| Implicit polynomials are among the most effective representations for complex object recognition because of their stability, robustness and invariant characteristics. This thesis presents a general overview of the problem and focuses on the key issues of implicit polynomial technology for representing and recognizing complicated 2D and 3D shapes subject to partial occlusion and missing data. It covers new concepts and results for fast, robust, and repeatable fitting of implicit polynomials to data, invariantly representing and recognizing complicated shapes, mutual geometry and mutual invariants, object signature curves and invariant patches/parts, PIMs (Polynomial Interpolated Measures) and orthogonal decomposition, and closed-form pose estimation, etc. With these, we lay down a foundation that enables a technology based on implicit polynomial curves and surfaces for various object representation/recognition applications.; This thesis also discusses our approaches in applying this implicit polynomial technology to the content-based large pictorial database indexing and searching area. It deals with the following problems: (1) 3D shape reconstruction and modeling from video data. We present a methodology of 3D string geometry-based indexing of video data. (2) Image query using sketches. A fully automatic curvelet structure (segments of implicit polynomial curves) extraction method is introduced. We built a prototype image-query-by-sketch system using this representation and Java technology which allows queries over the web. Special attention is also given to the user interface part in such applications. The preliminary results are very promising. The method performs much better than does a pixel-based method that has been adopted by a number of well-known content-based image indexing and retrieval systems. |
