Vasile Patrascu

Vasile Patrascu

This article presents a new method of segmenting grayscale images by minimizing Shannon's neutrosophic entropy. For the proposed segmentation method, the neutrosophic information components, i.e., the degree of truth, the degree of neutrality and the degree of falsity are defined taking into account the belonging to the segmented regions and at the same time to the separation threshold area. The principle of the method is simple and easy to understand and can lead to multiple thresholds. The efficacy of the method is illustrated using some test gray level images. The experimental results show that the proposed method has good performance for segmentation with optimal gray level thresholds.

Vasile Patrascu

The paper presents an extension of Shannon entropy for neutrosophic information. This extension uses a new formula for distance between two neutrosophic triplets. In addition, the obtained results are particularized for bifuzzy, intuitionistic and paraconsistent fuzzy information.

Vasile Patrascu

The paper presents an extension of Shannon fuzzy entropy for intuitionistic fuzzy one. Firstly, we presented a new formula for calculating the distance and similarity of intuitionistic fuzzy information. Then, we constructed measures for information features like score, certainty and uncertainty. Also, a new concept was introduced, namely escort fuzzy information. Then, using the escort fuzzy information, Shannon's formula for intuitionistic fuzzy information was obtained. It should be underlined that Shannon's entropy for intuitionistic fuzzy information verifies the four defining conditions of intuitionistic fuzzy uncertainty. The measures of its two components were also identified: fuzziness (ambiguity) and incompleteness (ignorance).

Vasile Patrascu

This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: entropy, neutro-entropy and anti-entropy.

Vasile Patrascu

Starting from the primary representation of neutrosophic information, namely the degree of truth, degree of indeterminacy and degree of falsity, we define a nuanced representation in a penta valued fuzzy space, described by the index of truth, index of falsity, index of ignorance, index of contradiction and index of hesitation. Also, it was constructed an associated penta valued logic and then using this logic, it was defined for the proposed penta valued structure the following operators: union, intersection, negation, complement and dual. Then, the penta valued representation is extended to a hexa valued one, adding the sixth component, namely the index of ambiguity.

Vasile Patrascu

This paper presents a five-valued representation of bifuzzy sets. This representation is related to a five-valued logic that uses the following values: true, false, inconsistent, incomplete and ambiguous. In the framework of five-valued representation, formulae for similarity, entropy and syntropy of bifuzzy sets are constructed.

Vasile Patrascu

In this paper one presents new similarity, cardinality and entropy measures for bipolar fuzzy set and for its particular forms like intuitionistic, paraconsistent and fuzzy set. All these are constructed in the framework of multi-valued representations and are based on a penta-valued logic that uses the following logical values: true, false, unknown, contradictory and ambiguous. Also a new distance for bounded real interval was defined.

Vasile Patrascu

In this paper, we define a distance for the HSL colour system. Next, the proposed distance is used for a fuzzy colour clustering algorithm construction. The presented algorithm is related to the well-known fuzzy c-means algorithm. Finally, the clustering algorithm is used as colour reduction method. The obtained experimental results are presented to demonstrate the effectiveness of our approach.

Vasile Patrascu

In this paper two knowledge representation models are proposed, FP4 and FP6. Both combine ideas from fuzzy sets and four-valued and hexa-valued logics. Both represent imprecise properties whose accomplished degree is unknown or contradictory for some objects. A possible application in the color analysis and color image processing is discussed.

Vasile Patrascu

In this paper a knowledge representation model are proposed, FP5, which combine the ideas from fuzzy sets and penta-valued logic. FP5 represents imprecise properties whose accomplished degree is undefined, contradictory or indeterminate for some objects. Basic operations of conjunction, disjunction and negation are introduced. Relations to other representation models like fuzzy sets, intuitionistic, paraconsistent and bipolar fuzzy sets are discussed.

Vasile Patrascu

Image enhancement is an important stage in the image-processing domain. The most known image enhancement method is the histogram equalization. This method is an automated one, and realizes a simultaneous modification for brightness and contrast in the case of monochrome images and for brightness, contrast, saturation and hue in the case of color images. Simple and efficient methods can be obtained if affine transforms within logarithmic models are used. A very important thing in the affine transform determination for color images is the coordinate system that is used for color space representation. Thus, the using of the RGB coordinates leads to a simultaneous modification of luminosity and saturation. In this paper using the lrgb perceptual coordinates one can define affine transforms, which allow a separated modification of luminosity l and saturation s (saturation being calculated with the component rgb in the chromatic plane). Better results can be obtained if partitions are defined on the image support and then the pixels are separately processed in each window belonging to the defined partition. Classical partitions frequently lead to the appearance of some discontinuities at the boundaries between these windows. In order to avoid all these drawbacks the classical partitions may be replaced by fuzzy partitions. Their elements will be fuzzy windows and in each of them there will be defined an affine transform induced by parameters using the fuzzy mean, fuzzy variance and fuzzy saturation computed for the pixels that belong to the analyzed window. The final image is obtained by summing up in a weight way the images of every fuzzy window.

Vasile Patrascu

In this paper one presents a new fuzzy clustering algorithm based on a dissimilarity function determined by three parameters. This algorithm can be considered a generalization of the Gustafson-Kessel algorithm for fuzzy clustering.

Vasile Patrascu

This paper presents two variants of penta-valued representation for neutrosophic entropy. The first is an extension of Kaufmann's formula and the second is an extension of Kosko's formula. Based on the primary three-valued information represented by the degree of truth, degree of falsity and degree of neutrality there are built some penta-valued representations that better highlights some specific features of neutrosophic entropy. Thus, we highlight five features of neutrosophic uncertainty such as ambiguity, ignorance, contradiction, neutrality and saturation. These five features are supplemented until a seven partition of unity by adding two features of neutrosophic certainty such as truth and falsity. The paper also presents the particular forms of neutrosophic entropy obtained in the case of bifuzzy representations, intuitionistic fuzzy representations, paraconsistent fuzzy representations and finally the case of fuzzy representations.

Vasile Patrascu

In this paper we use a new logarithmic model of image representation, developed in [1,2], for edge detection. In fact, in the framework of the new model we obtain the formulas for computing the "contrast of a pixel" and the "contrast" image is just the "contour" or edge image. In our setting the range of values is preserved and the quality of the contour is good for high as well as for low luminosity regions. We present the comparison of our results with the results using classical edge detection operators.

Vasile Patrascu

This paper presents a new method of gray level image enhancement, based on point transforms. In order to define the transform function, it was used a generalization of the homographic function.

Vasile Patrascu

In this paper we use a logarithmic model for gray level image enhancement. We begin with a short presentation of the model and then, we propose a new formula for the mean dynamic range. After that we present two image transforms: one performs an optimal enhancement of the mean dynamic range using the logarithmic addition, and the other does the same for positive and negative values using the logarithmic scalar multiplication. We present the comparison of the results obtained by dynamic ranges optimization with the results obtained using classical image enhancement methods like gamma correction and histogram equalization.

Vasile Patrascu

This paper presents a method for enhancing the gray level images. This method takes part from the category of point transforms and it is based on interpolation functions. The latter have a graphic represented by polygonal lines. The interpolation nodes of these functions are calculated taking into account the statistics of gray levels belonging to the image.

Vasile Patrascu

This paper presents a method for enhancing the gray level images. This presented method takes part from the category of point operations and it is based on piecewise linear functions. The interpolation nodes of these functions are calculated using the Bernstein polynomials.

Vasile Patrascu, Vasile Buzuloiu

Images of a scene observed under a variable illumination or with a variable optical aperture are not identical. Does a privileged representant exist? In which mathematical context? How to obtain it? The authors answer to such questions in the context of logarithmic models for images. After a short presentation of the model, the paper presents two image transforms: one performs an optimal enhancement of the dynamic range, and the other does the same for the mean dynamic range. Experimental results are shown.

Vasile Patrascu, Vasile Buzuloiu

The logarithmic model offers new tools for image processing. An efficient method for image enhancement is to use an affine transformation with the logarithmic operations: addition and scalar multiplication. We define some criteria for automatically determining the parameters of the processing and this is done via mean and variance computed by logarithmic operations.

Vasile Patrascu, Vasile Buzuloiu

In this paper, we propose a new mathematical model for image processing. It is a logarithmical one. We consider the bounded interval (-1, 1) as the set of gray levels. Firstly, we define two operations: addition <+> and real scalar multiplication <x>. With these operations, the set of gray levels becomes a real vector space. Then, defining the scalar product (.|.) and the norm || . ||, we obtain an Euclidean space of the gray levels. Secondly, we extend these operations and functions for color images. We finally show the effect of various simple operations on an image.

Vasile Patrascu, Vasile Buzuloiu

In this paper, we propose a mathematical model for color image processing. It is a logarithmical one. We consider the cube (-1,1)x(-1,1)x(-1,1) as the set of values for the color space. We define two operations: addition <+> and real scalar multiplication <x>. With these operations the space of colors becomes a real vector space. Then, defining the scalar product (.|.) and the norm || . ||, we obtain a (logarithmic) Euclidean space. We show how we can use this model for color image enhancement and we present some experimental results.

Vasile Patrascu

In this paper we propose a new algebraical model for the gray level images. It can be used for digital image processing. The model adresses to those images which are generated in improper light conditions (very low or high level). The vector space structure is able to illustrate some features into the image using modified level of contrast and luminosity. Also, the defined structure could be used in image enhancement. The general approach is presented with experimental results to demonstrate image enhancement.

Vasile Patrascu

The paper presents some steps for multi-valued representation of neutrosophic information. These steps are provided in the framework of multi-valued logics using the following logical value: true, false, neutral, unknown and saturated. Also, this approach provides some calculus formulae for the following neutrosophic features: truth, falsity, neutrality, ignorance, under-definedness, over-definedness, saturation and entropy. In addition, it was defined net truth, definedness and neutrosophic score.