Survey on haptic rendering of data sets: Exploration of scalar and vector fields

Complementary to automatic extraction processes, Virtual Reality technologies provide an adequate framework to integrate human perception in the exploration of large data sets. In such multisensory system, thanks to intuitive interactions, a user can take advantage of all his perceptual abilities in the exploration task. In this context the haptic perception, coupled to visual rendering, has been investigated for the last two decades, with significant achievements. In this paper, we present a survey related to exploitation of the haptic feedback in exploration of large data sets. For each haptic technique introduced, we describe its principles and its effectiveness.

Control of Redundant Joint Structures Using Image Information During the Tracking of Non-Smooth Trajectories

Visual information is increasingly being used in a great number of applications in order to perform the guidance of joint structures. This paper proposes an image-based controller which allows the joint structure guidance when its number of degrees of freedom is greater than the required for the developed task. In this case, the controller solves the redundancy combining two different tasks: the primary task allows the correct guidance using image information, and the secondary task determines the most adequate joint structure posture solving the possible joint redundancy regarding the performed task in the image space. The method proposed to guide the joint structure also employs a smoothing Kalman filter not only to determine the moment when abrupt changes occur in the tracked trajectory, but also to estimate and compensate these changes using the proposed filter. Furthermore, a direct visual control approach is proposed which integrates the visual information provided by this smoothing Kalman filter. This last aspect permits the correct tracking when noisy measurements are obtained. All the contributions are integrated in an application which requires the tracking of the faces of Asperger children.

Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields

We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact.

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

A fast non-smooth nonnegative matrix factorization for learning sparse representation

Nonnegative matrix factorization (NMF) is a hot topic in machine learning and data processing. Recently, a constrained version, non-smooth NMF (NsNMF), shows a great potential in learning meaningful sparse representation of the observed data. However, it suffers from a slow linear convergence rate, discouraging its applications to large-scale data representation. In this paper, a fast NsNMF (FNsNMF) algorithm is proposed to speed up NsNMF. In the proposed method, it first shows that the cost function of the derived sub-problem is convex and the corresponding gradient is Lipschitz continuous. Then, the optimization to this function is replaced by solving a proximal function, which is designed based on the Lipschitz constant and can be solved through utilizing a constructed fast convergent sequence. Due to the usage of the proximal function and its efficient optimization, our method can achieve a nonlinear convergence rate, much faster than NsNMF. Simulations in both computer generated data and the real-world data show the advantages of our algorithm over the compared methods.

Biologically inspired vector fields to generate hair directions

This paper describes how biologically inspired vector fields can be used to partially automate the manual and time-consuming process of specifying hair directions. This approach replicates the consequence of stretching of skin from natural hair development process, in contrast to replicating the appearance of hair. The direction of each hair on the surface of an arbitrary 3D model is determined by interpolating the solution vector field that satisfies a set of user-defined constraints describing the stretching of skin. Results found that the generated hair directional pattern closely resembles that found naturally. Further investigation revealed that the presence of naturally occurring hair types and the varying distribution of hair directions induced by the calculated vector field enhanced the realism of hair coats generated using this approach. Aside from hair or fur, this approach can also be applied to hair-like masses such as grass, feathers, or scales.

Birth of limit cycles bifurcating from a nonsmooth center

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Piecewise Bounded Quadratic Systems in the Plane

In this paper we study the sliding mode of piecewise bounded quadratic systems in the plane given by a non-smooth vector field Z=(X,Y). Analyzing the singular, crossing and sliding sets, we get the conditions which ensure that any solution, including the sliding one, is bounded.

Conjuntos minimais e caóticos em campos de vetores planares suaves por partes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Horn-schunck optical flow with a multi-scale strategy

[EN] The seminal work of Horn and Schunck [8] is the first variational method for optical flow estimation. It introduced a novel framework where the optical flow is computed as the solution of a minimization problem. From the assumption that pixel intensities do not change over time, the optical flow constraint equation is derived. This equation relates the optical flow with the derivatives of the image. There are infinitely many vector fields that satisfy the optical flow constraint, thus the problem is ill-posed. To overcome this problem, Horn and Schunck introduced an additional regularity condition that restricts the possible solutions. Their method minimizes both the optical flow constraint and the magnitude of the variations of the flow field, producing smooth vector fields. One of the limitations of this method is that, typically, it can only estimate small motions. In the presence of large displacements, this method fails when the gradient of the image is not smooth enough. In this work, we describe an implementation of the original Horn and Schunck method and also introduce a multi-scale strategy in order to deal with larger displacements. For this multi-scale strategy, we create a pyramidal structure of downsampled images and change the optical flow constraint equation with a nonlinear formulation. In order to tackle this nonlinear formula, we linearize it and solve the method iteratively in each scale. In this sense, there are two common approaches: one that computes the motion increment in the iterations, like in ; or the one we follow, that computes the full flow during the iterations, like in. The solutions are incrementally refined ower the scales. This pyramidal structure is a standard tool in many optical flow methods.

Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.

Bilateral smoothing of gradient vector field and application to image segmentation

Medical image segmentation finds application in computer-aided diagnosis, computer-guided surgery, measuring tissue volumes, locating tumors, and pathologies. One approach to segmentation is to use active contours or snakes. Active contours start from an initialization (often manually specified) and are guided by image-dependent forces to the object boundary. Snakes may also be guided by gradient vector fields associated with an image. The first main result in this direction is that of Xu and Prince, who proposed the notion of gradient vector flow (GVF), which is computed iteratively. We propose a new formalism to compute the vector flow based on the notion of bilateral filtering of the gradient field associated with the edge map - we refer to it as the bilateral vector flow (BVF). The range kernel definition that we employ is different from the one employed in the standard Gaussian bilateral filter. The advantage of the BVF formalism is that smooth gradient vector flow fields with enhanced edge information can be computed noniteratively. The quality of image segmentation turned out to be on par with that obtained using the GVF and in some cases better than the GVF.

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

Studies in non-Gaussian analysis

This thesis presents general methods in non-Gaussian analysis in infinite dimensional spaces. As main applications we study Poisson and compound Poisson spaces. Given a probability measure μ on a co-nuclear space, we develop an abstract theory based on the generalized Appell systems which are bi-orthogonal. We study its properties as well as the generated Gelfand triples. As an example we consider the important case of Poisson measures. The product and Wick calculus are developed on this context. We provide formulas for the change of the generalized Appell system under a transformation of the measure. The L² structure for the Poisson measure, compound Poisson and Gamma measures are elaborated. We exhibit the chaos decomposition using the Fock isomorphism. We obtain the representation of the creation, annihilation operators. We construct two types of differential geometry on the configuration space over a differentiable manifold. These two geometries are related through the Dirichlet forms for Poisson measures as well as for its perturbations. Finally, we construct the internal geometry on the compound configurations space. In particular, the intrinsic gradient, the divergence and the Laplace-Beltrami operator. As a result, we may define the Dirichlet forms which are associated to a diffusion process. Consequently, we obtain the representation of the Lie algebra of vector fields with compact support. All these results extends directly for the marked Poisson spaces.