Tom Mélange

Fuzzy Random Impulse Noise Removal From Color Image Sequences

In this paper, a new fuzzy filter for the removal of random impulse noise in color video is presented. By working with different successive filtering steps, a very good tradeoff between detail preservation and noise removal is obtained. One strong filtering step that should remove all noise at once would inevitably also remove a considerable amount of detail. Therefore, the noise is filtered step by step. In each step, noisy pixels are detected by the help of fuzzy rules, which are very useful for the processing of human knowledge where linguistic variables are used. Pixels that are detected as noisy are filtered, the others remain unchanged. Filtering of detected pixels is done by blockmatching based on a noise adaptive mean absolute difference. The experiments show that the proposed method outperforms other state-of-the-art filters both visually and in terms of objective quality measures such as the mean absolute error (MAE), the peak-signal-to-noise ratio (PSNR) and the normalized color difference (NCD).

On the role of complete lattices in mathematical morphology: From tool to uncertainty model

Mathematical morphology has a rich history. Originally introduced for binary images, it was quite soon extended to grayscale images, leading to grayscale morphology with the threshold approach and the umbra approach. Later on, different models based on fuzzy set theory were introduced. These models were based on the observation that, from a formal point of view, grayscale images and fuzzy sets are modeled in the same way. Consequently, techniques from fuzzy set theory could be applied in the context of mathematical morphology, and fuzzy mathematical morphology was born. In that framework, fuzzy set theory was only a tool to construct morphological models, and was not employed to model any fuzziness or uncertainty. Quite recently however, new extensions have led to the construction of fuzzy interval-valued and fuzzy intuitionistic mathematical morphologies. Here, extensions of fuzzy set theory actually take into account the uncertainty that comes along with image capture, specifically regarding the grayscale values, which in some cases is also related to the uncertainty regarding the spatial position of an object in an image. In this framework, (extended) fuzzy set theory not only serves as a tool to deal with grayscale images, but also as a model for uncertainty. This paper sketches this evolution of fuzzy set theory in the field of mathematical morphology, and also points out some directions for future research.

Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted.The concept of

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-Fuzzy Mathematical Morphology

-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of

A fuzzy filter for the removal of random impulse noise in image sequences

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Video denoising by fuzzy motion and detail adaptive averaging

-fuzzy sets forms a complete lattice whenever the underlying set

Color Image Retrieval using Fuzzy Similarity Measures and Fuzzy Partitions

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Image similarity: from fuzzy sets to color image applications

constitutes a complete lattice. Based on these observations, we develop a general approach towards

A soft-switching approach to improve visual quality of colour image smoothing filters

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