Identification of Space Curves from Two-Dimensional Perspective Views

This paper describes a new method to be used in the recognition of three-dimensional objects with curved surfaces from two-dimensional perspective views. The method requires for each three-dimensinal object a stored model consisting of a closed space curve representing some characteristic connected curved edges of the object. The input is a two-dimensional perspective projection of one of the stored models represented by an ordered sequence of points. The input is converted to a spline representation which is sampled at equal intervals to derive a curvature function. The Fourier transform of the curvature function is used to represent the shape. The actual matching is reduced to a minimization problem which is handled by the Levenberg-Marquardt algorithm [3]

Dynamic Estimation of Rigid Motion from Perspective Views via Recursive Identification of Exterior Differential Systems with Parameters on a Topological Manifold

We formulate the problem of estimating the motion of a rigid object viewed under perspective projection as the identification of a dynamic model in Exterior Differential form with parameters on a topological manifold. We first describe a general method for recursive identification of nonlinear implicit systems using prediction error criteria. The parameters are allowed to move slowly on some topological (not necessarily smooth) manifold. The basic recursion is solved in two different ways: one is based on a simple extension of the traditional Kalman Filter to nonlinear and implicit measurement constraints, the other may be regarded as a generalized "Gauss-Newton" iteration, akin to traditional Recursive Prediction Error Method techniques in linear identification. A derivation of the "Implicit Extended Kalman Filter" (IEKF) is reported in the appendix. The ID framework is then applied to solving the visual motion problem: it indeed is possible to characterize it in terms of identification of an Exterior Differential System with parameters living on a C0 topological manifold, called the "essential manifold". We consider two alternative estimation paradigms. The first is in the local coordinates of the essential manifold: we estimate the state of a nonlinear implicit model on a linear space. The second is obtained by a linear update on the (linear) embedding space followed by a projection onto the essential manifold. These schemes proved successful in performing the motion estimation task, as we show in experiments on real and noisy synthetic image sequences

From on-line sketching to 2D and 3D geometry: A fuzzy knowledge based system

The paper describes the development of a fuzzy knowledge based prototype system for conceptual design. This real time system is designed to infer user’s sketching intentions, to segment sketched input and generate corresponding geometric primitives: straight lines, circles, arcs, ellipses, elliptical arcs, and B-spline curves. Topology information (connectivity, unitary constraints and pairwise constraints) is received dynamically from 2D sketched input and primitives. From the 2D topology information, a more accurate 2D geometry can be built up by applying a 2D geometric constraint solver. Subsequently, 3D geometry can be received feature by feature incrementally. Each feature can be recognised by inference knowledge in terms of matching its 2D primitive configurations and connection relationships. The system accepts not only sketched input, working as an automatic design tools, but also accepts user’s interactive input of both 2D primitives and special positional 3D primitives. This makes it easy and friendly to use. The system has been tested with a number of sketched inputs of 2D and 3D geometry

First Stereoscopic Coronal Loop Reconstructions from Stereo Secchi Images

We present the first reconstruction of the three-dimensional shape of magnetic loops in an active region from two different vantage points based on simultaneously recorded images. The images were taken by the two EUVI telescopes of the SECCHI instrument onboard the recently launched STEREO spacecraft when the heliocentric separation of the two space probes was 12 degrees. We demostrate that these data allow to obtain a reliable three-dimensional reconstruction of sufficiently bright loops. The result is compared with field lines derived from a coronal magnetic field model extrapolated from a photospheric magnetogram recorded nearly simultaneously by SOHO/MDI. We attribute discrepancies between reconstructed loops and extrapolated field lines to the inadequacy of the linear force-free field model used for the extrapolation.Comment: 6 pages, 5 figure

Group Membership Prediction

The group membership prediction (GMP) problem involves predicting whether or not a collection of instances share a certain semantic property. For instance, in kinship verification given a collection of images, the goal is to predict whether or not they share a {\it familial} relationship. In this context we propose a novel probability model and introduce latent {\em view-specific} and {\em view-shared} random variables to jointly account for the view-specific appearance and cross-view similarities among data instances. Our model posits that data from each view is independent conditioned on the shared variables. This postulate leads to a parametric probability model that decomposes group membership likelihood into a tensor product of data-independent parameters and data-dependent factors. We propose learning the data-independent parameters in a discriminative way with bilinear classifiers, and test our prediction algorithm on challenging visual recognition tasks such as multi-camera person re-identification and kinship verification. On most benchmark datasets, our method can significantly outperform the current state-of-the-art.Comment: accepted for ICCV 201

Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence

We perform a multi-scale non-local geometrical analysis of the structures extracted from the enstrophy and kinetic energy dissipation-rate, instantaneous fields of a numerical database of incompressible homogeneous isotropic turbulence decaying in time obtained by DNS in a periodic box. Three different resolutions are considered: 256^3, 512^3 and 1024^3 grid points, with k_(max)η(overbar) approximately 1, 2 and 4, respectively, the same initial conditions and Re_λ ≈ 77. This allows a comparison of the geometry of the structures obtained for different resolutions. For the highest resolution, structures of enstrophy and dissipation evolve in a continuous distribution from blob-like and moderately stretched tube-like shapes at the large scales to highly stretched sheet-like structures at the small scales. The intermediate scales show a predominance of tube-like structures for both fields, much more pronounced for the enstrophy field. The dissipation field shows a tendency towards structures with lower curvedness than those of the enstrophy, for intermediate and small scales. The 256^3 grid resolution case (k_(max)η(overbar) ≈ 1) was unable to detect the predominance of highly stretched sheet-like structures at the smaller scales in both fields. The same non-local methodology for the study of the geometry of structures, but without the multi-scale decomposition, is applied to two scalar fields used by existing local criteria for the eduction of tube- and sheet-like structures in turbulence, Q and [A_ij]_+, respectively, obtained from invariants of the velocity-gradient tensor and alike in the 1024^3 case. This adds the non-local geometrical characterization and classification to those local criteria, assessing their validity in educing particular geometries. Finally, we introduce a new methodology for the study of proximity issues among structures of different fields, based on geometrical considerations and non-local analysis, by taking into account the spatial extent of the structures. We apply it to the four fields previously studied. Tube-like structures of Q are predominantly surrounded by sheet-like structures of [A_ij]_+, which appear at closer distances. For the enstrophy, tube-like structures at an intermediate scale are primarily surrounded by sheets of smaller scales of the enstrophy and structures of dissipation at the same and smaller scales. A secondary contribution results from tubes of enstrophy at smaller scales appearing at farther distances. Different configurations of composite structures are presented