Jesús Chamorro-Martínez

Retrieving images in fuzzy object-relational databases using dominant color descriptors

In this paper a fuzzy approach for image retrieval on the basis of color features is presented. The proposal deals with vagueness in the color description and introduces the use of fuzzy database models to store and retrieve imprecise data. To face the color description, the concept of dominant fuzzy color is proposed, using linguistic labels for representing the color information in terms of hue, saturation and intensity. To deal with fuzzy data in our database model, we use a general approach which can support the manipulation of fuzzy objects in an object-relational database system. This allows the retrieval of images by performing flexible queries on the database.

On a non-nested level-based representation of fuzziness

In this paper we describe a non-nested level-based representation of fuzziness, closely related to some existing models and concepts in the literature. Our objective is to motivate the use of this non-nested model by describing its theoretical possibilities, and illustrating them with some existing applications. From a theoretical point of view, we discuss the semantics of the representation, which goes beyond and has as a particular case fuzzy sets as represented by a collection of @a-cuts. In addition, the proposed operations on level-based representations, contrary to those of existing fuzzy set theories, satisfy all the properties of Boolean logic. We discuss the contributions of the representation and operation by levels to practical applications, in particular for extending crisp notions to the fuzzy case. In this respect, an important contribution of the proposal is that fuzzy mathematical objects (not only sets and the corresponding predicates) and operations are uniquely and easily defined as extensions of their crisp counterparts. In order to illustrate this claim, we recall level representations of quantities (gradual numbers) and their complementarity to fuzzy intervals (often inappropriately called fuzzy numbers).

Mining web documents to find additional query terms using fuzzy association rules

In this paper, we present an application of association rules to query refinement. Starting from an initial set of documents retrieved from the web, text transactions are constructed and association rules are extracted. A fuzzy extension of text transactions and association rules is employed, where the presence of the terms (items) in the documents (transactions) is determined with a value between 0 and 1. The obtained rules offer the user additional terms to be added to the query with the purpose of guiding the search and improving the retrieval.

A new approach for defining a fuzzy color space

In this paper we introduce formal definitions of the concepts of fuzzy color and fuzzy color space. We present an approach to the automatic design of customized fuzzy color spaces on the basis of a collection of crisp colors, each crisp color being fully representative of a certain color term. The approach works on any euclidean crisp space and is based on obtaining a Voronoi diagram having the aforementioned representative crisp colors as centroids. The proposal will be illustrated building fuzzy color spaces on RGB colors on the basis of the ISCC-NBS color naming system.

Region-based fit of color homogeneity measures for fuzzy image segmentation

In this paper we introduce an approach to automatically select a homogeneity measure for color image segmentation, on the basis of the characteristics of the region to be segmented. In a previous work we presented a fuzzy color path-based image segmentation proposal where membership degrees were computed from the connectivity between pixels, based on the homogeneity degree of the path joining them. To measure homogeneity, we aggregate resemblances between consecutive pixels using t-norms. Since a great variety of homogeneity measures can be found, we need to automatically select a suitable t-norm for a given region. For this purpose we firstly approximate a value characterizing the region surrounding the seed, studying a set of fixed paths. Secondly, we establish a functional relationship between this value and the parameter of a Weber t-norm. Based on this functional relationship we obtain the value of t-norms parameter, corresponding to the homogeneity measure to be used in the segmentation process. We show that our approach performs well in different types of regions.

Modelling subjectivity in visual perception of orientation for image retrieval

In this paper we combine computer vision and data mining techniques to model high-level concepts for image retrieval, on the basis of basic perceptual features of the human visual system. High-level concepts related to these features are learned and represented by means of a set of fuzzy association rules. The concepts so acquired can be used for image retrieval with the advantage that it is not needed to provide an image as a query. Instead, a query is formulated by using the labels that identify the learned concepts as search terms, and the retrieval process calculates the relevance of an image to the query by an inference mechanism. An additional feature of our methodology is that it can capture users subjectivity. For that purpose, fuzzy sets theory is employed to measure users assessments about the fulfillment of a concept by an image.

Describing images via linguistic features and hierarchical segmentation

In this paper we introduce a preliminary proposal for linguistic description of images. The approach is based on i) a hierarchical fuzzy segmentation of the image, ii) a collection of linguistic features describing each region, and iii) fuzzy spatial relations and locations. The procedure is independent from the way these elements have been obtained, and provides a description with the characteristics of a summary, i.e., a brief and accurate description of the whole image. As another characteristic of summaries, the method can be guided in the description by the users preferences and interest. Remarkably, we are able to provide a description containing sentences about disjoint regions appearing in different levels of detail.

A hierarchical approach to fuzzy segmentation of colour images

In this paper we introduce a methodology for the segmentation of colour images by means of a nested hierarchy of fuzzy partitions. Colour image segmentation attempts to divide the pixels of an image in several homogeneously-coloured and topologically connected groups, called regions. Our methodology deals with the different (but related) aspects of imprecision that are present in this process. First, the concept of homogeneity in a colour space is imprecise, so a measure of distance/similarity between colours is introduced. As a direct consequence, boundaries between regions are imprecise in general, so it is convenient to define regions as fuzzy subsets of items. The proposed distance in a perceptual colour space is employed to calculate fuzzy regions and membership degrees. In addition, fuzzy segmentation can be different depending on the precision level we consider when looking for homogeneity. Starting from an initial fuzzy segmentation, a hierarchical approach, based on a similarity relation between regions, is employed to obtain a nested hierarchy of regions at different precision levels.

A frequency-domain approach for the extraction of motion patterns

A new frequency-domain approach to represent motions is proposed. The new scheme is based on a band-pass filtering with a set of logGabor spatio-temporal filters. It is well known that one of the main problems of these approaches is that a filter response varies with the spatial orientation of the underlying signal. To solve this spatial dependency, the proposed model allows to recombine information of motions that has been separated in several filter responses due to its spatial structure. For this purpose, motion patterns are detected as invariance in statistical structure across a range of spatio-temporal frequency bands. This technique is illustrated on real and simulated data sets, including sequences with occlusion and transparencies.

A discussion on fuzzy cardinality and quantification. Some applications in image processing

In this paper we discuss on some different representations of the cardinality of a fuzzy set and their use in fuzzy quantification. We have considered the widely employed sigma-count, fuzzy numbers, and gradual numbers. Gradual numbers assign numbers to values of a relevance scale, typically 0,1. Contrary to sigma-count and fuzzy numbers, they provide a precise representation of the cardinality of a fuzzy set. We illustrate our claims by calculating the cardinality of the fuzzy set of pixels that match a certain fuzzy color in an image. For that purpose we consider fuzzy color spaces previously defined by the authors, consisting of a collection of fuzzy sets providing a suitable, conceptual quantization with soft boundaries of crisp color spaces. Finally, we show the suitability of our approaches to fuzzy quantification for different applications in image processing. First, the calculation of histograms. Second, the definition of the notion of dominant fuzzy color, and the calculation of the degree to which we can say that a certain color is dominant in an image.