STUDENT MEMBER, IEEE, Department of Electrical Engineering, University of Tennessee, Knoxville, TN 37916.
IEEE Trans Pattern Anal Mach Intell. 1980 Feb;2(2):127-36. doi: 10.1109/tpami.1980.4766990.
Recognition of three-dimensional objects independent of size, position, and orientation is an important and difficult problem of scene analysis. The use of three-dimensional moment invariants is proposed as a solution. The generalization of the results of two-dimensional moment invariants which had linked two-dimensional moments to binary quantics is done by linking three-dimensional moments to ternary quantics. The existence and number of nth order moments in two and three dimensions is explored. Algebraic invariants of several ternary forms under different orthogonal transformations are derived by using the invariant property of coefficients of ternary forms. The result is a set of three-dimensional moment invariants which are invariant under size, orientation, and position change. This property is highly significant in compressing the data which are needed in three-dimensional object recognition. Empirical examples are also given.
三维物体的识别与大小、位置和方向无关，这是场景分析的一个重要而困难的问题。提出使用三维矩不变量作为解决方案。通过将三维矩与三元二次型联系起来，对将二维矩与二元二次型联系起来的二维矩不变量的结果进行了推广。研究了二维和三维中 n 阶矩的存在性和数量。利用三元形式系数的不变性，推导出不同正交变换下几个三元形式的代数不变量。结果是一组在大小、方向和位置变化下不变的三维矩不变量。在压缩三维目标识别所需的数据方面，这一特性具有重要意义。还给出了实证例子。
