Axis Representation Research Articles

The explicit representation to the principal rotation angle and the principal rotation axis

By using Cayley-Hamilton theorem, two kinds of explicit representation for the rotation tensor are proposed. One contains the lower powers of deformation gradient, by which the formula of the principal rotation angle and the explicit representation of principal axis are obtained; the other, a high efficient method to obtain the rotation tensor, does not contain the complicated coefficients and uses few variables. Some properties about the principal rotation angle and the principal rotation axis are obtained.

Obtaining medial responses from steerable filters

In building up a multiscale, medial axis representation, the generation of medial responses from a set of boundary responses at multiple scales can be a computationally intensive process. Polar separable medial weighting kernels are applied to the computation of medial responses. An approximate method for the synthesis of rotated kernels is proposed. Because of the need to not only rotate, but to displace boundary responses by an amount dependent on the image scale, the traditional steerable filter approach must be modified to yield correct medial responses. Comparisons between integral evaluation and the adaptive filtering approximations show that 100-fold increases in modestly sized images at a single scale are possible. The error in the approximation is insignificant.

Analysis of Near-Infrared Spectra of Some Carbohydrates

Infrared, in particular near-infrared (NIR) is a very useful technique for the identification and the characterization of biomolecules. The complexity of the spectra tends to make direct interpretation difficult. However, from the spectroscopic representation of the factorial axes obtained by principal component analysis (PCA) performed on different sugar molecules, it is possible to determine the characteristic wavelengths (NIR) of monosaccharides, oligosaccharides and polysaccharides. The most characteristic wavelengths for monosaccharides are found to be: 1457 nm, 2062 nm, 2263 nm and 2440 nm; and for oligo- and polysaccharides: 1432 nm, 1931 nm, 2170 MI, 2310 nm and 2477 nm. These wavelengths, which have been identified from the spectral profiles, are the most appropriate for a quantitative study of unknown carbohydrate mixtures.

Scaled medial axis representation: evidence from position discrimination task.

Previous experimental studies (e.g. Kovacs I, Julesz B. Nature (London) 1994; 370:644-646) have found enhanced contrast sensitivity at medial locations, supporting theoretical speculations that the visual system represents simple spatial regions by their medial axes. The core model (Burbeck CA, Pizer SM. Vis Res 1995;35:1917-1930) hypothesizes that the medial representation arises in a scale-specific way: the scale is determined by local object width, and it controls the resolution at which the medial locus and object width are encoded. Here we look for further evidence for a medial representation and test the idea that the resolution of the axis depends on object width. A new experimental paradigm was developed to infer sensitivity to position within individual figural regions, using circles as the figural regions. A probe dot was presented within a circle along a diameter at one location in one temporal interval and at a slightly different location on that diameter in a second temporal interval. The observer's task was to report the direction in which the probe dot had been displaced. Position discrimination thresholds were calculated and compared to two-dot separation discrimination thresholds. Data were obtained for two circle sizes. It was found that positional sensitivity was strongly enhanced near the center of the circle, and it was enhanced in a scale-dependent way. The results were tested against a scaled medial (core) model and against models assuming no medial representation. The core model was better able to account for the results.

Scaled medial axis representation: evidence from position discrimination task

Scaled medial axis representation: evidence from position discrimination task

Modelling of magnetic saturation in smooth air-gap synchronous machines

Main flux saturation in d-q axis representation of synchronous machines is at present modelled by selecting either all the winding currents or all the winding flux linkages as state-space variables. However, these two available models are just a tiny portion of the complete set of models that can be obtained by selecting other combinations of state-space variables. This paper presents a general procedure for main flux saturation modelling in smooth air-gap synchronous machines, that is applicable for most selections of state-space variables. The method relies on the concept of 'generalised flux' and 'generalised inductance', that has been successfully applied in modelling of saturated single-cage and double-cage induction machines. The concept is extended to saturation modelling in smooth air-gap synchronous machines. A number of models, that result from the application of the method for different selections of state-space variables, are presented in detail.

Contact Stress Analysis in Ball Screw Mechanism Using the Tubular Medial Axis Representation of Contacting Surfaces

A simple method is presented for analysis of contact stresses and deformation conditions between the bearing balls, screw, and nut of the ball screw mechanism. The method is based on representation of contact geometry and curvature analysis of contacting surfaces using a generalization of the medial axis transform (MAT) to tubular surfaces. Simplified Hertzian contact solutions are obtained using the curvature information. The results are approximate but do include the effect of complex thread profiles as a result of the helical grooves and are suitable for mechanical design purposes.

Direct Spectroscopic Sucrose Determination of Raw Sugar Cane Juices

A more accurate, less time-consuming, and nonpolluting spectroscopic method than the currently used HPLC or polarimetric methods is proposed for the routine quantitative determination of sucrose in complex biological samples. Opaque raw sugar cane juices representative of a sugar cane harvest are analyzed by Fourier transformed mid-infrared attenuated total reflectance, and the spectral data are processed by principal component analysis (PCA) and principal component regression (PCR). The most suitable region for the measurement of sucrose was found to be the 1250−800 cm-1 region. The spectroscopic representation of the first axis as assessed by PCA in this spectral region featured characteristic absorption bands of sucrose. By PCR on the spectral data from a calibration set, a prediction equation was established to predict sucrose content in unknown samples. Good overall predictions were obtained. The values of the predicted sucrose concentration were more accurate (bias = 0.041 g/100 mL) than those obtai...

Extraction of Characteristic Bands of Sugars by Multidimensional Analysis of Their Infrared Spectra.

Abstract Collected Mid-IR Attenuated Total Reflectance (ATR) spectra of various sugars were assessed by multidimensional statistical analysis. Through Principal Component Analysis (PCA) of collected spectra of various pure 10% sugar solutions and from the spectroscopic representation of the factorial axes, characteristic frequencies of monosaccharides and oligosaccharides were directly and automatically obtained within a few seconds. Monosugars are characterised by a hollow at 998 cm−1 and by a single unique major peak (1049 cm−1) in the 1075–1030 cm−1 region while oligosaccharides showed three characteristic bands in the same region, the major peak is shifted to 1033 cm−1. Owing to the glycosidic link vibrational motion, oligosaccharides are also characterised by a band at 998 cm−1. Spectroscopic representation of the axes issued of data from both sugar families (mixture of mono and oligosaccharides) is an average of the two individual spectral patterns. Predictive measures of concentrations of sugar solutions were performed by principal component regression (PCR) of the factorial coordinates and prediction equations were obtained. The predicted concentrations of standard 10% pure sugar solutions averaged 10. 069% and 9. 909% for monosugars and oligosugars respectively and a concentration of 10. 015% from the mixed set of data was obtained. The ability of these factorial coordinates to predict quantitative variable are good with correlation coefficients ranging from 97. 4% to 99. 9%.

Abstracts for Solid Modeling Articles in March 1996 TVCG

Abstracts for Solid Modeling Articles in March 1996 TVCG

The Curve Axis

In this paper we examine various aspects of the medial axis representation of shapes, resulting in a novel, highly accurate skeletonization algorithm suitable for shapes with parametrically described boundaries such as, for example, polygons or “spline”-gons. The medial axis representation is first shown to be efficient in calculating local boundary features. Then the problem of deciding whether an axis-like function is indeed an axis of a shape is addressed, and two necessary and locally sufficient restrictions on axis functions are derived. The proposed skeletonization approach is based on another result which shows that the medial axis is the solution of a system of first order differential equations. The new skeletonization algorithm provides a discrete parametric representation of the axis for smooth shapes, the input to the algorithm being a parametric description of the shape boundary. Skeletonization examples using the proposed algorithm are presented.

A robust parallel thinning algorithm for binary images

The class of multi-pass iterative thinning algorithms is considered. A new algorithm in the same class is proposed and is shown, on the basis of experimental results, to be superior to the existing ones with respect to medial axis representation and robustness. Some basic properties of thinning like 1 pixel thickness, preservation of connectivity for the present algorithm are ensured for which theoretical proofs are also given.

On condition numbers and algorithms for determining a rigid body movement

Using a set of landmarks to represent a rigid body, a rotation of the body can be determined in least-squares sense as the solution of an orthogonal Procrustes problem. We discuss some geometrical properties of the condition number for the problem of determining the orthogonal matrix representing the rotation. It is shown that the condition number critically depends on the configuration of the landmarks. The problem is also reformulated as an unconstrained nonlinear least-squares problem and the condition number is related to the geometry of such problems. In the common 3-D case, the movement can be represented by using a screw axis. Also the condition numbers for the problem of determining the screw axis representation are shown to closely depend on the configuration of the landmarks. The condition numbers are finally used to show that the used algorithms are stable.

The re-establishment of the representation of the dorso-ventral retinal axis in the chiasmatic region of the ferret.

This study has examined the representation of the dorso-ventral retinal axis in the optic nerve and tract of the ferret, as well as the associated fiber transformations which take place within the chiasmatic region. In one series of experiments, dorsal or ventral retinal lesions were made to induce fiber degeneration along the pathway, from which semi-thin sections were then stained for degenerating myelin. In a second series, implants of the carbocyanine dye, DiI, were made into the caudo-medial or rostro-lateral optic tract in order to label retrogradely the axons as they course through the chiasmatic region. Additional observations were made from the optic pathways of ferrets that had been similarly lesioned or implanted, but employing either a reduced-silver technique to reveal the degenerating axons or horseradish peroxidase as the retrograde label. The axons arising from the dorsal and ventral retina course in the dorsal and ventral parts of the optic nerve posterior to the eye, but as they continue along the nerve they disperse producing a highly impoverished retinotopy in the prechiasmatic portion of the nerve. As they course through the chiasmatic region, however, they become segregated again: dorsal fibers cross the midline relatively caudally while ventral fibers cross further rostrally, although there is overlap between them. Nearer the threshold of the optic tract, the fibers from dorsal and ventral retina undergo a further and more striking segregation, placing the dorsal fibers caudo-medially and the ventral fibers rostro-laterally within the tract. This re-emergence of retinotopic order implicates a fiber-substrate interaction as being responsible for the axonal reordering, and suggests that fiber pre-ordering in the tract contributes to the formation of the orderly projection of the dorso-ventral retinal axis upon central visual targets.

Parallel computational geometry of rectangles

Rectangles in a plane provide a very useful abstraction for a number of problems in diverse fields. In this paper we consider the problem of computing geometric properties of a set of rectangles in the plane. We give parallel algorithms for a number of problems usingn processors wheren is the number of upright rectangles. Specifically, we present algorithms for computing the area, perimeter, eccentricity, and moment of inertia of the region covered by the rectangles inO(logn) time. We also present algorithms for computing the maximum clique and connected components of the rectangles inO(logn) time. Finally, we give algorithms for finding the entire contour of the rectangles and the medial axis representation of a givenn × n binary image inO(n) time. Our results are faster than previous results and optimal (to within a constant factor).

One-pass parallel thinning: analysis, properties, and quantitative evaluation

A one-pass parallel thinning algorithm based on a number of criteria, including connectivity, unit-width convergence, medial axis approximation, noise immunity, and efficiency, is proposed. A pipeline processing model is assumed for the development. Precise analysis of the thinning process is presented to show its properties, and proofs of skeletal connectivity and convergence are provided. The proposed algorithm is further extended to the derived-grid to attain an isotropic medial axis representation. A set of measures based on the desired properties of thinning is used for quantitative evaluation of various algorithms. Image reconstruction from connected skeletons is also discussed. Evaluation shows that the procedures compare favorably to others.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Pattern recognition applied to transient stability analysis of power systems with modelling including voltage and speed regulation

A pattern recognition approach to analyse transient stability using a higher order model is presented. A six order model based on two axis representation for generators including voltage and governor actions is described. Two pattern vectors based on physical considerations about the system behaviour are derived and several approximations on system trajectory are considered to deduce analytical formulas which can be computed quickly. To alleviate computational time, two discriminant analysis methods allowing reduction of pattern vectors are presented. These results are applied to an eight machine system with a three phase fault. The discriminatory power of the pattern vectors proposed is tested with Bayes classifier and the k nearest neighbour rule. A comparison is given.

Medial axis representation and encoding of scanned documents

The medial axis transform (MAT) is a sparse representation of shape, which, being reversible, has potential for binary image compression. The MAT also provides structural information not accessible with alternative binary image codes. This structural information is often used for line extraction and pattern recognition. Therefore, the MAT occupies an interesting middle ground between lower-level, compressible image codes and higher-level, meaningful image representations. In an attempt to realize this middle ground, a MAT-based coding scheme which respects its structural properties is developed. The MAT-based coding method is applied to the CCITT facsimile test images. The resulting compression is comparable to that of known coding schemes for textual and somewhat better for graphical data. Some simple modifications to improve skeleton coding performance are suggested. To substantiate the claim that the MAT is effective for higher-level processing, the representation is extended to perform line segment and curve extraction. The extraction takes place under the control of a global error tolerance parameter and thus provides a new method to trade off data compression with distortion for binary images.

Graphical Presentations of Data Envelopment Analyses: Management Implications from Parallel Axes Representations*

ABSTRACTThe conversion of multivariate data analysis into information that managers can readily use in their decision making has always been a challenging task. In this paper we provide a parallel axis representation of multivariate data and demonstrate how this representation may be used as a tool for implementing the results of data envelopment analysis. We use an analysis of the efficiency of electricity generating plants to illustrate the technique.

Determining motion from 3D line segment matches: a comparative study

Motion estimation is a very important problem in dynamic scene analysis. Although it is easier to estimate motion parameters from 3D data than from 2D images, it is not trivial, since the 3D data we have are almost always corrupted by noise. A comparative study on motion estimation from 3D line segments is presented. Two representations of line segments and two representations of rotation are described. With different representations of line segments and rotation a number of methods for motion estimation are presented, including the extended Kalman filter a general minimization process and the singular value decomposition. These methods are compared using both synthetic and real data obtained by a trinocular stereo. It is observed that the extended Kalman filter with the rotation axis representation of rotation is preferable. Note that all methods discussed can be directly applied to 3D point data.