A distribution-based approach to tracking points in velocity vector fields

In this paper, we present a surface reconstruction via 2D strokes and a vector field on the strokes based on a two-step method. In the first step, from sparse strokes drawn by artists and a given vector field on the strokes, we propose a nonlinear vector interpolation combining total variation (TV) and H 1 regularization with a curl-free con- straint for obtaining a dense vector field. In the second step, a height map is obtained by integrating the dense vector field in the first step. Jump discontinuities in surface and discontinuities of surface gradients can be well reconstructed without any surface distortion. We also provide a fast and efficient algorithm for solving the proposed func- tionals. Since vectors on the strokes are interpreted as a projection of surface gradients onto the plane, different types of strokes are easily devised to generate geometrically crucial structures such as ridge, valley, jump, bump, and dip on the surface. The stroke types help users to create a surface which they intuitively imagine from 2D strokes. We compare our results with conventional methods via many examples. AMS subject classifications: 65K10, 65D18, 65D17

Robust and fast stochastic 4D Flow Vector-field signature technique for quantifying composite flow dynamics from 4D Flow MRI: Application to left atrial flow in atrial fibrillation

The introduction of autonomous delivery systems is expected to improve productivity in numerous application fields. Since such systems comprise both unmanned and manned units, it is important to control the whole system using appropriate behavioral models of manned vehicles or humans. This work builds on the results of a previous study, where a velocity vector field was used to model human movement, and extends the use of velocity vector fields to the simulation of vehicle behavior by modeling variance in given trajectories. This extension enables the velocity vector field to regenerate an average trajectory with a band and consequently allows one to calculate the vehicle's predicted region in arbitrary future time steps and anomaly detection. These applications are expected to facilitate collision avoidance and should help one to control other applications of unmanned vehicles.

As of today, perioperative monitoring in the operating room is based on vital signs and clinical observations by the anesthesiologist. This, however, does not offer a complete monitoring of left ventricular function throughout the intervention. We hypothesize that functional monitoring of the heart can be performed automatically based on transesophageal echocardiographic (TEE) images. The main goal of this work is therefore to compute the non-linear deformation between subsequent images in a TEE sequence of the left ventricle and estimate basal longitudinal strain to assess regional myocardial function using a deep learning approach. An unsupervised approach based on a convolutional neural network (CNN) was implemented. The output of the CNN network is a dense vector field that describes the non-linear deformation required to maximize the similarity between two images.Recordings from 42 consecutive complete TEE exams from the Echocardiography Unit were anonymized and used for training. Recordings from 5 consecutive TEE exams performed during heart surgery, also anonymized, were used as test set. For the test set patients, the basal strain was manually annotated in EchoPac by an expert echocardiographer. For this work, 19 heart cycles were randomly selected from the test set and checked to ensure visibility of the points to be tracked. Overall when estimating strain there was a mean difference of 7.25%(±4.56%) in the strain values when compared to expert annotations.We have proven that point tracking is working as expected in most images, where the myocardium is well depicted. However, dropouts, noise generated by implants or air bubbles after surgery, confuse the tracker and drifting occurs.

In studio signal processing as well as in the television receiver the integration of different video media becomes more and more important. This paper introduces a new way of bridging different video production and transmission standards for digital television broadcasting. The proposed format is based on progressively scanned images and uses a reversible synthetic interlace for transmission. The format fits as well to the interlace based television infrastructure as to the professional multimedia production facilities using 35 mm film. Especially for motion vector based digital transmissions an algorithm is introduced to transcode the used dense vector field into a block vector field that meets MPEG-2 requirements and enables an appropriate upconversion process at the decoder side. >

Line integral convolution (LIC) is an effective and powerful technique for generating images from vector fields. In the 3D-LIC, it is very important to select an adequate region of interest (ROI) in the vector field. One way for specifying ROI is to use a surface defined in the vector field. The other way is to use a significance map that defines a ROI related values at each point in the vector field. To represent an anisotropic vector field around a vortex center in an understandable way, we introduced a time-oriented significance map. Our technique for specifying ROI is to use a passage-time for a mass-less particle to travel from near a vortex center to a pixel location. In our technique, what we call “restricted LIC technique (RLIC), ” we refer to the passage-time buffer before we start the convolution p.rocess at a pixel location. To confirm the effectiveness of our technique, we use an anisotropic swirl vector field and construct two types of significance maps, a distance-oriented map and a time-oriented map. We will show the difference in the resulting images are generated from these significance maps.

Investigating the effect of polydispersity on the dynamics of multiphase flows using computational fluid dynamics tools

Vector fields may come from video data (via optical flow and tracking), from weather phenomena (e.g., wind speed and direction), and from medical imaging. An important component in analyzing this data is to be able to quantitatively compare different points within a vector field or across different fields of the same type. We present a novel local descriptor to compare individual points in a vector field and rank them based on which are most similar to a selected point. The descriptor captures the statistics of the neighboring vector field around a central point and is discriminating, robust to noise, and efficient to generate and compare.

On the existence and uniqueness of connecting orbits

There is growing evidence that population-level brain activity is often organized into propagating waves that are structured in both space and time. Such spatiotemporal patterns have been linked to brain function and observed across multiple recording methodologies and scales. The ability to detect and analyze these patterns is thus essential for understanding the working mechanisms of neural circuits. Here we present a mathematical and computational framework for the identification and analysis of multiple classes of wave patterns in neural population-level recordings. By drawing a conceptual link between spatiotemporal patterns found in the brain and coherent structures such as vortices found in turbulent flows, we introduce velocity vector fields to characterize neural population activity. These vector fields are calculated for both phase and amplitude of oscillatory neural signals by adapting optical flow estimation methods from the field of computer vision. Based on these velocity vector fields, we then introduce order parameters and critical point analysis to detect and characterize a diverse range of propagating wave patterns, including planar waves, sources, sinks, spiral waves, and saddle patterns. We also introduce a novel vector field decomposition method that extracts the dominant spatiotemporal structures in a recording. This enables neural data to be represented by the activity of a small number of independent spatiotemporal modes, providing an alternative to existing dimensionality reduction techniques which separate space and time components. We demonstrate the capabilities of the framework and toolbox with simulated data, local field potentials from marmoset visual cortex and optical voltage recordings from whole mouse cortex, and we show that pattern dynamics are non-random and are modulated by the presence of visual stimuli. These methods are implemented in a MATLAB toolbox, which is freely available under an open-source licensing agreement.

Forme normale de perturbation de champs de vecteurs quasi-homogènes

At this time the Cheshire Cat vanished quite slowly, beginning with the end of the tail, ending with a grin, which remained some time after the rest of it had gone, [Ca].0. Introduction.Morse theory for distance functions was initiated by Grove-Shiohama [GS] and Gromov's [Gl] paper where basic notions of the theory were formulated; even this very initial level of the theory leads to important geometric applications.Grove and Shiohama [GS] established a generalized sphere theorem by constructing a vector field on a Riemannian manifold, with the property that the distance function had no stationary points along the integral curves at non-singular points of the vector field.They showed that this vector field had exactly two singular points and hence the manifold was homeomorphic to a sphere.Later Gromov [Gl] was able to bound the sum of the Betti numbers of a positively curved Riemannian manifold.He controlled the location of critical points of a Riemannian distance function on a positively curved manifold using Toponogov's theorem and then was able to bound the number of critical points of this function and hence the homology of the manifold, using a spectral sequence argument.Morse theory for Riemannian distance functions was discussed in [Gr], [L] and other papers, which explained its importance for geometric applications rather than developed the theory itself.Even a suitable concept of the index of a critical point has not been developed.As a result, the most powerful tools of the classical Morse theory such as Morse inequalities and the correspondence between critical points and the handle decomposition of the manifold cannot be used.The relationship with the classical Morse theory has not been investigated either; in particular, the connection between notions of the critical points in both theories is not obvious.In a different direction, the structure of Alexandrov spaces with curvatures bounded below was investigated using distance functions in several papers starting with [BGP] and continuing with [PI], [P2].A key result obtained is a canonical stratification of such Alexandrov spaces into topological manifolds and again the technique is a type of Morse theory, using the distance function.As Alexandrov spaces do not have as much structure as Riemannian manifolds, our theory gives more detailed information on the nature of critical points and index.M. Gromov pointed out in [Gl] that the Morse theory for Riemannian distance functions can be developed by analogy with the classical Morse theory.The aim of this paper is to construct a Morse theory for functions which are minima of finite families of smooth functions and clarify the connection with Riemannian distance functions for non-positively curved manifolds.We develop the theory in the classical style, including the notion of the index for critical points, and clarify relations with the Grove-Shiohama-Gromov approach.

Topological method for loop detection of surface intersection problems

The main theorem of the present paper is the bistability theorem for a four dimensional cancer model, in the variables representing primary cancer C, metastatic cancer , growth factor GF and growth inhibitor GI, respectively. It says that for some values of the para- meters this system is bistable, in the sense that there are exactly two positive singular points of this vector field. And one is stable and the other unstable. We also find an expression for for the discrete model T of the introduction, with variables , where C is cancer, are growth factors and growth inhibitors respectively. We find an affine vector field Y whose time one map is T2 and then compute , where is an integral curve of Y through . We also find a formula for the first escape time for the vector field associated to T, see section four.

An automated method to estimate vector fields of propagation velocity from observed epicardial extracellular potentials is introduced. The method relies on fitting polynomial surfaces T(x, y) to the space-time (x, y, t) coordinates of activity. Both speed and direction of propagation are computed from the gradient of the local polynomial surface. The components of velocity, which are total derivatives, are expressed in terms of the partial derivatives which comprise the gradient of T. The method was validated on two-dimensional (2-D) simulations of propagation and then applied to cardiac mapping data. Conduction velocity was estimated at multiple epicardial locations during sinus rhythm, pacing, and ventricular fibrillation (VF) in pigs. Data were obtained via a 528-channel mapping system from 23 x 22 and 24 x 21 arrays of unipolar electrodes sutured to the right ventricular epicardium. Velocity estimates are displayed as vector fields and are used to characterize propagation qualitatively and quantitatively during both simple and complex rhythms.