Fractal dimension, wavelet shrinkage and anomaly detection for mine hunting

Nelson, James; Kingsbury, Nick

doi:10.1049/iet-spr.2011.0070

Cited by 13 publications

(17 citation statements)

References 16 publications

(26 reference statements)

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“…(Previous work exploiting lacunarity with sonar data used the concept only for anomaly detection, namely, to distinguish pure speckle from regions with structure [21] and to detect objects within sand ripples [22], [23].) Specifically, we show that it is a very powerful quantity for characterizing seafloor to aid targetdetection tasks in side-looking sonar images.…”

Section: Introductionmentioning

confidence: 86%

Fast Unsupervised Seafloor Characterization in Sonar Imagery Using Lacunarity

Williams

2015

IEEE Trans. Geosci. Remote Sensing

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A new unsupervised approach for characterizing seafloor in side-looking sonar imagery is proposed. The approach is based on lacunarity, which measures the pixel-intensity variation, of through-the-sensor data. No training data are required, no assumptions regarding the statistical distributions of the pixels are made, and the universe of (discrete) seafloor types need not be enumerated or known. It is shown how lacunarity can be computed very quickly using integral-image representations, thereby making real-time seafloor assessments on-board an autonomous underwater vehicle feasible. The promise of the approach is demonstrated on high-resolution synthetic-aperture-sonar imagery of diverse seafloor conditions measured at various geographical sites. Specifically, it is shown how lacunarity can effectively distinguish different seafloor conditions and how this fact can be exploited for target-detection performance prediction in mine-countermeasure operations.

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Section: Introductionmentioning

confidence: 86%

Fast Unsupervised Seafloor Characterization in Sonar Imagery Using Lacunarity

Williams

2015

IEEE Trans. Geosci. Remote Sensing

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“…Algorithms for determining lacunarity and related texture parameters have been proposed and analyzed, e.g. in [3,47,4,5] and used successfully in very different fields such as pattern recognition [4], signal processing [32], DNA classification [9], the analysis of aggregation clusters in statistical mechanics [41] and of breast tumors in medicine [43], to mention just a few recent studies. Despite these many positive examples, one can not hope that a single texture parameter like lacunarity will always be able to successfully distinguish or classify fractal structures of a given class.…”

Section: Introductionmentioning

confidence: 99%

Estimation of fractal dimension and fractal curvatures from digital images

Spodarev

Straka

Winter

2015

Chaos, Solitons & Fractals

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Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several geometric characteristics, namely all the intrinsic volumes (i.e. volume, surface area, Euler characteristic etc.) of the parallel sets of a fractal. Motivated by recent results on their limiting behaviour, we use these functionals to estimate the fractal dimension of sets from digital images. Simultaneously, we also obtain estimates of the fractal curvatures of these sets, some fractal counterpart of intrinsic volumes, allowing a finer classification of fractal sets than by means of fractal dimension only. We show the consistency of our estimators and test them on some digital images of self-similar sets.

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“…Dual-tree complex wavelet transform (DTCWT) can reduce spectral aliasing for vibration signals and enjoys nearly shift invariance compared to other wavelets, which are attractive properties favorable to signal processing [7,25,26]. Owing to these advantages, DTCWT is utilized to conduct study in the next couple of sections.…”

Section: Bayesian Denoising Based Onmentioning

confidence: 99%

Mechanical Vibration Signal Denoising Using Quantum‐Inspired Standard Deviation Based on Subband Based Gaussian Mixture Model

Huang

Chen

et al. 2018

Shock and Vibration

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Aiming at improving noise reduction effect for mechanical vibration signal, a Gaussian mixture model (SGMM) and a quantuminspired standard deviation (QSD) are proposed and applied to the denoising method using the thresholding function in wavelet domain. Firstly, the SGMM is presented and utilized as a local distribution to approximate the wavelet coefficients distribution in each subband. Then, within Bayesian framework, the maximum a posteriori (MAP) estimator is employed to derive a thresholding function with conventional standard deviation (CSD) which is calculated by the expectation-maximization (EM) algorithm. However, the CSD has a disadvantage of ignoring the interscale dependency between wavelet coefficients. Considering this limit for the CSD, the quantum theory is adopted to analyze the interscale dependency between coefficients in adjacent subbands, and the QSD for noise-free wavelet coefficients is presented based on quantum mechanics. Next, the QSD is constituted for the CSD in the thresholding function to shrink noisy coefficients. Finally, an application in the mechanical vibration signal processing is used to illustrate the denoising technique. The experimental study shows the SGMM can model the distribution of wavelet coefficients accurately and QSD can depict interscale dependency of wavelet coefficients of true signal quite successfully. Therefore, the denoising method utilizing the SGMM and QSD performs better than others.

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Fractal dimension, wavelet shrinkage and anomaly detection for mine hunting

Cited by 13 publications

References 16 publications

Fast Unsupervised Seafloor Characterization in Sonar Imagery Using Lacunarity

Fast Unsupervised Seafloor Characterization in Sonar Imagery Using Lacunarity

Estimation of fractal dimension and fractal curvatures from digital images

Mechanical Vibration Signal Denoising Using Quantum‐Inspired Standard Deviation Based on Subband Based Gaussian Mixture Model

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