Line Segment Approximation Research Articles

Multilevel Feature Selection Method for Improving Classification of Microarray Gene Expression Data

Microarray gene expression profiles provide valuable answers to a variety of problems, and contributes to advances in clinical medicine. Gene expression data typically has a high dimension and a small sample size. Gene selection from microarray gene expression data is a challenge due to high dimensionality of the data. The number of samples in the microarray dataset is much smaller compared to the number of genes as features. To extract useful gene information from cancer microarray data and reduce dimensionality, selection of significant genes is necessary. An effective method of gene feature selection helps in dimensionality reduction and improves the classification performance. Experimental results suggest that appropriate combination of filter gene selection methods is more effective than individual techniques for microarray data classification. In this paper, we propose a two-layered feature selection method. In the first layer, t-test statistical method is used to remove the features that have little correlation with the classification results. In the second layer, line segment approximation method is used to transform the feature subset into a less dimensional feature space. Four well known classifiers kNN, SVM, NBC, DT were used to verify the performance of the proposed feature selection algorithm on binary class microarray data. The experimental results show that the proposed method can effectively select relevant gene subsets, and achieves higher classification accuracy.

Surface-based modeling of muscles: Functional simulation of the shoulder

Musculoskeletal simulations are an essential tool for studying functional implications of pathologies and of potential surgical outcomes, e.g., for the complex shoulder anatomy. Most shoulder models rely on line-segment approximation of muscles with potential limitations. Comprehensive shoulder models based on continuum-mechanics are scarce due to their complexity in both modeling and computation.In this paper, we present a surface-based modeling approach for muscles, which simplifies the modeling process and is efficient for computation.We propose to use surface geometries for modeling muscles, and devise an automatic approach to generate such models, given the locations of the origin and insertion of tendons. The surfaces are expressed as higher-order tensor B-splines, which ensure smoothness of the geometrical representation. They are simulated as membrane elements within a finite element simulation. This is demonstrated on a comprehensive model of the upper limb, where muscle activations needed to perform desired motions are obtained by using inverse dynamics.In synthetic examples, we demonstrate our proposed surface elements both to be easy to customize (e.g., with spatially varying material properties) and to be substantially (up to 12 times) faster in simulation compared to their volumetric counterpart. With our presented automatic approach of muscle wrapping around bones, the humeral head is exemplified to be wrapped physiologically consistently with surface elements. Our functional simulation is shown to successfully replicate a tracked shoulder motion during activities of daily living.We demonstrate surface-based models to be a numerically stable and computationally efficient compromise between line-segment and volumetric models, enabling anatomical correctness, subject-specific customization, and fast simulations, for a comprehensive simulation of musculoskeletal motion.

Inversion of temporal gravity changes by the method of local corrections: A case study from Mayon volcano, Philippines

The 3D inversion method based on local corrections has been introduced by Prutkin to invert potential field data. It has been applied to gravity data inversion on local, regional, and global scales. Here we introduce the application of this method to invert temporal gravity changes. The inversion procedure is demonstrated by a case study on gravity changes observed at the Mayon stratovolcano between campaigns spanning a period of 1992–1996. Residual gravity changes are compiled from the observed ones. No significant surface deformation was observed within the accuracy of the campaign GPS measurements during the considered period. Residual gravity changes were first inverted in terms of sources represented by 3D line segments. The line segment approximation facilitates the second step of the iterative non-linear inversion based on local corrections. In the second step, the residual gravity changes were inverted in terms of 3D star-convex homogenous bodies representing sources of subsurface mass/density changes. Published geological evidence indicates a shallow magma system at Mayon. The absence of significant deformation accompanying the gravity changes indicates that this system was nearly open during 1992–1996. We hypothesize that the sources of the gravity signal represent mass transport, namely injection of magma into voids of the shallow system. Inversion results for campaign differences 3–1 and 4–1 are presented. For both epochs the inversion results in a source located at a depth of about 4.4km (±0.3km) below sea level. The mass of injected magma was estimated at 0.35 (±0.10)MU and 0.12 (±0.04)MU for the two epochs, respectively. We also compare our results with previous interpretations of the same data.

Measuring positional error of circular curve features in Geographic information systems (GIS)

This paper addresses the task of modeling positional uncertainty of circular features. The specific interest provided by this study is the consideration of the actual curve function in the measurement of circular curve error. This approach differs from the existing methods based on line segment approximation. A least-squares adjustment method, composed of a series of discrete points and the covariance of these parameters, is adopted to estimate the parameters of a circular curve. Two geometric measures are developed, based on the error ellipses of the points on the circular curve: the standard deviation-based measure and the maximum distance-based measure. A comparison of the two measures for circular curves was conducted by means of a simulation experiment. The implementation of the two geometric measures is further illustrated by two case studies; one describes the positional error of digital shorelines and the other digitizes circular road curves.

INVESTIGATION ON MULTISETS MIXTURE LEARNING BASED OBJECT DETECTION

By minimizing the mean square reconstruction error, multisets mixture learning (MML) provides a general approach for object detection in image. To calculate each sample reconstruction error, as the object template is represented by a set of contour points, the MML needs to inefficiently enumerate the distances between the sample and all the contour points. In this paper, we develop the line segment approximation (LSA) algorithm to calculate the reconstruction error, which is shown theoretically and experimentally to be more efficient than the enumeration method. It is also experimentally illustrated that the MML based algorithm has a better noise resistance ability than the generalized Hough transform (GHT) based counterpart.

AUTOMATIC FEATURE EXTRACTION AND CLASSIFICATION OF CROSSBILL (LOXIA SPP.) FLIGHT CALLS

ABSTRACT In this paper a new method for the automatic classification of bird sounds is presented. Our method is based on acoustic parameters (features) taken from the first harmonic component computed from the sound spectrogram. The features are based on a line segment approximation of the first harmonic component. The final feature vectors, consisting of 16 real numbers, are then classified using a self-organizing map (SOM) neural network. Flight calls of four crossbill species (Loxia spp.) are used as a test example. In the first phase, an unsupervised network was trained and tested using common crossbill L. curvirostra flight calls recorded mainly in the Netherlands. The network was tested using two-barred L. leucoptera, Scottish L. scotica and parrot L. pytyopsittacus crossbill flight calls in the second phase. Finally, the results were validated applying the same network to flight calls of common crossbills and parrot crossbills recorded in Finland. The method automatically separated common crossbill flight calls from those of parrot crossbills. The classification accuracy of the Dutch recordings was 58% in the first phase and 54% in the second phase. The Finnish recordings were classified with 54% accuracy.

Improving convergence of the PNLMS algorithm for sparse impulse response identification

A proportionate normalized least mean square (PNLMS) algorithm has been proposed for sparse impulse response identification. It provides fast initial convergence, but it begins to slow down dramatically after the initial period. In this letter, we analyze the coefficient adaptation process of the steepest descent algorithm and derive how to calculate the optimal proportionate step size in order to achieve the fastest convergence. The results bring forward a novel view of the concept of proportion. We propose a /spl mu/-law PNLMS (MPNLMS) algorithm using an approximation of the optimal proportionate step size. Line segment approximation and partial update techniques are discussed to bring down the computational complexity.

Numerically Controlled Machining of Freeform Curves Using Biarc Approximation

To machine a shape incorporating freeform curves, the freeform curves must be approximated and represented in a form suitable for numerically controlled (NC) tool-path generation. Instead of the commonly used line segment approximation, a new method using biarc approximation is presented here. The purpose is to reduce sudden changes in tool movement and increase continuity and smoothness. A biarc can be described as two consecutive circular arcs with an identical tangent at the connecting point. Therefore, tangent continuity can be maintained. Furthermore, curvature continuity can be improved if the difference between the two curvatures is minimised. In this research, biarc segments are used to approximate the freeform curves by controlling the largest deviation distance between the curves and the biarcs. The test results show that the biarc approximation method generates fewer tool-path segments than the traditional line approximation. The definitions of the biarcs are used to generate NC tool paths. A new tool-path generation method is developed for processing rough cutting and finish cutting paths. Example parts modelled with B-spline curves are tested and machined.

Envelope matching with genetic algorithms

Abstract This paper introduces a genetic algorithm‐based method for envelope modeling. The new method selects a set of basis envelopes from the original tone that best represent all the harmonic amplitude envelopes. The method yields much more intuitive envelopes than statistical methods like principal components analysis, and the quality of the matches is about the same. We give results using the method for the trumpet, Chinese erhu, and pipa. We show how to extend the technique to matching frequency envelopes and multiple tones using the same basis envelope set. We also show how to use the procedure as a preprocessing step to line segment approximation of the envelopes.

Analysis of the Precision of Generalized Chain Codes for the Representation of Planar Curves

This paper examines a set of line-segment approximation codes for the representation of planar curves (the so-called generalized chain codes) and shows that the average quantization error (measure of code's precision) is directly proportional to the grid size and is independent of the form of the code. Thus, to achieve a desired level of precision for the representation of a line drawing, only the size of the grid need be determined; the form of the code can be chosen on the basis of other criteria, such as compactness, smoothness, or relative ease of encoding and processing.

Perceptual evaluations of synthesized musical instrument tones

An analysis-based synthesis technique for the computer generation of musical instrument tones was perpetually evaluated in terms of the discriminability of 16 original and resynthesized tones taken from a wide class of orchestral instruments having quasiharmonic series. The analysis technique used was the heterodyne filter—which produced a set of intermediate data for additive synthesis, consisting of time-varying amplitude and frequency functions for the set of partials of each tone. Three successive levels of data reduction were applied to this intermediate data, producing types of simplified signals that were also compared with the original and resynthesized tones. The results of this study, in which all combinations of signals were compared, demonstrated the perceptual closeness of the original and directly resynthesized tones. An orderly relationship was found between the form of data reduction incurred by the signals and their relative discriminability, measured by a modified AAAB discrimination procedure. Direct judgments of the relative sizes of the differences between the tones agreed with these results; multidimensional scaling of the latter data provided a visual display of the relationships among the different forms of tones and pointed out the importance of certain small details existing in the attack segments of tones. Of the three forms of simplification attempted with the tones, the most successful was a line-segment approximation to time-varying amplitude and frequency functions for the partials. The pronounced success of this modification strongly suggests that many of the microfluctuations usually found in the analyzed physical attributes of music instrument tones have little perceptual significance.

The Logarithmic Tunnel Diode Amplifier

This paper describes design techniques and performance characteristics of a high-frequency logarithmic amplifier. The technique used is to sum the detected outputs of each amplifier in a cascade in order to generate a straight line segment approximation to the desired logarithmic responses. It is shown that the normal RF characteristics of tunnel diode amplifiers approximate this performance when operated at minimum negative resistance. A 3.05 GHz tunnel diode amplifier is designed using these principles, and its performance is described in this paper. It is shown that the amplifier has an experimental error of /spl plsmn/0.625 dB over a compression range of 60 dB input signal power.

The Nature of and System Inferences of Delay Distortion Due to Mode Conversion in Multimode Transmission Systems

Quantitative estimates of delay distortion due to mode conversion in a multimode medium are made using an analysis based on modes coupled through power-transfer coefficients. This results in a simple translation from the spatial distribution of mode conversion to delay distortion without an intermediate step in the frequency domain. The expected value of the reconversion magnitude and its delay distribution relative to a driving impulse are found for (i) the case where the undesired mode loss is distributed (helix damped modes and higher-order circular electric modes) and (ii) the case where discrete mode filters are inserted (as in smooth-walled waveguide). Numerical estimates are given for TE 01 in 2-inch I.D. guides at 55 kmc. For both cases the power in the reconversion echo varies directly as the system length, and the shape of the echo is independent of length. For the case of distributed undesired mode loss the echo to impulse-excitation has an exponential shape in relative delay τ, varying as e−τ/τ 0, and for the case of partially absorbing mode filters the echo is a line-segment approximation to an exponential in τ (Fig. 4). The characteristic delay constant τ 0 is about 0.035 nanosecond for helix damped modes in an all-helix line, and is about 0.106 microsecond for TE 02 in either helix or smooth-walled guide. For solid-walled guide with mode filters every 300 feet the characteristic delay constant (similar to τ 0 ) is about 2 nanoseconds. Estimates are made for signal interference effects from such echoes, taking account of the fact that the most limiting requirements on echoes in some system arrangements occur at τ ≫ τ 0 , where the reconversion power is small. For PCM in smooth-walled copper waveguide with mode filters every 300 or 150 feel, it is concluded that pulse rates of 200 or 400 megabits might be used, with up to 20 or 40 miles respectively between regenerators; beat wavelength straightness variation mode conversion is controlling. for PCM in an all-helix waveguide, it is confluded that a pulse rate up to 5000 megabits and up to 746 miles between regenerators is permitted by mode conversion effects; diameter variations (TE02 conversion) are controlling. For transmission of frequency division multiplex multiplex via a frequency-modulated carrier (FDM-FM), estimates based on the discrete-echo theory of Bennett, Curtis and Rice suggest that 4000-mile transmission of 2000 channel groups is possible in all-helix waveguide; diameter variations are controlling. An rms frequency deviations (σ) increase the allowed system length (z) according to z ≈ (σ)2.8 Even in solid-walled waveguide there is a good prospect for 4000-mile FDM-FM using guide toleraces already achievable. Separate consideration is being given to delay distortion due to wave-guide cutoff dispersion, which will be appreciable in some configurations described and will require equalization.

Transient Response of a Nonlinear System by a Bilinear Approximation Method

Abstract A line-segment approximation for a nonlinear elastic force has been developed which makes it possible to obtain analytical solutions to a number of transient-load problems which formerly could be solved only by graphical or numerical methods. It is shown that for many problems involving even large nonlinearities, two line segments only are sufficient to give satisfactory accuracy. For some problems where the classical analytical approximate methods of Lindstedt or of Kryloff and Bogoliuboff can be applied, it is shown that the bilinear method leads to an improved accuracy.