Pair Of Ellipses Research Articles

Through‐the‐floor localization of a static person by a multistatic UWB radar

AbstractA new approach to through‐the‐floor localization of a static person using an ultra‐wide band (UWB) radar is introduced in this article. The proposed solution is based on a multilateration method appropriately modified for target localization by a multistatic UWB radar employing 1 transmitting (Tx) and 4 receiving antennas (Rxi). Due to an appropriate radar antenna array layout, a geometrical interpretation of the considered problem of localization allows finding the target coordinates by a simple computation of 2 intersections of 2 pairs of ellipses. The mentioned ellipses are defined by the antenna layout and time‐of‐arrivals corresponding to the target that were estimated for the particular pairs of Tx–Rxi antennas. Experimental analysis of the proposed method of through‐the‐floor localization of a person confirmed its good accuracy, despite being such a complex scenario.

Orthogonal grids on meander-like regions: A database approach

We deal with the automatic construction of orthogonal grids on meander-like regions. These are similar to riverbeds and appear naturally in geography (rivers, regions between two fixed heights in a hilly landscape) and medicine (longitudinal slices of organs such as veins and arteries). We use pairs of lemniscates of two foci and pairs of ellipses to approximate subregions of the meander-like region. A subregion determines an approximating lemniscatic or elliptic sector given by two confocal lemniscates or two ellipses from a certain family and, in both cases, two orthogonal hyperbolas. We use the fact that a sector is conformally equivalent to a region bounded by two concentric circles and two rays, to map the orthogonal grid on this disc domain, given by polar coordinates, into a grid in the approximating sector. Finally the lemniscatic and elliptic sectors that approximate the subregions are assembled to conform an orthogonal grid on the meander-like region.

Anomaly Detection in Environmental Monitoring Networks [Application Notes

We apply a recently developed model for anomaly detection to sensor data collected from a single node in the Heron Island wireless sensor network, which in turn is part of the Great Barrier Reef Ocean Observation System. The collection period spanned six hours each day from February 21 to March 22, 2009. Cyclone Hamish occurred on March 9, 2009, roughly in the middle of the collection period. Our system converts sensor measurements to elliptical summaries. Then a dissimilarity image of the data is built from a measure of focal distance between pairs of ellipses. Dark blocks along the diagonal of the image suggest clusters of ellipses. Finally, the single linkage algorithm extracts clusters from the dissimilarity data. We illustrate the model with three two-dimensional subsets of the three dimensional measurements of (air) pressure, temperature and humidity. Our examples show that iVAT images of focal distance are a reliable basis for estimating cluster structures in sets of ellipses, and that single linkage can successfully extract the indicated clusters. In particular, we are able to clearly isolate the cyclone Hamish event with this method, which demonstrates the ability of our model to detect anomalies in environmental monitoring networks.

Properties of the Bennett Mechanism Derived From the RRRS Closure Ellipse

For many single-loop closed-chain mechanisms, mobility may be characterized by the closure of sets in the theory of Lie groups. The four-revolute (4R) Bennett mechanism remains a persistent exception, requiring the formulation and expression of solutions to the loop closure relations, either directly or indirectly through spatial geometric figures. The simpler loop closure relations of the revolute-revolute-revolute-spherical (RRRS) loop, however, place conditions on the mobility of the 4R mechanism. That loop closure in turn may be interpreted as the congruence of a pair of ellipses. This new result is applied to proving the uniqueness of the Bennett mechanism along with deriving conditions where it is free from singularities. Design parameters are also identified for overconstrained RRRS mechanisms with 1DOF that are neither plane nor line symmetric. Such mechanisms, however, place the S-joint along the revolute axis of an underlying Bennett mechanism.

Discrimination of face-like patterns in the giant panda (Ailuropoda melanoleuca).

The black-and-white pattern of the giant panda's (Ailuropoda melanoleuca) fur is a conspicuous signal and may be used for mate-choice and intraspecific communication. Here the authors examined whether they have the perceptual and cognitive potential to make use of this information. Two juvenile subjects were trained on several discrimination problems in steps of increasing difficulty, whereby the stimuli required to discriminate ranged from geometric figures to pairs of differently orientated ellipses, pairs of ellipses with the same orientation but different angles, and finally discrimination of panda-like eye-mask patterns that differed only subtly in shape. Not only did both subjects achieve significant levels of discrimination in all these tasks, they also remembered discriminations for 6 months or even 1 year after the first presentation. Thus this study provided the first solid evidence of sufficient visual and cognitive potential in the giant panda to use the fur pattern or the facial masks for individual recognition, social communication, and perhaps, mate choice.

Apse Alignment of Narrow Eccentric Planetary Rings

The boundaries of the Uranian ∈, α, and β rings can be fitted by Keplerian ellipses. The pair of ellipses that outline a given ring share a common line of apsides. Apse alignment is surprising because the quadrupole moment of Uranus induces differential precession. We propose that rigid precession is maintained by a balance of forces due to ring self-gravity, planetary oblateness, and interparticle collisions. Collisional impulses play an especially dramatic role near ring edges. Pressure-induced accelerations are maximal near edges because there (1) velocity dispersions are enhanced by resonant satellite perturbations and (2) the surface density declines steeply. Remarkably, collisional forces felt by material in the last ~100 m of a ~10 km wide ring can increase equilibrium masses up to a factor of ~100. New ring surface densities are derived that accord with Voyager radio measurements. In contrast to previous models, collisionally modified self-gravity appears to allow for both negative and positive eccentricity gradients; why all narrow planetary rings exhibit positive eccentricity gradients remains an open question.

Projectively invariant decomposition and recognition of planar shapes

An algorithm is presented for computing a decomposition of planar shapes into convex subparts represented by ellipses. The method is invariant to projective transformations of the shape, and thus the ellipses can be used for matching and definition of invariants in the same way as points and lines. The method works for arbitrary planar shapes admitting at least four distinct tangents and is based on finding ellipses with four points of contact to the given shape. The cross ratio computed from the four points on the ellipse can then be used as a projectively invariant index. For a given shape, each pair of ellipses can be used to compute two independent projective invariants. The set of invariants computed for each ellipse pair can be used as indexes to a hash table from which a model hypothesis can be generated. >