Using a point matching method, we have numerically analyzed resonance frequencies and unloaded Q factor of whispering gallery modes in a millimeter wave region that are well known as an intrinsic mode of a dielectric disk resonator. We express field distributions of the resonance modes by a summation of spherical waves. Tangential electromagnetic fields inside the disk are matched to those outside the disk at appropriate matching points on a boundary. As the result, a 4N 4N (N; number of matching points) determinant is derived as an eigenvalue equation of the disk resonator. Since elements of the determinant are complex numbers, a complex angular frequency is introduced to make a value of the determinant zero. For a location of the matching points, we also introduce a new technique which is derived from a field expression of the whispering gallery modes. Since an azimuthal angle dependence of the field distributions with a resonance mode number m is presented by the associated Legendre function Pnm(cos θ), we define abscissas θi of the matching points as solutions of Pm+2N-1m (cos θ) = 0. Considering the field symmetry, we also modify the eigenvalue equation to a new eigenvalue equation which is expressed (4N - 2) (4N - 2) determinant. From the results of our numerical analysis, we can find that the resonance frequencies and unloaded Q factor well converge for number of matching points N. A comparison of numerical results and experimental ones, in a millimeter wave band (50 - 100 GHz), shows a good agreement with each other. It is found that our analysis is effective for practical use in the same wave band.

Correspondence problem in road image sequence is discussed and a method to establish road correspondence from its perspective image sequence is suggested. The proposed method is mainly based on the features of turn angles of road edge points, while the turn angle for each edge point at one time can be computed from the frame based on the determination of matching points whin that frame. The turn angles will change from frame to frame according to the panning rotation of the camera and, each stationary edge point, the difference of turn angles between two frames equals the panning angle of the camera. Thus we develop an algorithm to estimate the value of panning angle of the camera by which correspondence in road image sequence can be established.

This paper introduces a new method to recover 3-D road plane from its 2-D monocular perspective image. The research is aimed at the reconstruction of depth information from the 2-D visual input in road following and navigation. Planar road model is considered and the road-centered coordinate system which forms slope and turn angles with camera-centered coordinate system is used to describe boundary points on road plane. We develop approaches to find matching points of boundaries of road and to obtain angular parameters thereafter. A way of finding depth of matching points from the perspective images and angular parameters together is proposed. Therefore the 3-D road reconstruction can be replicated without introducing any parameters of inverse perspective.