A Regularized Nonlinear Diffusion Approach for Texture Image Denoising

Casaca, Wallace; Boaventura, Maurílio

doi:10.1109/sibgrapi.2009.33

Cited by 5 publications

(6 citation statements)

References 21 publications

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“…The imaginary parts of the images produced at each noise level by the two methods (E2I and E2II) were used to produce the numerical values given in Table 5. As seen from Table 5, the metric values because of the application of the proposed method, equation (17), are higher than those belonging to the existing method at all considered noise levels. Again, higher metric values produced by the proposed method are evident of its better suitability and applicability to denoising and enhancing the processed image as compared with the existing method.…”

Section: Schrö Dinger Diffusion With Non-zero Potential Experimentsmentioning

confidence: 89%

“…The discrete form of the modification given by (16) is I n+1 p,q = I n p,q + l(ĉ N ∇ N I) +ĉ S ∇ S I +ĉ E ∇ E I +ĉ W ∇ W I) n p,q and that of (17) is Equations (16) and (17) are two different complex diffusion processes. Each equation is solved iteratively to enhance the noisy images and improve the signal-to-noise ratio.…”

Section: Complex Diffusion Coefficient Modificationsmentioning

confidence: 99%

“…However, the iterative application of G to the reactive term of the diffusion coefficient is retained for the intended improvement purposes. Proper changes were made in a MatLab w code referenced in [15] to formulate a code representing the complex diffusion given by equation (16), and the same was done to a second code referenced in [15] to represent the complex diffusion given by (17). The methods proposed here with zero and non-zero potential, (16) and (17), are labelled 'E1III' and 'E2II', respectively.…”

Section: Complex Diffusion Coefficient Modificationsmentioning

confidence: 99%

“…Examples include using denoising filters based on anisotropic diffusion for improvement of image quality in [16]; non-linear diffusion for texture image denoising in [17]; a combination of anisotropic diffusion and independent component analysis for image denoising in [18]; and an inhomogeneous anisotropic diffusion scheme for the enhancement of digital images in [19]. In an effort to further improve the nature of the complex diffusion coefficient and its effects on the image attributes, this paper proposes two modifications for the complex diffusion coefficients of diffusion processes being applied to an image corrupted by random noise.…”

Section: Introductionmentioning

confidence: 99%

“…Lena' imagery results from Schrödinger diffusion with non-zero potential using E2I and E2II methods (left image is imaginary part in columns 2 and 3) † Method E2II: equation(17) I t = ∇[(C R + iG{C I })∇I] + aVI,C R |iC I = e iu 1 + Im(I)ku 2…”

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confidence: 99%

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Image enhancement through complex conduction coefficient modifications

Ahmad

Fuhrmann

Kerr

et al. 2012

IET Image Processing

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One important term in the diffusion equation applied to image processing is the conduction coefficient. It could be a real or complex function, depending on the chosen diffusion processes. A modification in the form of the application of filter convolution to the real-value conduction coefficient has been recommended for the improvement of the signal-to-noise ratio and the speed by which the diffusion is performed. In this study, the developments of the approximately circularly symmetric two-dimensional Lagrange filter and the Teager operator are presented. They are proposed here for the modification of the complex-value conduction coefficient for the improvement of the image diffusion process. Performance of the proposed modifications is evaluated through simulation and the use of three metrics. Experimental results suggest the validity and applicability of the proposed modifications.

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Section: Schrö Dinger Diffusion With Non-zero Potential Experimentsmentioning

confidence: 89%

Section: Complex Diffusion Coefficient Modificationsmentioning

confidence: 99%

Section: Complex Diffusion Coefficient Modificationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Image enhancement through complex conduction coefficient modifications

Ahmad

Fuhrmann

Kerr

et al. 2012

IET Image Processing

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Image decomposition and denoising using fractional‐order partial differential equations

Bai

Feng

2020

IET image process

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Spectral Segmentation Using Cartoon-Texture Decomposition and Inner Product-Based Metric

Casaca

Paiva

Nonato

2011

2011 24th SIBGRAPI Conference on Graphics, Patterns and Images

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This paper presents a user-assisted image partition technique that combines cartoon-texture decomposition, inner product-based similarity metric, and spectral cut into a unified framework. The cartoon-texture decomposition is used to first split the image into textured and texture-free components, the latter being used to define a gradient-based inner-product function. An affinity graph is then derived and weights are assigned to its edges according to the inner product-based metric. Spectral cut is computed on the affinity graph so as to partition the image. The computational burden of the spectral cut is mitigated by a fineto-coarse image representation process, which enables moderate size graphs that can be handled more efficiently. The partitioning can be steered by interactively by changing the weights of the graph through user strokes. Weights are updated by combining the texture component computed in the first stage of our pipeline and a recent harmonic analysis technique that captures waving patterns. Finally, a coarse-to-fine interpolation is applied in order to project the partition back onto the original image. The suitable performance of the proposed methodology is attested by comparisons against state-of-art spectral segmentation methods.

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A Regularized Nonlinear Diffusion Approach for Texture Image Denoising

Cited by 5 publications

References 21 publications

Image enhancement through complex conduction coefficient modifications

Image enhancement through complex conduction coefficient modifications

Image decomposition and denoising using fractional‐order partial differential equations

Spectral Segmentation Using Cartoon-Texture Decomposition and Inner Product-Based Metric

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