In this paper, the authors present general views of computer vision and image processing based on optimization. Relaxation and regularization in both broad and narrow senses are used in various fields and problems of computer vision and image processing, and they are currently being combined with general-purpose optimization algorithms. The principle and case examples of relaxation and regularization are discussed; the application of optimization to shape description that is a particularly important problem in the field is described; and the use of a genetic algorithm (GA) as a method of optimization is introduced.

This paper proposes a new framework of managing virtual spaces based on spatial databases as an extension of VRML-based systems. The framework is suitable for treating continuous virtual spaces and for managing the quality of service (QoS) of the virtual spaces depending on user's operations and situations of computer resources. Levels of detail (LoD) of 3D objects is the most important rule for rendering scenes dynamically while managing the QoS. This paper describes a method of managing the QoS depending on the LoD in the form of spatial queries. An advantage of the framework is that spatial databases can incrementally construct virtual spaces in clients using differential descriptions based on VRML, that is, DVRML, proposed in this paper. Dynamic spatial data such as avatar's movement and real-time multimedia data such as videos should be shared by all participants in a virtual space in real time. Our framework can also handle dynamic spatial data by means of real-time updating of some spatial objects in spatial databases as well as static spatial data. We developed some experimental applications based on the framework in order to prove that it is feasible for networked virtual spaces with video components.