Bessel Filter Analysis

In this technical report, we prove two fundamental theorems for an edge detection algorithm based on a Bessel filter. These theorems are bases of a scale invariant feature extraction method in which extracted features are independent of scale

Discontinuity Preserving Noise Removal Method based on Anisotropic Diffusion for Band Pass Signals

nonlinear discontinuity-preserving method for noise removal for band pass signals such as signals modulated with Binary Phase-Shift Keying (BPSK) modulation is proposed in this paper. This method is inspired by the anisotropic diffusion algorithm to remove noise and preserve discontinuities in band pass signals modulated with a single frequency. It is demonstrated here that nonlinear noise removal method for a real valued band pass signal requires a solution for a nonlinear partial differential equation which is of fourth order in space and second order in time. The results presented in this work show better performance in nonlinear noise removal for real valued band pass signals in comparison with the previous work in the literature

A nonlinear variational method for signal segmentation and reconstruction using level set algorithm

A nonlinear functional is considered in this letter for segmentation and noise removal of piecewise continuous signals containing binary information contaminated with Gaussian noise. A discontinuity is defined as points in time scale that separates two signal segments with different amplitude spectra. Segmentation and noise removal of a piecewise continuous signal are obtained by deriving equations minimising the nonlinear functional. An algorithm based on the level set method is employed to implement the solutions minimising the functional. The proposed method is robust in noisy signals and can avoid local minima

Contour evolution scheme for variational image segmentation and smoothing

An algorithm, based on the Mumford–Shah (M–S) functional, for image contour segmentation and object smoothing in the presence of noise is proposed. However, in the proposed algorithm, contour length minimisation is not required and it is demonstrated that the M–S functional without contour length minimisation becomes an edge detector. Optimisation of this nonlinear functional is based on the method of calculus of variations, which is implemented by using the level set method. Fourier and Legendre’s series are also employed to improve the segmentation performance of the proposed algorithm. The segmentation results clearly demonstrate the effectiveness of the proposed approach for images with low signal-to-noise ratios

Signal segmentation and denoising algorithm based on energy optimisation

A nonlinear functional is considered in this short communication for time interval segmentation and noise reduction of signals. An efficient algorithm that exploits the signal geometrical properties is proposed to optimise the nonlinear functional for signal smoothing. Discontinuities separating consecutive time intervals of the original signal are initially detected by measuring the curvature and arc length of the smoothed signal. The nonlinear functional is then optimised for each time interval to achieve noise reduction of the original noisy signal. This algorithm exhibits robustness for signals characterised by very low signal to noise ratios

Scale Space Smoothing, Image Feature Extraction and Bessel Filters

The Green function of Mumford-Shah functional in the absence of discontinuities is known to be a modified Bessel function of the second kind and zero degree. Such a Bessel function is regularized here and used as a filter for feature extraction. It is demonstrated in this paper that a Bessel filter does not follow the scale space smoothing property of bounded linear filters such as Gaussian filters. The features extracted by the Bessel filter are therefore scale invariant. Edges, blobs, and junctions are features considered here to show that the extracted features remain unchanged by varying the scale of a Bessel filter. The scale invariance property of Bessel filters for edges is analytically proved here. We conjecture that Bessel filters also enjoy this scale invariance property for other kinds of features. The experimental results presente

Geometrical-based algorithm for variational segmentation and smoothing of vector-valued images

An optimisation method based on a nonlinear functional is considered for segmentation and smoothing of vector-valued images. An edge-based approach is proposed to initially segment the image using geometrical properties such as metric tensor of the linearly smoothed image. The nonlinear functional is then minimised for each segmented region to yield the smoothed image. The functional is characterised with a unique solution in contrast with the Mumford–Shah functional for vector-valued images. An operator for edge detection is introduced as a result of this unique solution. This operator is analytically calculated and its detection performance and localisation are then compared with those of the DroGoperator. The implementations are applied on colour images as examples of vector-valued images, and the results demonstrate robust performance in noisy environments

Nonlinear optimisation method for image segmentation and noise reduction using geometrical intrinsic properties

This paper considers the optimisation of a nonlinear functional for image segmentation and noise reduction. Equations optimising this functional are derived and employed to detect edges using geometrical intrinsic properties such as metric and Riemann curvature tensor of a smooth differentiable surface approximating the original image. Images are then smoothed using a Helmholtz type partial differential equation. The proposed approach is shown to be very efficient and robust in the presence of noise, and the reported results demonstrate better performance than the conventional derivative based edge detectors

The effect of time on ear biometrics

We present an experimental study to demonstrate the effect of the time difference in image acquisition for gallery and probe on the performance of ear recognition. This experimental research is the first study on the time effect on ear biometrics. For the purpose of recognition, we convolve banana wavelets with an ear image and then apply local binary pattern on the convolved image. The histograms of the produced image are then used as features to describe an ear. A histogram intersection technique is then applied on the histograms of two ears to measure the ear similarity for the recognition purposes. We also use analysis of variance (ANOVA) to select features to identify the best banana wavelets for the recognition process. The experimental results show that the recognition rate is only slightly reduced by time. The average recognition rate of 98.5% is achieved for an eleven month-difference between gallery and probe on an un-occluded ear dataset of 1491 images of ears selected from Southampton University ear database

Unsupervised Texture Segmentation using Active Contours and Local Distributions of Gaussian Markov Random Field Parameters

In this paper, local distributions of low order Gaussian Markov Random Field (GMRF) model parameters are proposed as texture features for unsupervised texture segmentation.Instead of using model parameters as texture features, we exploit the variations in parameter estimates found by model fitting in local region around the given pixel. Thespatially localized estimation process is carried out by maximum likelihood method employing a moderately small estimation window which leads to modeling of partial texturecharacteristics belonging to the local region. Hence significant fluctuations occur in the estimates which can be related to texture pattern complexity. The variations occurred in estimates are quantified by normalized local histograms. Selection of an accurate window size for histogram calculation is crucial and is achieved by a technique based on the entropy of textures. These texture features expand the possibility of using relativelylow order GMRF model parameters for segmenting fine to very large texture patterns and offer lower computational cost. Small estimation windows result in better boundarylocalization. Unsupervised segmentation is performed by integrated active contours, combining the region and boundary information. Experimental results on statistical and structural component textures show improved discriminative ability of the features compared to some recent algorithms in the literature