Edge Discontinuities Research Articles

Image Denoising Using Derotated Complex Wavelet Coefficients

A method for removing additive Gaussian noise from digital images is described. It is based on statistical modeling of the coefficients of a redundant, oriented, complex multiscale transform. Two types of modeling are used to model the wavelet coefficients. Both are based on Gaussian scale mixture (GSM) modeling of neighborhoods of coefficients at adjacent locations and scales. Modeling of edge and ridge discontinuities is performed using wavelet coefficients derotated by twice the phase of the coefficient at the same location and the next coarser scale. Other areas are modeled using standard wavelet coefficients. An adaptive Bayesian model selection framework is used to determine the modeling applied to each neighborhood. The proposed algorithm succeeds in providing improved denoising performance at structural image features, reducing ringing artifacts and enhancing sharpness, while avoiding degradation in other areas. The method outperforms previously published methods visually and in standard tests.

Laser-induced focused ultrasound for nondestructive testing and evaluation

Focused ultrasound pulses generated by photoacoustic transformation at a metal surface immersed in water possess a pronounced compression phase on the nanosecond time scale. For 8 ns laser pump pulses, the spectrum of the initially generated ultrasonic pulse covered a frequency range between 0.1 and 150 MHz. A concave spherical geometry of the light-absorbing metal surface can be used to achieve focusing. In the present experiments a conical ultrasound beam was directed at a solid glass plate or silicon wafer, where the tilt of the normal of the metal mirror defined the efficiency of mode conversion at the water-solid interface. Depending on the configuration, focused bulk waves as well as Rayleigh and Lamb waves could be launched in the sample with this setup. The laser probe-beam-deflection method was employed for local detection of elastic disturbances at the sample surface. Due to the nonlinear elastic response of water and harmonics generation, frequencies >100 MHz were realized, despite a strong attenuation in this frequency range. Gradual increase of the laser power density from 5 to 14 MW/cm2 led to shock formation in the compressive pressure pulse in water and shortening of the Rayleigh pulse induced at the surface of the glass plate. The observed transient surface profiles were highly sensitive to nearby mechanical discontinuities such as a microcrack in glass or an edge discontinuity in silicon. Therefore, laser-induced focused ultrasound seems to be a very promising method of accomplishing diverse tasks of nondestructive evaluation.

Data processing issues in large‐area GPR surveys: correcting trace misalignments, edge discontinuities and striping

AbstractGround‐penetrating radar (GPR) lags behind other archaeogeophysical methods in terms of speed, efficiency and ability to produce clean site‐wide composites owing to complex and time‐consuming data processing requirements. Two North American case studies illustrate problems that occur when survey is conducted over long and short periods of time. Some GPR defects have been blamed on differential solar heating of antennae and battery power levels but we show these effects to be negligible. Major problems include gradual changes over time in ground moisture and low‐level background noise, which can create discontinuities between adjacent survey blocks when data are collected at different times. These problems are often remedied by globally aligning traces using a stable trace position. Variations in ground moisture through time also cause differences in reflection amplitudes, necessitating different range gain curves to match amplitudes between survey blocks. In some cases changes in ground moisture cause noticeable differences in velocity between survey blocks requiring time‐scales to be converted to depths to correctly match the data. These problems must be remedied before horizontal slicing can be considered. Subsequent image processing may also be necessary to generate a seamless mosaic and eliminate striping artefacts commonly seen in slice maps. The latter are probably caused by antenna lift and tilt and can be removed by a de‐striping algorithm that uses a one‐dimensional low‐pass filter to characterize stripes followed by their subtraction from the data. Copyright © 2008 John Wiley & Sons, Ltd.

Apparent Motion by Edge Discontinuities

When the eyes move vertically across a jagged diamond, a local shift (LS) of edge discontinuities and a global shape distortion (GD) (ie expansion/contraction opposite to that expected by the aperture effect) are perceived. These phenomena cannot be accounted for by a local motion signals integration rule based either on the intersection of constraint lines or on the velocity vector summation. The threshold for GD perception and the salience of LS and GD (1 to 10 scale) were measured in two experiments by different methods and displays. In experiment 1 we induced GD through mimicking LS with a kinetic pattern constituted of a set of circular illusory apertures revealing drifting gratings. The point of subjective equality for compression/expansion was reached for gratings the linear extrapolations of which form an angle of 94.4 degrees. In experiment 2 observers followed a dot moving along the vertical elongation axis of a static jagged diamond (with 70 degrees or 90 degrees angles), varying in the shape (triangular, wave, square), frequency, and amplitude of edge discontinuities. GD scores were correlated with LS scores that were inversely related to frequency/amplitude ratios of triangular edge discontinuities. Data are partially accounted for by averaging neighbouring local motion-capture vectors. Results prove that there are strong interrelations between phenomena in which visual motion affects visual localisation and phenomena involving apparent deformation of global shape.

Fingerprint lines may not directly affect SA-I mechanoreceptor response

Understanding how skin microstructure affects slowly adapting type I (SA-I) mechanoreceptors in encoding edge discontinuities is fundamental to understanding our sense of touch. Skin microstructure, in particular papillary ridges, has been thought to contribute to edge and gap sensation. Cauna's 1954 model of touch sensibility describes a functional relationship between papillary ridges and edge sensation. His lever arm model proposes that the papillary ridge (exterior fingerprint line) and underlying intermediate ridge operate as a single unit, with the intermediate ridge acting as a lever which magnifies indentation imposed at the papillary ridge. This paper contests the validity of the lever arm model. While correctly representing the anatomy, this mechanism inaccurately characterizes the function of the papillary ridges. Finite element analysis and assessment of the critical anatomy indicate that papillary ridges have little direct effect on how SA-I receptors respond to the indentation of static edges. Our analysis supports a revised (stiff shell–elastic bending support) interpretation where the epidermis is split into two major layers with a stiff, deformable shell over an elastic bending support. Recent physiological, electrophysiological, and psychophysical findings support our conclusion that the function of the intermediate ridge is distinct from the function of the papillary ridge.

Incremental theory of diffraction for complex point source illumination

The complex point source (CPS) is a solution of the Helmholtz equation obtained by analytical continuation of the free‐space Green's function for complex position of the point source. The CPS representation of radiated fields can be used within a ray code to predict the interaction between an antenna and its actual environment, when standard diffraction formulations are extended to the CPS illumination. In the past, ray‐based diffraction theories such as the geometrical theory of diffraction and its uniform version (UTD) were extended to complex point source fields, leaving, however, open some problematic issues concerning the “complex ray tracing”. In this paper, the generalization of the incremental theory of diffraction (ITD) to CPS is formulated. The total field scattered by the object is given in terms of line integration along edge discontinuities of ITD diffraction coefficients plus the discontinuous geometrical optics (GO). An incremental form of the discontinuous GO is also proposed to overcome GO “complex ray tracing” difficulties. The final formulation is very simple and leads to accurate results that are successfully validated by comparison against a method of moment solution.

Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques

This paper introduces and analyzes new approximation procedures for bivariate functions. These procedures are based on an edge-adapted nonlinear reconstruction technique which is an intrinsically two-dimensional extension of the essentially non-oscillatory and subcell resolution techniques introduced in the one-dimensional setting by Harten and Osher. Edge-adapted reconstructions are tailored to piecewise smooth functions with geometrically smooth edge discontinuities, and are therefore attractive for applications such as image compression and shock computations. The local approximation order is investigated both in L p and in the Hausdorff distance between graphs. In particular, it is shown that for general classes of piecewise smooth functions, edge-adapted reconstructions yield multiscale representations which are optimally sparse and adaptive approximations with optimal rate of convergence, similar to curvelets decompositions for the L 2 error.

Simulation and optimization of GaN-based metal-oxide-semiconductor high-electron-mobility-transistor using field-dependent drift velocity model

Undoped GaN-based metal-oxide-semiconductor high-electron-mobility-transistors (MOS-HEMTs) with atomic-layer-deposited Al2O3 gate dielectrics are fabricated with gate lengths from 1 μm up to 40 μm. With a two-dimensional numerical simulator, we report simulation results of the GaN-based MOS-HEMTs using field-dependent drift velocity model. A developed model, taking into account polarization-induced charges and defect-induced traps at all of the interfaces and process-related trap levels of bulk traps measured from experiments, is built. The simulated output characteristics are in good agreement with reported experimental data. The effect of the high field at the drain-side gate edge and bulk trap density of GaN on the output performance is discussed in detail for the device optimization. AlGaN/GaN/AlN quantum-well (QW) MOS-HEMTs have been proposed and demonstrated based on numerical simulations. The simulation results also link the current collapse with electrons spreading into the bulk, and confirm that a better electron localization can dramatically reduce the current collapse for the QW-MOS-HEMTs. Due to the large band edge discontinuity and effective quantum confinement of the AlGaN/GaN/AlN quantum well, the parasitic conduction in the bulk is completely eliminated.

Contact problem for a plane crack under a normally incident antiplane shear wave

The contact-interaction problem for a stationary plane crack with friction between its edges under the action of a normal (to the crack plane) harmonic shear wave is addressed. Antiplane deformation conditions are considered. The distribution of contact forces and displacement discontinuity of crack edges are studied

An approach for edge matching large-area satellite image classifications

Large-area land cover mapping based on remotely sensed data often requires combining individual or large groups of classified images to produce final map products. Operational and logistical considerations are typically confronted when classifying medium spatial resolution satellite imagery (i.e., Landsat), with the mapping partitioned by spectral, ecological, or political considerations, or combinations thereof. Visual discontinuities can emerge at the locations where logistically based production zones join. Transparent and systematic approaches for addressing discontinuities are desired for the Earth Observation for Sustainable Development of Forests (EOSD) project. This large-area land cover mapping project is producing map products for Canada's forested ecozones. A distributed implementation plan, largely based on grouping provincial and territorial political units, was followed for production. Scene-to-scene discontinuities are rare within each production zone and are primarily related to image acquisition date and phenological state. In contrast, discontinuities can emerge at the production zone boundaries because of differences in support data available or more commonly because of differences in the attribution of density classes. Of the over 475 scenes classified for the EOSD project, it is estimated that fewer than 30 (about 6.3% of total) will require processing to minimize the cross-boundary discontinuity. Options for mitigating the discontinuities are described and demonstrated in the context of different scenarios of overlap found along the EOSD production zone boundaries (complete overlap, partial overlap, and no overlap) using two subsets of a Landsat scene along the shared provincial border between British Columbia and Alberta, Canada. Analysis of image gradients provides a quantitative basis for identification of discontinuities and also relates the results of the likelihood-based relabelling process. Through this process, only density descriptors of cover types are altered, largely maintaining classification integrity. The process as presented is generic and is suitable for addressing edge discontinuities that can emerge when undertaking a large-area land cover classification project.

Structure-Based Modulation of Inhibition of Return is Triggered by Object-Internal but not Occluding Shape Features

When attention is oriented to an object it is inhibited from returning to the same object following a short delay. This inhibition-of-return (IOR) effect is modulated by an edge discontinuity presented between cue and target--an effect referred to as structure-based modulation of IOR. Here we examined two alternative accounts for the structure-based modulation effect. On one account the modulation is caused by the presence of any intervening feature between cue and target. On another account the modulation is caused by edge-bounded (i.e., closed) regions of space, on which space-based selection mechanisms operate. We presented cues and targets on unsegmented and internally or externally segmented rectangles to examine the two alternative accounts for the effect. Contrary to the predictions of the two alternative accounts, structure-based modulation of IOR was found with the internally but not with the externally segmented displays. This supports our hypothesis that object-based IOR arises from perceptually complete and internally structured object representations.

P-doped μc-Si:H window layers prepared by hot-wire CVD for amorphous solar cell application

We report on boron-doped μc-Si:H films prepared by hot-wire chemical vapor deposition (HWCVD) using silane as a source gas and trimethylboron (TMB) as a dopant gas and their incorporation into all-HW amorphous silicon solar cells. The dark conductivity of these films was in the range of 1–10 (Ω cm) −1 . The open circuit voltage V oc of the solar cells was found to decrease from 840 mV at low hydrogen dilution H-dil=91% to 770 mV at high H-dil =97% during p-layer deposition which can be attributed to the increased crystallinity at higher H-dil and to subsequent band edge discontinuity between μc-Si:H p- and amorphous i-layer. The short circuit current density J sc and the fill factor FF show an optimum at an intermediate H-dil and decrease for the highest H-dil. To improve the conversion efficiency and the reproducibility of the solar cells, an amorphous-like seed layer was incorporated between TCO and the bulk p-layer. The results obtained until now for amorphous solar cells with and without the seed layer are presented. The I–V parameters for the best p–i–n solar cell obtained so far are J sc =13.95 mA/cm 2 , V oc =834 mV, FF=65% and η =7.6%, where the p-layers were prepared with 2% TMB. High open circuit voltages up to 847 mV could be achieved at higher TMB concentrations.

Doubling of conductance steps in Si∕SiO2 quantum point contact

We have calculated the effect of the oxidation-induced strain on the ballistic conductance in a Si∕SiO2 quantum point contact. The strain-induced deformation potential was calculated semiempirically using a viscoelastic continuum model. The charge carriers are confined to the corners of the waveguide by both the strain-induced deformation potential and the Si∕SiO2 band edge discontinuity. As a consequence nearly degenerate symmetric and antisymmetric transverse states are formed for the Si [001] minima. This additional degeneracy within the Landauer-Büttiker formalism leads to doubling of conductance steps for electrons in the [001] minima which govern the conductance near the cutoff energy. Due to the additional strain-induced confinement, the effective channel width of the quantum point contact is smaller and therefore the conductance steps are sharper.

Combined edge detection using wavelet transform and signal registration

This paper presents a novel edge detection algorithm, using Haar wavelet transform and signal registration. The proposed algorithm has two stages: (a) adaptive edge detection with the maximum entropy thresholding technique on time-scale plane and (b) edge linkage into a contour line with signal registration in order to close edge discontinuities and calculate a confidence index for contour linkages. This index measures the level of confidence in the linkage of two adjacent points in the contour structure. Experimenting with synthetic images, we found out the lower level of confidence can be set to approximately e −2. The method was tested on 200 synthetic images at different signal-to-noise ratios (SNRs) and 11 clinical images. We assessed its reliability, accuracy and robustness using the mean absolute distance (MAD) metric and our confidence index. The results for MAD on synthetic images yield the mean of 0.7 points and standard deviation (std) of 0.14, while the mean confidence level is 0.48 with std of 0.19 (the values are averaged over SNRs from 3 to 50 dB each in 20 Monte-Carlo runs). Our assessment on clinical images, where the references were expert’s annotations, give MAD equal 1.36 ± 0.36 (mean ± std) and confidence level equal 0.67 ± 0.25 (mean ± std).

Wavelet-domain approximation and compression of piecewise smooth images

The wavelet transform provides a sparse representation for smooth images, enabling efficient approximation and compression using techniques such as zerotrees. Unfortunately, this sparsity does not extend to piecewise smooth images, where edge discontinuities separating smooth regions persist along smooth contours. This lack of sparsity hampers the efficiency of wavelet-based approximation and compression. On the class of images containing smooth C2 regions separated by edges along smooth C2 contours, for example, the asymptotic rate-distortion (R-D) performance of zerotree-based wavelet coding is limited to D(R) (< or = 1/R, well below the optimal rate of 1/R2. In this paper, we develop a geometric modeling framework for wavelets that addresses this shortcoming. The framework can be interpreted either as 1) an extension to the "zerotree model" for wavelet coefficients that explicitly accounts for edge structure at fine scales, or as 2) a new atomic representation that synthesizes images using a sparse combination of wavelets and wedgeprints--anisotropic atoms that are adapted to edge singularities. Our approach enables a new type of quadtree pruning for piecewise smooth images, using zerotrees in uniformly smooth regions and wedgeprints in regions containing geometry. Using this framework, we develop a prototype image coder that has near-optimal asymptotic R-D performance D(R) < or = (log R)2 /R2 for piecewise smooth C2/C2 images. In addition, we extend the algorithm to compress natural images, exploring the practical problems that arise and attaining promising results in terms of mean-square error and visual quality.

Numerical analysis of Lamb wave generation in piezoelectric composite IDT

An equivalent, single-layer model for Lamb wave generation by interdigital transducer (IDT) on composite host structures is developed. The additional complexities generally encountered while launching the surface acoustic wave (SAW) on composite structure, such as the coupling between the Lamb wave modes, the complicated nature of the electromechanical actuation etc. are considered. The model of infinite IDT is extended to deal with the finite IDT with edge discontinuities. The effect of electromechanical actuation on the wavelength shifts with respect to the passive case is investigated. The problem of electrically driven instability within the IDT is analyzed. Numerical results are reported by considering a model of the IDT integrated with the host structure, which shows that there are significant deviations from the conventional design estimates while launching a targeted mode. The proposed approach may enable one to obtain new designs in material systems and geometry that avoid mode-mixing, or to introduce it by choice.

Recovering depth-order from orientation-defined junctions

This study investigated how visual systems recover depth-order from orientation-defined junctions. Stimuli were superimposed stripes defined by Gabor micro-patterns (Gabors). In one stripe (random stripe), Gabor orientation was randomly selected from a given range, while in the other (constant stripe) it was selected so as to be different from the mean orientation of the random stripe by 90 degrees . Observers reported which of the two stripes, the right- or left-tilted one, they perceived as "nearer" than the other. Observers frequently reported that the random stripe was nearer than the constant stripe. The results appeared to stem from detection of discontinuity of texture edges of the constant stripe due to masking by the random stripe at junctions. This idea was confirmed in the following experiments where discontinuity of the texture edges at junctions was introduced by changing the Gabor luminance contrast in one stripe but keeping it intact in the other. The results indicated that processing of texture edges at junctions can contribute to the perception of depth-order.

Improvement of current gain of C-doped GaAsSb-base heterojunction bipolar transistors by using an InAlP emitter

Large conduction band edge discontinuity (ΔEc) at the emitter/base interface in InP∕GaAs0.51Sb0.49∕InP heterojunction bipolar transistor (HBT) is one of the possible reasons that the recombination process in the emitter/base depletion region dominates the characteristics of this HBT. We fabricate an InAlP emitter∕GaAs0.51Sb0.49base∕InP collector HBT for reducing the ΔEc at the emitter/base interface. It is demonstrated that a HBT with an InAlP emitter shows a relatively lower recombination current than one with an InP emitter, resulting in the higher current gain. It is also found that the decrease of recombination current depends on the Al content of InAlP emitter. Additionally, the ideality factor of the emitter-base current is smallest at the Al content of 0.15 in the InAlP emitter. These results indicate that using an InAlP emitter is effective for improving the current gain of GaAsSb-base HBTs.

Lamb wave characteristics of thickness-graded piezoelectric IDT

An equivalent single layer model of Lamb wave generation by thickness-graded piezoelectric IDT on host structure is developed. Various additional complexities, such as the coupling between the Lamb wave modes, complicated nature of the electro-mechanical excitation are considered. The model of infinite IDT is extended to deal with the finite IDT with edge discontinuities. The effects of electromechanical coupling and thickness gradation on the wavelength shifts are investigated. The problem of electrically driven instability within the IDT is analyzed. Numerical results are reported by considering Al 2O 3/PZT IDT as integral part of the host structure, which show that there are significant changes and improvements in the Lamb wave characteristics due to the graded configuration. Most important among these is the reduced dispersiveness of the Lamb wave modes, which is useful in launching a SAW that propagates with narrower pulse width and less attenuation.

Simple local interpolation of surfaces using normal vectors

A simple algorithm for surface interpolation is proposed. Its central idea is quadratic interpolation of a curved segment from the position and normal vectors at the end points, with the aid of generalized inverses. It is then used to recover the curvature of triangular or quadrilateral patches. The methodology has the following distinctive features: (i) The algorithm is efficient and completely local, requiring only the position vectors and normals given at the nodes of a patch, and hence it is suitable for parallel processing. (ii) The C 0 continuity is always attained, and errors in the normals diminish rapidly with the increase in the number of nodes. (iii) Since the approach can account for discontinuity (multiplicity) of normals, sharp edges and singular points, as well as non-manifolds, can be treated quite easily. (iv) Because of the low degree of the interpolation, it is rather robust and amenable to numerical analyses in comparison with the traditional cubic and more elaborate approximations. Validity and effectiveness of the formulation are checked through several examples.