Gaussian Derivatives Research Articles

A neural contextual model for detecting perceptually salient contours

A computational model, inspired by visual cortical mechanisms of contextual modulation, is presented in this paper, and is applied to detect perceptually salient contours. The presented model incorporates two mechanisms of contextual modulation, surround suppression and collinear facilitation. An oriented filterbank generated by Gaussian derivatives and their Hilbert transform is proposed for pre-processing. The operators of surround suppression and collinear facilitation are applied to the orientation energy resulting from the outputs of oriented filterbank. To avoid augmenting the noise when the facilitation operator enhances the saliency parts, we employ a contrast enhancement transformation for the facilitation operator. For drawing the binary contours, we present an automatic thresholding approach for post-processing. The performance of our model is tested by artificial images with heavy noise and nature images with texture background. Results show that the model has a good performance on extracting the salient contours from images.

Remote bitumen content estimation of Athabasca oil sand from hyperspectral infrared reflectance spectra using Gaussian singlets and derivative of Gaussian wavelets

Modeling of the total bitumen content, TBC, in Athabasca oil sands was undertaken on the basis of its hyperspectral reflectance spectra. Spectra (8 cm −1 resolution) were obtained that covered both the short-wave infrared and thermal infrared (TIR: 3.00–30.00 μm). Two methods, Gaussian fitting and wavelet analyses, were investigated to identify useful bitumen features as well as the best removal of the baseline. We aim to obtain the best determination of the TBC for a suitable suite of test and validation oil sands samples. The Gaussian model relied explicitly on features at 2.282 and 2.532 μm though these were only two of 10 features simultaneously fit with a quadratic baseline to the range of 2.230–2.603 μm of the spectra. The wavelet model relied on bitumen features selected at 2.274, 2.396 and 3.725 μm that could be isolated from the baseline and noise. Both models yielded similar dispersion in their estimates of TBC (±∼1–2%) while the wavelet model proved to be more robust when applied to the validation and blind data suites. We also considered the effects of using the L2 optimization (classical least-squares) and L1 optimization (minimization of largest outlier) schemes for both models. Both schemes produced similar results for the model suite of samples for TBC but the L1 was superior when applied to the validation and blind data suites. The wavelet model using the L1 optimization appeared to be quite robust producing estimates of TBC (±∼1.0–1.7%).

Object Recognition Using Boosted Oriented Filter Based Local Descriptors

Object recognition system based on local descriptors is increasingly used recently because of their perceived robustness with respect to occlusions and to global geometrical deformations. Such a descriptor — based on a set of oriented Gaussian derivative filters—is used in our recognition system. In this paper, we explore the multiview 3D object recognition and multiview face identification. Basic idea is to find discriminant features to describe an object across different views. Boosting framework is used to select features out of huge feature pool created by collecting the local features from the positive training examples. We conduct experiments on 3D objects and face images and get excellent recognition rate. Comparison to SVM is also noted in the paper.

Using Multiscale Product for ECG Characterization

This paper introduces a new method for R wave′s locations using the multiscale wavelet analysis, that is based on Mallat′s and Hwang′s approach for singularity detection via local maxima of the wavelet coefficients signals. Using a first derivative Gaussian function as prototype wavelet, we apply the pointwise product of the wavelet coefficients (PWCs) over some successive scales, in order to enhance the peak amplitude of the modulus maxima line and to reduce noise. The R wave corresponds to two modulus maximum lines with opposite signs (min‐max) of multi‐scale product. The proposed algorithm does not include regularity analysis but only amplitude‐based criteria. We evaluated the algorithm on two manually annotated databases, such as MIT‐BIH Arrhythmia and QT.

Optimal waveform design for ultra-wideband communication based on Gaussian derivatives

Ultra-wideband (UWB) radios have attracted great interest for their potential application in short-range high-data-rate wireless communications. High received signal to noise ratio and compliance with the Federal Communications Commissions (FCC) spectral mask call for judicious design of UWB pulse shapers. In this paper, even and odd order derivatives of Gaussian pulse are used respectively as base waveforms to produce two synthesized pulses. Our method can realize high efficiency of spectral utilization in terms of normalized effective signal power (NESP). The waveform design problem can be converted into linear programming problem, which can be efficiently solved. The waveform based on even order derivatives is orthogonal to the one based on odd order derivatives.

변분 근사화 분포의 유도 및 변분 베이지안 가우시안 혼합 모델의 구현

그래프 모델에서 가장 중요한 부분은 관찰 데이터가 주어진 상황에서 은닉 변수와 더불어 파라미터의 사후확률 분포의 계산이다. 이 논문에서는 가우시안 혼합 모델에 대한 변분 베이지안 방법의 구현과 변분 근사화 분포의 분해 유도를 제안한다. 이 방법은 정보 검색이나 데이터 시각화와 같은 데이터 분석 등에 적용이 가능하다. The crucial part of graphical model is to compute the posterior distribution of parameters plus with the hidden variables given the observed data. In this paper, implementation of variational Bayes method for Gaussian mixture model and derivation of factorial variational approximation have been proposed. This result can be used for data analysis tasks like information retrieval or data visualization.

Local image phase, energy and orientation extraction using FPGAs

Local features such as phase, energy and orientation have been widely used in the literature for multiple computer vision applications such as edge detection, texture analysis, motion estimation, depth computation, etc. They can be computed using wavelet image decomposing based on Quadrature filters tuned at different scales and orientations. Although this represents a very powerful image analysis technique, its feasibility for real-time domain applications is still beyond current computer capabilities due to the high demand of computational resources. In this article, we present an architecture developed for real-time processing of these features using reconfigurable hardware. Although, to the best of our knowledge, previous implementations of Gabor or steerable filters on chip already exist, none of them provides energy, phase, and orientation information at the same time. We show how to implement quadrature filters based on Gaussian derivatives. We develop a hardware friendly technique to interpolate between a multi-oriented filter bank to compute features at their main orientation which has not been used before. We finally describe the system resource requirements, performance and some system illustrative results.

Wavelet neural network (WNN) approach for calibration model building based on gasoline near infrared (NIR) spectra

In this paper we have compared the abilities of two types of artificial neural networks (ANN): multilayer perceptron (MLP) and wavelet neural network (WNN) — for prediction of three gasoline properties (density, benzene content and ethanol content). Three sets of near infrared (NIR) spectra (285, 285 and 375 gasoline spectra) were used for calibration models building. Cross-validation errors and structures of optimized MLP and WNN were compared for each sample set. Four different transfer functions (Morlet wavelet and Gaussian derivative – for WNN; logistic and hyperbolic tangent – for MLP) were also compared. Wavelet neural network was found to be more effective and robust than multilayer perceptron.

Identification of isotope lines in two-dimensional spectra of nuclear multifragmentation

In the paper, we propose new algorithm of the determination of ridges in two-dimensional spectra of nuclear multifragmentation. The algorithm is based on slicing the raw data and their subsequent linearization. To find corresponding points, which contribute to the estimate of fitted line parameters in sparsely distributed linearized data, as well as to span gaps and decrease statistical fluctuations, the algorithm is based on smoothing technique using second derivatives of Gaussian. In the paper, we analyze and study thoroughly the influence of various parameters. Illustrative examples prove in favor of the proposed algorithm.

Generalised-structure-tensor-based infrared small target detection

An efficient method based on generalised structure tensor is presented to detect infrared small targets under complex sky backgrounds. The second conjugate symmetry derivative of a 2D Gaussian is applied to the orientation field to model the small target and the final target detection is accomplished by adaptive segmentation. Experiments show that the method is robust.

Classifying CT Image Data Into Material Fractions by a Scale and Rotation Invariant Edge Model

A fully automated method is presented to classify 3-D CT data into material fractions. An analytical scale-invariant description relating the data value to derivatives around Gaussian blurred step edges--arch model--is applied to uniquely combine robustness to noise, global signal fluctuations, anisotropic scale, noncubic voxels, and ease of use via a straightforward segmentation of 3-D CT images through material fractions. Projection of noisy data value and derivatives onto the arch yields a robust alternative to the standard computed Gaussian derivatives. This results in a superior precision of the method. The arch-model parameters are derived from a small, but over-determined, set of measurements (data values and derivatives) along a path following the gradient uphill and downhill starting at an edge voxel. The model is first used to identify the expected values of the two pure materials (named L and H) and thereby classify the boundary. Second, the model is used to approximate the underlying noise-free material fractions for each noisy measurement. An iso-surface of constant material fraction accurately delineates the material boundary in the presence of noise and global signal fluctuations. This approach enables straightforward segmentation of 3-D CT images into objects of interest for computer-aided diagnosis and offers an easy tool for the design of otherwise complicated transfer functions in high-quality visualizations. The method is applied to segment a tooth volume for visualization and digital cleansing for virtual colonoscopy.

Size-dependent photo-induced shift of the first exciton band in CdTe quantum dots in glass prepared by a two-stage heat-treatment process

CdTe nanocrystals were grown from commercially available RG850 Schott filter glass by two-step heat-treatment process which almost doubles the particle to matrix volume fraction. A calculation shows that a quantized-state effective mass model in the strong confinement regime might be used to deduce the average radius for the nanocrystals larger than 2 nm in radius from the energetic position of the first exciton peak in optical absorption spectrum. Size-induced shift of ∼360 meV in the first exciton peak position was observed. The steady state photoluminescence spectra exhibit a broad band red shifted relative to the first exciton band, which indicates the existence of shallow trap states. The non-linear optical properties of CdTe nanocrystals were studied by room temperature resonant photoabsorption spectroscopy. The differential absorption spectra had three-lobed structure whose size-dependent evolution was explained by bleaching of the absorption, red shift and broadening in the Gaussian absorption band used to fit the first exciton peak. A maximum red shift of 2.32 meV for the average nanocrystal radius of 4.65 nm was estimated by fitting the photomodulation spectra with a combination of first and second derivative Gaussian absorption bands. We presume that the red shift is induced by the electric field of trapped charges in surface states. Internal electric field strengths of 23 and 65 kV/cm were predicted for the average nanocrystal radii of 3.95 and 4.65 nm, respectively, with the help of second-order perturbation theory in the strong confinement limit.

From filters to features: Scale–space analysis of edge and blur coding in human vision

To make vision possible, the visual nervous system must represent the most informative features in the light pattern captured by the eye. Here we use Gaussian scale-space theory to derive a multiscale model for edge analysis and we test it in perceptual experiments. At all scales there are two stages of spatial filtering. An odd-symmetric, Gaussian first derivative filter provides the input to a Gaussian second derivative filter. Crucially, the output at each stage is half-wave rectified before feeding forward to the next. This creates nonlinear channels selectively responsive to one edge polarity while suppressing spurious or "phantom" edges. The two stages have properties analogous to simple and complex cells in the visual cortex. Edges are found as peaks in a scale-space response map that is the output of the second stage. The position and scale of the peak response identify the location and blur of the edge. The model predicts remarkably accurately our results on human perception of edge location and blur for a wide range of luminance profiles, including the surprising finding that blurred edges look sharper when their length is made shorter. The model enhances our understanding of early vision by integrating computational, physiological, and psychophysical approaches.

An objective comparison of pre-processing methods for enhancement of liquid chromatography–mass spectrometry data

Four data pre-processing methods have been applied with different settings to data sets obtained from the analysis of a pharmaceutical drug and its degradation products by liquid chromatography–mass spectrometry (LC–MS). The methods compared were the frequently used component detection algorithm (CODA) and three kinds of digital filters—matched filtration (MF), Gaussian second derivative (GSD) and Savitzky–Golay. The aim was to evaluate the performance and robustness of these methods for extracted ion chromatogram (XIC), total ion chromatogram (TIC) and base peak chromatogram (BPC) in the presence of different types of noise. In accordance with theory, the best improvements in signal-to-noise ratio (S/N) of the XICs were obtained with MF under the ideal case with random white noise. However, when highly coloured noise was present, it was found that no improvements in XIC S/N could be obtained with any of the pre-processing methods studied. GSD and CODA did, however, improve the S/N for both TIC and BPC. GSD and CODA also significantly reduced the background in the spectral domain, thereby facilitating the interpretation of the mass spectra. Another advantage associated with CODA and to some extent also with GSD is their data reduction ability.

Generalized Computation of Gaussian Derivatives Using ITK

Computation of local image derivatives is an important operation in many image processing tasks that involve feature detection and extraction, such as edges, corners or more complicated features. However, derivative computation in discrete images is an ill-posed problem and derivative operators without any prior smoothing are known to enhance noise. Here we present a new convolution operator, the GaussianDerivativeOperator, that allows to calculate locally Gaussian derivatives of N order. Furthermore, we present some useful classes and examples that make use of this new operator.

Computing Gaussian derivative waveforms of any order

The first and second derivatives of a Gaussian, also known as Ricker wavelets, are often used as source waveforms in forward modeling of seismic and electromagnetic wavefields. In applications such as borehole acoustics, the source waveform has more cycles than traditional Ricker wavelets. For such sources, the higher-order derivatives of a Gaussian are a more accurate representation. Such a source waveform can be computed as the product of a Hermite polynomial and the Gaussian; taking the required derivative is not necessary. Explicit expressions for these polynomials are not required because they satisfy a recurrence relation and thus can be computed from the two lowest-order polynomials. The Gaussian is formulated in terms of the dominant frequency of the derivative order of the desired source waveform. Strictly causal waveforms are not possible with a Gaussian because of its infinite length. However, the computed waveform can be made (pseudo-) causal by shifting it along the positive time axis until its amplitude at time zero is less than a user-defined threshold. Numerical tests reveal that amplitudes at zero time are on the order of [Formula: see text] if this shift is equal to the dominant frequency times the square root of the derivative order.

Non-Gaussianity analysis on local morphological measures of WMAP data

The decomposition of a signal on the sphere with the steerable wavelet constructed from the second Gaussian derivative gives access to the orientation, signed-intensity and elongation of the signal's local features. In the present work, the non-Gaussianity of the Wilkinson Microwave Anisotropy Probe (WMAP) temperature data of the cosmic microwave background (CMB) is analysed in terms of the first four moments of the statistically isotropic random fields associated with these local morphological measures, at wavelet scales corresponding to angular sizes between 27.5 arcmin and 30° on the celestial sphere. While no detection is made either in the orientation analysis or in the elongation analysis, a strong detection is made in the excess kurtosis of the signed-intensity of the WMAP data. The non-Gaussianity is observed with a significance level below 0.5 per cent at a wavelet scale corresponding to an angular size around 10°, and confirmed at neighbouring scales. This supports a previous detection of an excess of kurtosis in the wavelet coefficient of the WMAP data with the axisymmetric Mexican hat wavelet. Instrumental noise and foreground emissions are not likely to be at the origin of the excess of kurtosis. Large-scale modulations of the CMB related to some unknown systematics are rejected as possible origins of the detection. The observed non-Gaussianity may therefore probably be imputed to the CMB itself, thereby questioning the basic inflationary scenario upon which the present concordance cosmological model relies. Taking the CMB temperature angular power spectrum of the concordance cosmological model at face value, further analysis also suggests that this non-Gaussianity is not confined to the directions on the celestial sphere with an anomalous signed-intensity.

Detection of coronary calcifications from computed tomography scans for automated risk assessment of coronary artery disease

A fully automated method for coronary calcification detection from non-contrast-enhanced, ECG-gated multi-slice computed tomography (CT) data is presented. Candidates for coronary calcifications are extracted by thresholding and component labeling. These candidates include coronary calcifications, calcifications in the aorta and in the heart, and other high-density structures such as noise and bone. A dedicated set of 64 features is calculated for each candidate object. They characterize the object's spatial position relative to the heart and the aorta, for which an automatic segmentation scheme was developed, its size and shape, and its appearance, which is described by a set of approximated Gaussian derivatives for which an efficient computational scheme is presented. Three classification strategies were designed. The first one tested direct classification without feature selection. The second approach also utilized direct classification, but with feature selection. Finally, the third scheme employed two-stage classification. In a computationally inexpensive first stage, the most easily recognizable false positives were discarded. The second stage discriminated between more difficult to separate coronary calcium and other candidates. Performance of linear, quadratic, nearest neighbor, and support vector machine classifiers was compared. The method was tested on 76 scans containing 275 calcifications in the coronary arteries and 335 calcifications in the heart and aorta. The best performance was obtained employing a two-stage classification system with a k-nearest neighbor (k-NN) classifier and a feature selection scheme. The method detected 73.8% of coronary calcifications at the expense of on average 0.1 false positives per scan. A calcium score was computed for each scan and subjects were assigned one of four risk categories based on this score. The method assigned the correct risk category to 93.4% of all scans.

Finite Discrete, Shift-Invariant, Directional Filterbanks for Visual Information Processing, I : Construction

As is well known in neuroscience, simple cells of the mammalian’s striate cortex possess both orientation and spatial-frequency selectivity, and are similar to the Gabor filters or Gaussian derivative filters in shape. The purpose of this paper is to propose a method of designing perfect reconstruction 2D filterbanks which act on finite dimensional linear spaces consisting of 2D signals of a certain size, and have several analogous features to simple cells: (1) the filterbanks consist of several spatial-frequency channels with orientation selectivity, (2) the filterbanks have shift-invariant multiresolution (multiscale) structures, (3) filters contained in them are FIR, and are similar in appearance to not only Gaussian derivatives of 1st and 2nd order, but also ones of higher order. Moreover, they are constructed by finite linear combinations of separable filters. As is described in the text, by virtue of these properties, our 2D filterbanks can become bases of constructing computational nonlinear models of visual information processing. In this paper we construct the 2D filterbanks, and discuss them from the viewpoint of vision science. For example we disclose a possible role of “Gaussian-derivative-like” filters of higher order in our filterbanks. Practical applications of our 2D filterbanks to vision science and image processing will be given in our subsequent papers.

A unified scheme for the calculation of differentiated and undifferentiated molecular integrals over solid-harmonic Gaussians

Utilizing the fact that solid-harmonic combinations of Cartesian and Hermite Gaussian atomic orbitals are identical, a new scheme for the evaluation of molecular integrals over solid-harmonic atomic orbitals is presented, where the integration is carried out over Hermite rather than Cartesian atomic orbitals. Since Hermite Gaussians are defined as derivatives of spherical Gaussians, the corresponding molecular integrals become the derivatives of integrals over spherical Gaussians, whose transformation to the solid-harmonic basis is performed in the same manner as for integrals over Cartesian Gaussians, using the same expansion coefficients. The presented solid-harmonic Hermite scheme simplifies the evaluation of derivative molecular integrals, since differentiation by nuclear coordinates merely increments the Hermite quantum numbers, thereby providing a unified scheme for undifferentiated and differentiated four-center molecular integrals. For two- and three-center two-electron integrals, the solid-harmonic Hermite scheme is particularly efficient, significantly reducing the cost relative to the Cartesian scheme.