Signal segmentation and denoising algorithm based on energy optimisation

Mahmoodi, Sasan; Sharif, B.S.

doi:10.1016/j.sigpro.2005.03.016

Cited by 15 publications

(23 citation statements)

References 22 publications

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“…Functional (13) was initially developed for one-dimensional signals [24,25], and it was demonstrated in [25] that its second variation with respect to points representing discontinuities is positive. This indicates that points representing discontinuities are minimisers of such a functional.…”

Section: Modifications and Implementationmentioning

confidence: 99%

Contour evolution scheme for variational image segmentation and smoothing

Mahmoodi¹,

Sharif²

2007

IET Image Process.

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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.

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Section: Modifications and Implementationmentioning

confidence: 99%

Contour evolution scheme for variational image segmentation and smoothing

Mahmoodi¹,

Sharif²

2007

IET Image Process.

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“…Mahmoodi et al proposed a generic approach for signal and image segmentation and smoothing applicable to signals with any dimension, based on the second variation with respect to points and contours that represent discontinuities [26][27][28][29]. It was demonstrated that points or contours that represent discontinuities were minimisers of the functional proposed in [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

“…It was demonstrated that points or contours that represent discontinuities were minimisers of the functional proposed in [26][27][28][29]. A variational-based solution to the functional for piecewise continuous low-pass signals was proposed in [27].…”

Section: Introductionmentioning

confidence: 99%

“…A variational-based solution to the functional for piecewise continuous low-pass signals was proposed in [27]. An operator-based geometrical approach being faster and more robust in the presence of excessive noise was proposed in [28] to implement the functional introduced in [27]. This operator-based approach was generalised for grey-scale images based on the geometrical properties of surfaces (smoothed images) [26].…”

Section: Introductionmentioning

confidence: 99%

“…One of the novelties of this paper is that the geometrical approach proposed in [28] for signals and in [26] for greyscale images is generalised for vector-valued images. The generalisation of the variational framework presented in [26 -29] for the vector-valued images demonstrates that this variational framework is generic and applicable to signals with any dimension.…”

Section: Introductionmentioning

confidence: 99%

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

Mahmoodi

Sharif

2007

IET Image Process.

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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 DroG operator. The implementations are applied on colour images as examples of vector-valued images, and the results demonstrate robust performance in noisy environments. IntroductionVector-valued images such as colour, multi-spectral and multi-modal images can provide more valuable information than scalar images in applications ranging from satellite remote sensing to medical imaging. Vector-valued images can also be generated by extracting feature vectors from a single image as a part of image segmentation. In this paper, a variational method is considered for segmentation and smoothing of vector-valued images. Variational methods in image processing and computer vision are well established. The restoration known as 'inverse' problem was initially considered by Tikhonov and Arsenin [1] as an energy optimisation problem based on L 2 norm. The advantage of Tikhonov and Arsenin's method was that it was linear and easy to implement. Owing to its linearity, the smoothing was performed across discontinuities as well as every where else. Such a method therefore leads to blurred edges in restoration. This method was further modified by Rudin et al.[2] to introduce the notion of total variation based on L 1 norm in order to preserve edges when removing the noise. The minimisation of the functional proposed in the total variation method leads to a nonlinear differential equation whose solution was demonstrated in [2] to preserve discontinuities when it approaches to a low-pass image in regions where there are no discontinuities, hence removing the noise. This method was further generalised for vectorvalued images in [3] and applied to RGB images as an example. The generalisation of the total variation method for noise removal in textures is still a challenge. In another development, Kass et al.[4] initially introduced a contour evolution method known as the 'snake' algorithm for image segmentation based on the optimisation of a linear functional in which three terms were minimised. The first and second terms were proportional to the first and second derivatives of an affinely parametrised contour. The third term was associated with the gradient of a given input image. One of the major drawbacks of the method proposed in [4] was that its implementation was not able automatically to adjust the topology of the evolving con...

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An Augmented Lagrangian Model for Signal Segmentation

Moll

Pallardó

2022

Mediterr. J. Math.

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In this paper, we provide a new insight to the two-phase signal segmentation problem. We propose an augmented Lagrangian variational model based on Chan–Vese’s original one. Using both energy methods and PDE methods, we show, in the one-dimensional case, that the set of minimizers to the proposed functional contains only binary functions and it coincides with the set of minimizers to Chan–Vese’s one. This fact allows us to obtain two important features of the minimizers as a by-product of our analysis. First of all, for a piecewise constant initial signal, the jump set of any minimizer is a subset of the jump set of the given signal. Second, all of the jump points of the minimizer belong to the same level set of the signal, in a multivalued sense. This last property permits to design a trivial algorithm for computing the minimizers.

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Signal segmentation and denoising algorithm based on energy optimisation

Cited by 15 publications

References 22 publications

Contour evolution scheme for variational image segmentation and smoothing

Contour evolution scheme for variational image segmentation and smoothing

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

An Augmented Lagrangian Model for Signal Segmentation

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