Mitsuhiko Fujio

Morphological texture analysis using optimization of structuring elements

This paper proposes a method of texture analysis using morphological size distribution. Our framework is based on the concept that a texture is described by estimation of primitive, size distribution of grains derived from the primitive, and spatial distribution of the grains. We concentrate on estimation of primitive using an assumption on grain size distribution. We assume a model that grains are derived from one primitive, and a uniform size distribution since we consider target textures containing grains of various sizes. Thus the structuring element used for the measurement of size distribution is optimized to obtain the most uniform size density function. The optimized structuring element is an estimate of the primitive under the assumption. Simulated annealing algorithm is employed for the optimization.

Wavelet analysis of EEG signals during motor imagery

ERS and ERD (event-related synchronization and desynchronization) are observed in EEG (electroencephalogram) signals around such events as sensitive stimulus, motions, cognitive actions etc. Usually, ERS/ERD features of EEG are extracted as variances of band-passed signals of several trials. To make use of these features to recognize inputs for BCI (brain-computer interface), we applied discrete wavelet analysis to extraction of ERS/ERD features from a small number of EEG signals during motor imagery. We employed Daubechies, convolution and spline biorthogonal mothers for linear wavelet analysis, also Haar type structural function for morphological wavelet analysis. Then our extraction method was estimated by the pattern recognition based on AR model.

Feature Extraction of EEG Waves Based on Morphological Multiresolution Analysis

Electroencephalograph (EEG) recordings during right and left hand motor imagery can be used to move a cursor to a target on a computer screen. Such an EEG-based brain-computer interface (BCI) can provide a new communication channel to replace an impaired motor function. It can be used by e.g., handicap users with amyotrophic lateral sclerosis (ALS). In this paper, feature extraction based on morphological multiresolution analysis is introduced to discriminate the EEG signals recorded during left and right hand motor imagery, and oddball task. The mixture features in the brain wave signal of single channel is able to separate to various bands. The structural function to decide the filter characteristic is discussed using the experimental studies.

The Number of Orbits of Periodic Box-Ball Systems

A box-ball system is a kind of cellular automata obtained by the ultradiscrete Lotka-Volterra equation. Similarities and differences between behavious of discrete systems (cellular automata) and continuous systems (differential equations) are investigated using techniques of ultradiscretizations. Our motivations is to take advantage of behavious of box-ball systems for new kinds of computations. Especially, we tried to find out useful periodic box-ball systems(pBBS) for random number generations. Applicable pBBS systems should have long fundamental cycles. We focus on pBBS with at most two kinds of solitons and investigate their behaviours, especially, the length of cycles and the number of orbits. We showed some relational equations of soliton sizes, a box size and the number of orbits. Varying a box size, we also found out some simulation results of the periodicity of orbits of pBBS with same kinds of solitons.In this paper we suggest the use of light for performing useful computations. Namely, we propose a special device which uses light rays for solving the Hamiltonian path problem on a directed graph. The device has a graph-like representation and the light is traversing it following the routes given by the connections between nodes. In each node the rays are uniquely marked so that they can be easily identified. At the destination node we will search only for particular rays that have passed only once through each node. We show that the proposed device can solve small and medium instances of the problem in reasonable time.

REDUNDANT MORPHOLOGICAL WAVELET AND LOCAL PATTERN SPECTRUM

Time-frequency analysis methods such as wavelet analysis are applied to investigate characteristic from non-stationary signals. In this study, we proposed redundant morphological wavelet analysis that was a kind of nonlinear discrete wavelet and redundant wavelet. This method analyzes a transition of shape information from signals in detail since this method keeps property of shift invariance though information of decomposition includes redundancy. Local pattern spectrum which corresponds to nonlinear short time Fourier transform is derived from this nonlinear wavelet. The characteristics of these methods were confirmed by applying to simulation data and actual data.

A Comparison of Implications in Orthomodular Quantum Logic—Morphological Analysis of Quantum Logic

Morphological operators are generalized to lattices as adjunction pairs (Serra, 1984; Ronse, 1990; Heijmans and Ronse, 1990; Heijmans, 1994). In particular, morphology for set lattices is applied to analyze logics through Kripke semantics (Bloch, 2002; Fujio and Bloch, 2004; Fujio, 2006). For example, a pair of morphological operators as an adjunction gives rise to a temporalization of normal modal logic (Fujio and Bloch, 2004; Fujio, 2006). Also, constructions of models for intuitionistic logic or linear logics can be described in terms of morphological interior and/or closure operators (Fujio and Bloch, 2004). This shows that morphological analysis can be applied to various non-classical logics. On the other hand, quantum logics are algebraically formalized as orhomodular or modular ortho-complemented lattices (Birkhoff and von Neumann, 1936; Maeda, 1980; Chiara and Giuntini, 2002), and shown to allow Kripke semantics (Chiara and Giuntini, 2002). This suggests the possibility of morphological analysis for quantum logics. In this article, to show an efficiency of morphological analysis for quantum logic, we consider the implication problem in quantum logics (Chiara and Giuntini, 2002). We will give a comparison of the 5 polynomial implication connectives available in quantum logics.

Morphological interpretation of local composition of Cellular Automata of groups

The notion of local composition of local transition rules for Cellular Automaton (CA for short) on groups was introduced in a straightforward way to achieve compatibility with the composition of global transition functions. In this article, we give a Morphological interpretation of local composition.

Design Method of Morphological Structural Function for Pattern Recognition of EEG Signals During Motor Imagery and Cognition

Electroencephalograph (EEG) recordings during right and left hand motor imagery can be used to move a cursor to a target on a computer screen (such system is called BCI). Recently, we have proposed the detection method of Error Potential in order to add the fail safe function to BCI system. In this paper, feature extraction method based on morphological multi-resolution analysis is introduced to extract features concerned with motor imagery and cognition simultaneously from the EEG signals. Morphological filter is composed of nonlinear operation between signal and structural function and this multi-resolution analysis can be constructed by repeating this filtering to signal while changing structural function. This method is a kind of discrete wavelet analysis with non-linear characteristics and is effective to extract specific shapes. The structural function which decides the filter characteristic is designed to obtain optimal separation based on mutual information algorithm or spectrum dividing algorithm.

The number of orbits of periodic box-ball systems

A box-ball system is a kind of cellular automata obtained by the ultradiscrete Lotka-Volterra equation. Similarities and differences between behavious of discrete systems (cellular automata) and continuous systems (differential equations) are investigated using techniques of ultradiscretizations. Our motivations is to take advantage of behavious of box-ball systems for new kinds of computations. Especially, we tried to find out useful periodic box-ball systems(pBBS) for random number generations. Applicable pBBS systems should have long fundamental cycles. We focus on pBBS with at most two kinds of solitons and investigate their behaviours, especially, the length of cycles and the number of orbits. We showed some relational equations of soliton sizes, a box size and the number of orbits. Varying a box size, we also found out some simulation results of the periodicity of orbits of pBBS with same kinds of solitons.