Image reduction operators based on non-monotonic averaging functions

Wilkin, Tim

doi:10.1109/fuzz-ieee.2013.6622458

Cited by 15 publications

(20 citation statements)

References 18 publications

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“…On the other hand, the averaging must be robust to the noise in the image, so that even large increases/ decreases in the intensity of the individual pixels (due to corruption) do not lead to the undesired changes in the intensity of the output. In fact discarding such outliers may lead to changes in the intensity in the opposite direction [7,8,31], as to minimize the dissimilarity between the non-corrupt inputs and the output. Hence weak monotonicity is one of the basic requirements in that application.…”

Section: Weak Monotonicitymentioning

confidence: 97%

See 1 more Smart Citation

On the weak monotonicity of Gini means and other mixture functions

Beliakov

Calvo

Wilkin

2015

Information Sciences

Self Cite

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Section: Weak Monotonicitymentioning

confidence: 97%

“…Recently proposed density based means [1] and their generalizations [10] also turn out to be proper weakly monotone. Another application comes from the processing of noisy images, where mode-like weakly monotone averages were used [7,8,31].…”

Section: Weak Monotonicitymentioning

confidence: 99%

On the weak monotonicity of Gini means and other mixture functions

Beliakov

Calvo

Wilkin

2015

Information Sciences

Self Cite

View full text Add to dashboard Cite

“…On the other hand, the averaging must be robust to the noise in the image, so that even large increases/decreases in the intensity of the individual pixels (due to corruption) do not lead to the undesired changes in the intensity of the output. In fact discarding such outliers may lead to changes in the intensity in the opposite direction [9,10,30], as to minimize the dissimilarity between the non-corrupt inputs and the output. Hence weak monotonicity is one of the basic requirements in that application.…”

Section: Monotonicity In Applicationsmentioning

confidence: 97%

“…Another application comes from the processing of noisy images, where mode-like weakly monotone averages were used [9,10,30]. Image reduction refers to reducing the resolution of an image so that it can fit a particular display, or to speed up its analysis [6,22].…”

Section: Monotonicity In Applicationsmentioning

confidence: 99%

Three types of monotonicity of averaging functions

Beliakov

Calvo²,

Wilkin³

2014

Knowledge-Based Systems

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“…This technique was further adapted to the identification of clusters of pixels that represent fine-scale details in images and applied in the problem of image reduction [2]. In that study, a variety of intensity-based, mode-seeking algorithms were evaluated, and these mode-like averages were justified as a basis for identifying tonal clusters.…”

Section: Introductionmentioning

confidence: 99%

Characterizing Compactness of Geometrical Clusters Using Fuzzy Measures

Beliakov

et al. 2015

IEEE Trans. Fuzzy Syst.

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Certain tasks in image processing require the preservation of fine image details, while applying a broad operation to the image, such as image reduction, filtering, or smoothing. In such cases, the objects of interest are typically represented by small, spatially cohesive clusters of pixels which are to be preserved or removed, depending on the requirements. When images are corrupted by the noise or contain intensity variations generated by imaging sensors, identification of these clusters within the intensity space is problematic as they are corrupted by outliers. This paper presents a novel approach to accounting for spatial organization of the pixels and to measuring the compactness of pixel clusters based on the construction of fuzzy measures with specific properties: monotonicity with respect to the cluster size; invariance with respect to translation, reflection, and rotation; and discrimination between pixel sets of fixed cardinality with different spatial arrangements. We present construction methods based on Sugenotype fuzzy measures, minimum spanning trees, and fuzzy measure decomposition. We demonstrate their application to generating fuzzy measures on real and artificial images.

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Image reduction operators based on non-monotonic averaging functions

Cited by 15 publications

References 18 publications

On the weak monotonicity of Gini means and other mixture functions

On the weak monotonicity of Gini means and other mixture functions

Three types of monotonicity of averaging functions

Characterizing Compactness of Geometrical Clusters Using Fuzzy Measures

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