Tatsunari Sakurai

Detection of motion fields under spatio-temporal non-uniform illumination

In actual scene analysis, the influence of non-ideal conditions such as non-uniform illumination should be taken into account. The conventional methods for the estimation of motion fields are violated in this situation. In this study, two approaches are proposed to extract reliable motion fields under spatio-temporal non-uniform illumination. These are an extended constraint equation with spatio-temporal local optimization and a pixel-based temporal filtering. Experiments have been made to confirm the performance of the proposed methods and to clarify the difference of characteristics between them.

Realizing Visual Functions with the Reaction–Diffusion Mechanism

The present paper proposes a computational model for the realization of visual functions of edge and/or feature detection and segmentation. The model utilizes a reaction–diffusion model which is an extended version of the diffusion-based Difference of Gaussians (DOG) filter previously proposed by Marr and Hildreth as an edge detection model. The proposed model self-organizes spatial patterns having edges and/or features and segments. These patterns are sustained by the intrinsic mechanism of the proposed model under specific conditions. In addition, the model also helps to solve the stereo matching problem in random dot stereograms and the aperture problem in optical flow computation. These visual functions of the proposed model are demonstrated with both artificial and real images.

Oscillation and Synchronization in the Combustion of Candles

We investigate a simple experimental system using candles; stable combustion is seen when a single candle burns, while oscillatory combustion is seen when three candles burn together. If we consider a set of three candles as a component oscillator, two oscillators, that is, two sets of three candles, can couple with each other, resulting in both in-phase and antiphase synchronization depending on the distance between the two sets. The mathematical model indicates that the oscillatory combustion in a set of three candles is induced by a lack of oxygen around the burning point. Furthermore, we suggest that thermal radiation may be an essential factor of the synchronization.

Motion enhancement for preprocessing of optical flow detection and scientific visualization

Abstract We introduce a simple method for motion enhancement. The method enables us to realize brightness enhancement of moving objects, to reduce the influence of non-uniform illumination in motion analysis and to visualize dynamic streamlines in fluid flow analysis.

Oscillatory motion of a camphor grain in a one-dimensional finite region.

The motion of a self-propelled particle is affected by its surroundings, such as boundaries or external fields. In this paper, we investigated the bifurcation of the motion of a camphor grain, as a simple actual self-propelled system, confined in a one-dimensional finite region. A camphor grain exhibits oscillatory motion or remains at rest around the center position in a one-dimensional finite water channel, depending on the length of the water channel and the resistance coefficient. A mathematical model including the boundary effect is analytically reduced to an ordinary differential equation. Linear stability analysis reveals that the Hopf bifurcation occurs, reflecting the symmetry of the system.

Feedback stabilization of non-uniform spatial pattern in reaction-diffusion systems

In this paper, we formulate and solve feedback stabilization problem of unstable non-uniform spatial pattern in reaction-diffusion systems. By considering spatial spectrum dynamics, we obtain a finite dimensional approximation that takes over the semi-passivity of the original partial differential equation. By virtue of this property, we can show the diffusive coupling in the spatial frequency domain achieves the desired pattern formation.

Numerical Experiments on the Turing Instability in the Oregonator Model

Numerical experiments on the Oregonator model of the Belousov-Zhabotinsky reaction with 2 variables (activator and inhibitor) are carried out. Influences of an inhibitory diffusion coefficient and inhibitory initial condition (concentration) on its pattern dynamics are studied for several values of a stoichiometric factor of the model. As a result, several pattern formation processes such as decrementally propagating waves and self replicating processes are found by changing the initial condition of the inhibitor and the stoichiometric factor under the Turing instability. In the self replicating process, new pattern dynamics acting as birth and death of waves is also found.

Structure of Surface Deformation Waves Induced in Spiral Pattern in the Belousov–Zhabotinsky Reaction

A surface deformation wave coupled with an oscillatory hydrodynamic flow is observed in a thin solution layer of the Belousov–Zhabotinsky reaction. The observation is carried out with a Mach–Zehnder interferometric system under the excitation of chemical spiral waves in the solution. The surface deformation wave is induced spontaneously at the end of a dish. It propagates towards the center of the spiral waves, and disappears there. This fact leads to understand the oscillatory flow as a propagating convection waves having long-scale surface deformation. The Marangoni effect or surface tension driven convection with deformable surface plays an important role to establish the oscillatory flow.

Spiral flow wave in a reaction-diffusion-convection system

The excitable Belousov–Zhabotinsky (BZ) reaction coupled with diffusion can exhibit a large variety of spatial patterns. In this letter, we report on superimposed spiral structures, providing evidence of a hierarchical self-organized order that connects two complex phenomena involving the coupling of a reaction–diffusion pattern with convection. A macroscopic propagating spiral flow wave (wavelength about 50 mm) is induced spontaneously by the preexcited reaction–diffusion structure of chemical spiral waves (wavelength about 1 mm). The pattern dynamics links two different hierarchical levels of structure formation in a nonlinear system.

Image edge detection with discretely spaced FitzHugh-Nagumo type excitable elements

This paper presents a computer algorithm of detecting edges from a grey scale image with FitzHugh-Nagumo type excitable elements discretely spaced at image grid points. A previous edge detection algorithm utilising the elements is not applicable to darker intensity areas surrounded by brighter ones; the algorithm fails in detecting edges in the areas. In order to solve the problem in detecting edges in relatively dark areas, we proposed to utilise an intensity inverted image as well as its original one. The proposed algorithm firstly provides a tentative edge map from the original image, and simultaneously provides an additional tentative edge map from the inverted image. Then, the algorithm provides a final edge map by merging the two edge maps. We quantitatively confirm performance of the proposed algorithm, in comparison with that of the previous one and that of the Canny algorithm for an artificial grey scale image not having noise. We furthermore confirm robustness and convergence of the proposed algorithm for a noisy image and real ones. These results shows that the performance of the proposed algorithm is much higher than the previous one and is comparable with the Canny algorithm for a noise-less image, and the proposed algorithm converges for all of the images. However, the proposed algorithm is vulnerable for additive noise, in comparison with the Canny algorithm and the anisotropic diffusion algorithm.