Gaussian Derivatives Research Articles

Decorative Line and Edge Extraction in Cartoon Images

Decorative Lines and edges in a cartoon image are the most important elements to convey its semantic information. In this study, we propose a method to extract both decorative lines and edges of the cartoon image at the same time. Firstly, we use the Hessian matrix to compute the direction perpendicular to the decorative lines in the image. Then, non-maximum suppression is applied to the image’s second derivative of Gaussian to locate the possible decorative line’s center. Secondly, we use directional zero-crossing (the zero-crossing of the first Gaussian derivative on the precomputed direction) to verify the existence of the decorative lines. Finally, decorative lines and the edges detected by non-maximum suppression on the first Gaussian derivative are fused together. The experimental results show that our method is more effective than other existed methods in literature for complicated cartoon images.

Sistema de apoio ao diagnóstico da Doença de Chagas baseado em escalogramas e redes neurais auto-organizáveis

INTRODUCAO: A Doenca de Chagas e uma endemia rural, prevalente em grande parte da America Central e America do Sul e, aproximadamente, metade dos pacientes contaminados com o parasita Trypanosoma cruzi nao apresentam sinais clinicos, eletrocardiograficos e radiologicos de envolvimento cardiaco. Este trabalho, entretanto, propoe uma tecnica de auxilio ao diagnostico da Doenca de Chagas baseada em sinais de eletrocardiografia, que extrai informacoes relevantes desses sinais. METODOS: Duas abordagens sao estudadas e implementadas. Ambas utilizam sinais de variabilidade da frequencia cardiaca (VFC) e classificacao por meio de rede neural, mais especificamente, o mapa auto-organizavel de Kohonen. A VFC, que reflete a modulacao neural autonomica simpatica e parassimpatica do coracao, e avaliada com base em series continuas de intervalos RR do ECG convencional registradas durante 5 minutos. Na primeira abordagem, indicadores estatistico-temporais obtidos diretamente dos sinais de VFC sao utilizados como entrada da rede neural para treinamento e teste do metodo de classificacao. Na segunda proposta, sao utilizados escalogramas wavelet com funcao de base DoG (derivative of Gaussian) para avaliacao dos sinais de VFC. Indicadores obtidos dos escalogramas sao utilizados como entrada da rede neural no treinamento e no teste do algoritmo. Os mapas topologicos de Kohonen sao utilizados para comparar a capacidade dos indicadores calculados dos sinais de VFC em discriminar pacientes chagasicos cardiopatas, chagasicos indeterminados e individuos normais. Os indicadores temporais convencionais e os indicadores escalograficos sao comparados. RESULTADOS: Os resultados mostram que os indicadores escalograficos tem poder discriminatorio estatisticamente superior aos indicadores temporais convencionais. Em particular, a potencia media da densidade de potencia do escalograma na banda de altas frequencias mostrou ser estatisticamente o indicador de maior poder discriminatorio (p < 0,05 para os 3 casos). CONCLUSAO: A metodologia proposta mostrou-se capaz de distinguir entre individuos normais, chagasicos cardiopatas e chagasicos indeterminados. Os indices escalograficos propostos mostraram maior capacidade classificatoria que os indices temporais tradicionais.

Efficient blur estimation using multi-scale quadrature filters

Blur estimation is required in image processing techniques such as auto-focussing, quality assessment for compressed images and image fusion. In this paper a multi-scale local blur estimation method is proposed. We use the energy of a pair of quadrature filters with first and second derivatives of a Gaussian at several scales as its constituents. A new strategy for analyzing the extrema of energy across scale is proposed. Comparing to the methods which use just a Gaussian first derivative kernel, a smaller number of scales needs to be processed. Also our method yields only one response at the centroid of line-shape features at a position independent of the scale. This is in contrast to other methods which yield multiple responses at scale dependent positions. We evaluated the method for synthetic and real images from the LIVE database. Depending on details of the image, the proposed method is several to tens of times faster in comparison with using just a Gaussian first derivative. The accuracy of the blur estimation is found to be the best or second best while comparing with 16 different methods for Gaussian blur. In addition, the performance is still good for motion blurred images.

A Steerable, Multiscale Singularity Index

We propose a new steerable, multiscale ratio index for detecting impulse singularities in signals of arbitrary dimensionality. For example, it responds strongly to curvilinear masses (ridges) in images, but minimally to step discontinuities. The ratio index employs directional derivatives of gaussians, making it naturally steerable and scalable. Experiments on real images demonstrate the efficacy of the index for detecting multiscale curvilinear structures. A software version of the index can be downloaded from: http://live.ece.utexas.edu/research/SingularityIndex/SingularityIndex.zip.

A Propagation Model for Subsurface and Through-Wall Imaging Applications under the Frequency Dispersion Perspective

The frequency-dependent behavior in subsurface and through-the-wall media is analyzed in this paper as well as the formation of the Brillouin precursor waveforms inherently related to this feature. The emergence of these forerunners is presented as a plausible form to explain classical impairments observed in imaging technologies. The evolution of mono- and multicycle rectangular and first derivative Gaussian pulses through two dispersive media—concrete blocks and soil—is analyzed using a frequency-domain technique and the Debye dielectric model to characterize the media, at operating frequencies below 3 GHz. The frequency-domain approach facilitated to check the influence of some parameters considered critical for the precursor emergence—operating frequency, input pulse configuration, and internal structure of the underlying medium—results in a versatile tool suitable for any kind of modulated input signal propagated through any dispersive medium. The internal multireflection model has been considered as the most suitable model to describe the transmission process underlying both subsurface and through-wall imaging technologies. Two different moisture contents have been considered for concrete as a parameter to determine the performance of through-wall imaging radar from the precursor formation perspective. The results reveal that precursor is a phenomenon to take into account for application demanding larger signal-to-noise ratios.

Continuous rotation invariant local descriptors for texton dictionary-based texture classification

Texton dictionary-based texture representation approaches have been proven to be effective for texture classification. We propose two types of local descriptors based on Gaussian derivatives filters, both of them have the property of continuous rotation invariance. The first descriptor directly uses the maximum of the filter responses named continuous maximum responses (CMR). The second descriptor rectifies the filter responses to calculate principal curvatures (PC) of the image surface. The texton dictionary is learned from the training images by clustering the local descriptors, and the representation of each image is the frequency histogram of the textons. The classification results compared with some other popular methods on the CUReT, KTH-TIPS and KTH-TIPS2-a datasets show that representation based on CMR achieves best classification result on the CUReT dataset. The representation based on PC achieves the best classification results on the KTH-TIPS and KTH-TIPS2-a datasets, and the classification performance is robust on different datasets. The experiments of rotation invariant analysis implemented on the Brodatz album illustrate that the CMR descriptor has good inter-class distinguish ability and PC descriptor has strong intra-class congregate ability. The results demonstrate that the proposed local descriptors achieve remarkable performance to classify the rotated textures.

Design and Multiplierless Implementations of ECG-Based 1st Order Gaussian Derivative Wavelet Filter with Lattice Structures

In this paper, the 1st order Gaussian derivative wavelet function utilized in the design of some corresponding filter banks. Since the 1st order Gaussian derivative function has a similar shape to QRS complex part of the ECG, it can be used in QRS feature extraction. Using this characteristic of such wavelet function, the designed FIR wavelet filter banks can be realized in highly-efficient lattice structures which are easy to implement in two standard deviation values ( σ=1 and σ=2 ). The resulting lattice structures reduce the number of filter banks coefficients and this reduces, in turn the number of multiplications and improves the filter banks efficiencies as it reduces the number of computations performed. The resulting quantized multiplier values can also lead to multiplierless realizations using sum-of-power-of-two (SOPOT) method. FPGA implementations of such structures are achieved with less-complexity.

New Families of Fourier Eigenfunctions for Steerable Filtering

A new diadic family of eigenfunctions of the 2-D Fourier transform has been discovered. Specifically, new wavelets are derived by steering the elongated Hermite-Gauss filters with respect to rotations, thus obtaining a natural generalization of the Laguerre-Gauss harmonics. Interestingly, these functions are also proportional to their 2-D Fourier transform. Their analytical expression is provided in a compact and treatable form, by means of a new ad hoc matrix notation in which the cases of even and odd orders of the Hermite polynomials are unified. Moreover, these functions can be efficiently implemented by means of a recursive formula that is derived in this paper. The proposed filters are applied to the problem of gradient estimation to improve the theoretical Canny tradeoff of position accuracy versus noise rejection that occurs in edge detection. Experimental results show considerable improvements in using the new wavelets over both isotropic Gaussian derivatives and other elongated steerable filters more recently introduced. Finally, being the proposed wavelets a set of Fourier eigenfunctions, they can be of interest in other fields of science, such as optics and quantum mechanics.

Numerical comparison of X-ray differential phase contrast and attenuation contrast

We present a numerical tool to compare directly the contrast-to-noise-ratio (CNR) of the attenuation- and differential phase-contrast signals available from grating-based X-ray imaging for single radiographs. The attenuation projection is differentiated to bring it into a modality comparable to the differential phase projection using a Gaussian derivative filter. A Relative Contrast Gain (RCG) is then defined as the ratio of the CNR of image values in a region of interest (ROI) in the differential phase projection to the CNR of image values in the same ROI in the differential attenuation projection. We apply the method on experimental data of human breast tissue acquired using a grating interferometer to compare the two contrast modes for two regions of interest differing in the type of tissue. Our results indicate that the proposed method can be used as a local estimate of the spatial distribution of the ratio δ/β, i.e., real and imaginary part of the complex refractive index, across a sample.

Image bilevel thresholding based on multiscale gradient multiplication

This paper introduces a novel global thresholding approach that exploits the multiscale gradient information. The multiscale gradient information, that is, the product of gradient magnitude (PGM), is obtained by multiplying the responses of the first derivative of Gaussian (FDoG) filter at three adjacent space scales. The output threshold is selected as the one that maximizes a new objective function of the gray level variable t. The objective function is defined as the ratio of the mean PGM values of the boundary and non-boundary regions in the binary image obtained by thresholding with variable t. Through analysis of 35 real images from different application areas, our results show that the proposed method can perform bilevel thresholding on the images with different histogram patterns, such as unimodal, bimodal, multimodal, or comb-like shape. Its segmentation quality is superior to five popular thresholding algorithms.

Separation of structure and ripples on sand mounds using Hermite functions

A simple method is proposed for the separation of a large-scale structure from small-scale ripples during the evolution of an isolated sand hill or spoil heap eroded by an oscillatory or steady flow by bed-load transport. This method is based on Hermite functions, a mother Gaussian hill and derivatives modified to be orthogonal. It is straightforward to apply and could be used to characterise the geometric properties of any isolated localised hill-like feature such as pollution concentration levels away from an outfall.

Spectral efficient impulse radio-ultra-wideband transmission model in presence of pulse attenuation and timing jitter

This study investigates the spectrum shaping observed in ultra-wideband (UWB) communications. An auxiliary independent signal (AIS) to limit undesired spectral lines because of periodicity or unbalanced data sources (i.e. non-uniformly distributed) and or non-symmetric data modulation schemes are introduced. Each transmitted symbol is represented by a preamble AIS pulse followed by a set of transmitted data pulses that are weighted, delayed and summed in accordance with a predefined modulation. The use of the fifth derivative Gaussian pulse ensures that the UWB spectrum mask established by the Federal Communications Commission (FCC) is met, and a preamble signal is designed to eliminate spectral lines at specific frequencies that appear mainly by existing balanced or unbalanced binary data sources. A unified spectral analysis is adapted for general uncorrelated and correlated quaternary bi-orthogonal modulations. An optimisation problem is also introduced in the case of unbalanced data sources in order to minimise undesired spectral lines subject to comply with the FCC spectrum mask and maximise spectral utilisation.

A No-Reference Objective Image Sharpness Metric Based on a Filter Bank of Gaussian Derivative Wavelets

A No-Reference Objective Image Sharpness Metric Based on a Filter Bank of Gaussian Derivative Wavelets

A Feature‐Preserving Hair Removal Algorithm for Dermoscopy Images

Accurate segmentation and repair of hair-occluded information from dermoscopy images are challenging tasks for computer-aided detection (CAD) of melanoma. Currently, many hair-restoration algorithms have been developed, but most of these fail to identify hairs accurately and their removal technique is slow and disturbs the lesion's pattern. In this article, a novel hair-restoration algorithm is presented, which has a capability to preserve the skin lesion features such as color and texture and able to segment both dark and light hairs. Our algorithm is based on three major steps: the rough hairs are segmented using a matched filtering with first derivative of gaussian (MF-FDOG) with thresholding that generate strong responses for both dark and light hairs, refinement of hairs by morphological edge-based techniques, which are repaired through a fast marching inpainting method. Diagnostic accuracy (DA) and texture-quality measure (TQM) metrics are utilized based on dermatologist-drawn manual hair masks that were used as a ground truth to evaluate the performance of the system. The hair-restoration algorithm is tested on 100 dermoscopy images. The comparisons have been done among (i) linear interpolation, inpainting by (ii) non-linear partial differential equation (PDE), and (iii) exemplar-based repairing techniques. Among different hair detection and removal techniques, our proposed algorithm obtained the highest value of DA: 93.3% and TQM: 90%. The experimental results indicate that the proposed algorithm is highly accurate, robust and able to restore hair pixels without damaging the lesion texture. This method is fully automatic and can be easily integrated into a CAD system.

Composed complex-cue histograms: An investigation of the information content in receptive field based image descriptors for object recognition

Recent work has shown that effective methods for recognizing objects and spatio-temporal events can be constructed based on histograms of receptive field like image operations.This paper presents the results of an extensive study of the performance of different types of receptive field like image descriptors for histogram-based object recognition, based on different combinations of image cues in terms of Gaussian derivatives or differential invariants applied to either intensity information, color-opponent channels or both. A rich set of composed complex-cue image descriptors is introduced and evaluated with respect to the problems of (i) recognizing previously seen object instances from previously unseen views, and (ii) classifying previously unseen objects into visual categories.It is shown that there exist novel histogram descriptors with significantly better recognition performance compared to previously used histogram features within the same class. Specifically, the experiments show that it is possible to obtain more discriminative features by combining lower-dimensional scale-space features into composed complex-cue histograms. Furthermore, different types of image descriptors have different relative advantages with respect to the problems of object instance recognition vs. object category classification. These conclusions are obtained from extensive evaluations on two mutually independent data sets.For the task of recognizing specific object instances, combined histograms of spatial and spatio-chromatic derivatives are highly discriminative, and several image descriptors in terms rotationally invariant (intensity and spatio-chromatic) differential invariants up to order two lead to very high recognition rates. For category classification, primary information is contained in both first-and second-order derivatives, where second-order partial derivatives constitute the most discriminative cue.Dimensionality reduction by principal component analysis and variance normalization prior to training and recognition can in many cases lead to a significant increase in recognition or classification performance. Surprisingly high recognition rates can even be obtained with binary histograms that reveal the polarity of local scale-space features, and which can be expected to be particularly robust to illumination variations.An overall conclusion from this study is that compared to previously used lower-dimensional histograms, the use of composed complex-cue histograms of higher dimensionality reveals the co-variation of multiple cues and enables much better recognition performance, both with regard to the problems of recognizing previously seen objects from novel views and for classifying previously unseen objects into visual categories.

Second Derivative Gaussian Algorithm in Engine Fault Image

In this paper, we proposed an improved Second Derivative Gaussian (SDG); the endoscopic image of the engine fault was treated by a combination of wavelet and improved SDG, in order to enhance the quality of the image and denosing. The results shows that the propose method can reduce the noise and improve the detail of the image. Provide support for further diagnosis.

Design of Quadratic Time Frequency Distribution and Application to the Analysis and Detection of Fetal Movements

Background: Fetal movements are clinically correlated to fetal wellbeing. Ultrasounds are the most accurate measurements of the fetal movement but expensive and intrusive. To avoid these constraints, Fetal activity is captured through data acquired using low cost and nonintrusive accelerometer . Time-frequency distributions (TFDs) are often used to represent the energy, temporal and spectral characteristics of non-stationary signals in the time and frequency plane. Many quadratic TFDs were proposed in the literature such as Wigner-Ville distribution, Spectrogram, B-Distribution, Choi-Williams , etc. The drawbacks of the majority of these techniques is that only a few parameters can be modified in the kernel, generally the lag and Doppler parameters, so that they cannot be easily adapted to the data. Objectives: This work aims at designing a new kernel with several parameters that leads to a higher resolution time frequency representation (TFR) of the signal, therefore improving the characteristic of the fetal movement. Methods: The proposed TFD can be considered as an extension of the Gaussian TFD (also called Choi-Williams distribution). The kernel function of the proposed kernel is given by the sum of the weighted derivative Gaussian TFD (refer to the equation). Results and Conclusion: The weighted parameters in the above formula can be estimated by maximizing the concentration of the instantaneous frequency. The resulting TFD is compared with other methods and applied to the analysis and classification of the fetal movement data recorded by the accelerometers. The results obtained indicate that the proposed time-frequency methodology allows the detection of fetal movement data recorded by accelerometers.

Motion control of a cruise ship by using active stabilizing fins

The present study considers the motion control of a cruise ship by using active stabilizing fins. One or two pairs of stabilizing fins are equipped to reduce the roll and/or pitch motions of the cruise ship. Each fin is controlled by algorithms based on proportional–integral–derivative (PID) and linear quadratic Gaussian (LQG) control. Numerical analysis of the wave-induced motion of a cruise ship with stabilizing fins is carried out by using the time-domain ship motion program which has been developed through this study. The resultant motion response as the performance of each controller is compared between different control algorithms. Based on the present simulation results, the stabilizing fin can be considered a good instrument to reduce pitch motion as well as roll motion of the present cruise ship model. The present results show that the PID control algorithm, a simple but practical algorithm, can be an appropriate method to reduce the roll motion in a moderate sea state, while the LQG control algorithm shows good performance in reducing not only the roll motion but also the coupled roll and pitch motions simultaneously in all of environmental conditions considered.

A Differential Model of the Complex Cell

The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modeled by Gabor functions or gaussian derivatives. Gabor functions can also be combined in an energy model of the complex cell response. This letter proposes an alternative model of the complex cell, based on gaussian derivatives. It is most important to account for the insensitivity of the complex response to small shifts of the image. The new model uses a linear combination of the first few derivative filters, at a single position, to approximate the first derivative filter, at a series of adjacent positions. The maximum response, over all positions, gives a signal that is insensitive to small shifts of the image. This model, unlike previous approaches, is based on the scale space theory of visual processing. In particular, the complex cell is built from filters that respond to the 2D differential structure of the image. The computational aspects of the new model are studied in one and two dimensions, using the steerability of the gaussian derivatives. The response of the model to basic images, such as edges and gratings, is derived formally. The response to natural images is also evaluated, using statistical measures of shift insensitivity. The neural implementation and predictions of the model are discussed.

Investigation of image sharpness characteristics in the field of automated microscopy of cytological preparations

Comparative study of 23 image sharpness characteristics was carried out and their quality for the task of automated microscopic analysis of cytological preparations was defined. It was established that sharpness characteristics "Sum of squared Gaussian derivatives" and "Bayes-spectral-entropy-based focus measure" manifest the best performance for images with different scales.