In order to analyze images and recognize complex objects, it is necessary to not only recognize the different parts of the objects but also consider spatial relations between parts of the objects. For the recognition of objects with a complex structure, a suitable representation of the spatial relations between the different parts taking account their shape features is required, as it is necessary to capture the coherence of the various positional relations between the different parts of the objects. Therefore, it is impossible to assume that the sub-region of a complex object is a point, and it must be treated as a lump region. There are many problems related to the representation of spatial relations between lump regions. In previous studies, the relations are represented using typical features of the regions such as center of the gravity, leftmost or rightmost points, or characteristic points for polygon approximation. However it is impossible to determine positional relations considering the lumps. In this paper, we propose a method for the representation of spatial relations between two lump regions based on the histogram that can be defined when we consider the angle θ between the line connecting two points (one in each lump region) and the horizontal line, and on the fuzzy sets, defined on θ , expressing the spatial relations between two objects. The method is applied to the representation of the spatial relations between free shape regions and its efficiency is discussed.

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Grading of dried seaweed by subjective sense inspection of an expert(an inspector of grade) generally includes fuzziness or ambiguity. Although our final purpose would develop an automatic grading machine of dried seaweed, this paper aims to get fundamental knowledge on how to objectively discriminate the grade of dried seaweed as a first stage. In order to know features of graded dried seaweed, first, the statistics has been taken in terms of X, Y, Z of CIE three stimulus' values and normal reflection rate R obtained from image processing equipments and so on. As results of Investigating the relation between the grade and the fundamental statistics, an average of X(color tone), an average of Y(brightness), standard deviations of X and Y have been proved to increase with a lowering of seaweed's grade. On the other hand, a normal reflection rate(gloss) has a tendency to decrease with a lowering of grade. Next, the principal component analysis which is one of the multivariate analysis was carried out so as to examine the features of discrimination by the expert again. As a result, it was shown that ranking of dried seaweed by gains of principal components has a good agreement with grading of sense inspection by the expert. Moreover, after making the criterion of each grade by discrimination analysis of Mahalanobis' generalized distance, by using test samples for verification we inspected them to be belong to which grade. As a result, the comparatively good discrimination was obtained.

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Human's image understanding process can be roughly divided into the following two kinds of processes; a perceptual grouping phase and a hypothesis recognition phase. In the former, uncertainties mainly come from the quality of the image itself, while in the latter phase some "dynamic" uncertainties are brought about during mutual interactions between the pre-existing knowledge and the arriving data. The image dealt with in this paper is the one called as a "lineament map", that represents a distribution of linear features on the surface of the earth that are observed in the remotely sensed satellite imagery, and the final goal is to identify one of the prototypical geological hypotheses for the input image. For this purpose, we at first propose a way of applying fuzzy clustering methods in an incremental fashion for extracting fuzzy features out of the input image. Then, to model a mutually interacting process between the data and the knowledge, we propose structured neural networks that consist of three different Hopfield-type networks and play a number of different roles in a hypothesis recognition phase.

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A human face retrieval system based on the linguistic description of impression is developed as one of intelligent human interface technology. This system consists of followingtwo parts. One is the generating linguistic description block. This block generates the certainty degree according to the linguistic description by using fuzzy rules and fuzzy inference, for example "the certainty grade that eyes are big is 0.7". The other is retrieval block based on linguistic description. This block generates the concrete pattern for the subjective linguistic input, and estimates the candidates in the database by usingfuzzy matching. This system is implemented on workstation and its peripheral system.

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In this paper, we present algorithms in recognition of unconstrained handwritten numerals. We carry out the feature extraction from the pattern of handwritten numerals. In the conventional fuzzy methods, we recognize the pattern by using the combination of the similarities for the basic elements such as straight lines, circles and arcs. Therefore, we constrain the writer to work under certain restrictions such as print handwriting and neat writing. In order to relax these restrictions, we propose a new method which can classify the numeral patterns by using the several kinds of elemental strokes with fuzziness. The fuzzy elemental stroke consists of a string like S- or Q-shaped character, which is different from the conventional basic elements of straight lines, circles, arcs and so on. Using our feature extraction method, we can obtain a high recognition rate in the classification of unconstrained handwritten numerals.

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Lip reading through visual processing techniques help provide some useful systems for the hearing impaired to learn communication assistance. This paper proposes a method to understand spoken words by using visual images taken by a camera with a video-digitizer. The image is processed to obtain the contours of lip, which is approximated into a hexagon. The pattern lists, consisting of lengths and angles of hexagon, are compared and computed to get the fuzzy similarity between two lists. By similarity matching, the mouth shape is recognized as the one which has the pronounced voice. Some experiments, exemplified by recognition of the Japanese vowels, are given to show feasibility of this method.

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Thepurpose of this study is torealize image-understanding by computer.Image is consideredas an informational medium for human, and image-understanding is defined as the translation of the connotation of picture into natural language. A landscape, which is composed of natural things, is chosen as an example. This paper consists of three phases. In the first phase, a kind of elements are recognized by using fuzzy inference, because natural things which are constituent elements of landscape are so ・・ various in size, shape and color that ordinary method of pattern recognition is hardly applied. So, representing in advance the basic and general characteristics of elements in natural language should be considered. This representation is stored in date base in the form of fuzzy sets. On the other hand, the characteristics of the target image should be detected and represented by the form of fuzzy sets. By matching of the two, which images would enable qualitative comparisons of the characteristics, the recognition is facilitated. In the second phase, we analyze human behavior for image understanding by eye-motion cameraand also analyze how human expresses the image linguistically. According to experimental results, the flow-chart and the membership functions in words used in sentences are identified. In the third phase, the information processing of human is simulated by a computer, that is, the elements of image are represented by using information of contour. After that, the global meaning of the image is represented in a sentence automatically. These results are verified by experiment using some simple pictures of scenery.

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A new optical fuzzy image recognizing system, which can recognize a number from a numerical letter and distinguish sex from a picture of person, has been proposed. The system quantifies a similarity between images on the basis of fuzzy theory using the optics. This optical calculating system uses images of a membership function depicted with a pulse width modulated image transformed two-dimensional picture. The similarity is represented with a function based on an algebraic product between membership functions. These membership functions represent shapes of a standard picture and a test picture. The test picture is recognized as being similar to a picture for which the value of similarity is the highest. This picture is also classified into a group of the similar picture. The paper has cleared that the optical system can recognize a numerical letter, 0 to 9,as a number indicated by the letter. Furthermore, the system was able to distinguish sex form a picture of person like a human.

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A new algorithm for fuzzy c-means clustering in color image processing is proposed for possible application to automatic segmentation of scene pictures. This algorithm automatically determines the number of colors for a given input color scene, and divides the scene into meaningful regions. It is evaluated for four color scenes in comparison with non-fuzzy and former fuzzy algorithms by labeled color images and contours of segmented regions.

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