along with the associated processing time. Results of successful tracking of rolling leukocytes from a number of digital video sequences are reported and compared with the results from a correlation tracking scheme. Index Terms—Cell detection, level set, tracking. I.

We consider rendezvous problems in which two players move on the plane and wish to cooperate in order to minimise their first meeting time. We begin by considering the case when they know that they are a distance d apart, but they do not know the direction in which they should travel. We also consider a situation in which player 1 knows the initial position of player 2, while player 2 is only given information on the initial distance of player 1. Finally we give some results for the case where one of the players is placed at an initial position chosen equiprobably from a finite set of points.

2. Isoperimetric inequalities in Carnot groups 6 3. Partial solution of the isoperimetric problem in H n 12

This paper introduces an active contour or snakebased method for tracking cells within a video sequence. Specifically, we apply our cell tracking techniques to rolling leukocytes observed in vivo (in living animal) from video microscopy. The analysis of leukocyte motion reveals cues about the mechanism of inflammatory disease. To attack the problem of tracking leukocytes in vivo, the proposed snake tracker utilizes shape and size information specific to the leukocytes. The principal contribution of this work lies in introducing the shape and size constraint as a geometric primitive in the parametric snake energy model. The energy functional is then minimized through the basic principles of the calculus of variations to obtain the Euler equations used in contour updating. We have developed a partial differential equation (PDE) based generalized gradient vector flow (GVF) that accommodates for contrast changes and weak cell edges. Whereas previous GVF models are sensitive to initial contour placement, the modified GVF construction with Dirichlet type boundary condition (BC) allows a snake tracker to be robust for a wide range of initial positions. Another contribution in this work is to incorporate an energy term in the snake model that eliminates the need for explicitly resampling the snake contour intermittently as performed in traditional snake evolution. Using animal experiments, we compare the accuracy of the proposed snake tracker with the correlation and centroid based tracker and show that the proposed tracker is superior in terms of increased number of frames tracked and reduced localization error.

In this paper we introduce an adaptive image thresholding technique via minimax optimization of a novel energy functional that consists of a non linear convex combination of an edge sensitive data fidelity term and a regularization term. While the proposed data fidelity term compels the threshold surface to intersect the image surface only at high gradient places, the regularization term enforces smoothness in the threshold surface. To the best of our knowledge, all the previously proposed energy functional-based adaptive image thresholding algorithms rely on manually setting the weighting parameters to achieve a balance between the data fidelity and the regularization terms. In contrast, we use minimax principle to automatically find this weighting parameter value, as well as the spatially adaptive threshold surface. Our conscious choice of the energy functional permits a variational formulation within the minimax principle leading to a globally optimum solution. The proposed variational minimax optimization is carried out with an iterative gradient descent line search technique, which we experimentally demonstrate to be computationally far more efficient than the Fibonacci search applied to find the minimax solution. Our method shows promising results to find lung boundary from magnetic resonance imagery – up to 28 % improvement on segmentation score (Pratt’s Figure of Merit) over other competing methods. Visual demonstrations of the application of the proposed method on different benchmark images reveal that that our method preserves better texture/edge information than other competing methods.

Abstract not found

The density profile of an elastic fiber like DNA will change in space and time as ligands associate with it. This observation affords a new direction in single molecule studies provided that density profiles can be measured in space and time. In fact, this is precisely the objective of seismology, where the mathematics of inverse problems have been employed with success. We argue that inverse problems in elastic media can be directly applied to biophysical problems of fiber-ligand association, and demonstrate that robust algorithms exist to perform density reconstruction in the condensed phase.