In this paper, we apply the geometric curve evolution approach to 3D reconstruction for a number of images in the stereo vision. The curve evolution approach is based on the Euclidean curve shortening evolution theory, and the level set method is introduced into it for numerical computation. The Euler-Lagrange equations that are deduced from the variational principle provide a set of curve evolving equations. These PDE's describe the process of the geometric curve evolution on the relevant epipolar plane. In 3D space, the each epipolar plane is monogamously projected as a unique pair of the intra-scanlines on stereo pairs. These PDE's are used to deform an initial set of curves that then move towards the object outlines to be detected. The level set implementation of these PDE's provides an efficient and robust computational way for the kind of the geometric-driven evolving equations. The velocity term in the level set equations can be obtained from the above geometric curve evolving equations. It is intrinsic and only depends upon the stereo problem. We present the close form of the velocity. Finally, the results of implementation of our theory are presented on synthetic images.
In this article, some basic problems on the level set methods are discussed, such as the method used to preserve the distance function, the existence and uniqueness of the solutions for the level set equations and the analysis of the singular points. It is presented that if the solutions of the level set equations with the distance function restriction exist, they must be the signed distance function to the evolving surface. And it is presented that there exists a unique solution in a neighborhood of the initial zero level set. However, the uniqueness of the solutions is hard to be guaranteed away from the initial zero level set. An important property of the singular points is given, which is a sufficient and necessary condition in distinguishing the singular points from ordinary points. The above results consummate the theoretical base of the level set methods. At meantime, the estimate method of the width of the narrow band is presented in order to avoid the singular points during the iterative process of the level set methods. The implementations of our theory are shown on real images and synthetic images.
KEYWORDS: Particles, Electrons, Photovoltaics, Surface plasmons, Neodymium, Solar energy, Transmission electron microscopy, Chemical species, Oxygen, Field spectroscopy
Nd2O3 nanometer powders were prepared by precipitation method. XRD analysis showed that Nd2O3 nanometer powders were cubic in structure at 600 degrees Celsius; and hexagonal at 850-1000 degrees Celsius, space group was D32-P 321. TEM analysis indicated that Nd2O3 particles were spherical in shape and increased in size with the increase of calcination temperature. The synthesized Nd2O3 nanometer powders were studied by surface photovoltaic spectroscopy (SPS) and field-modulated surface photovoltaic spectroscopy (FMSPS). The observed spectral features can be explained in terms of charge transfer and interband transition.
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