Abstract: Hu moment invariants play a very critical role in image description. In order to construct moment invariants suitable for certain requirements briefly and verify their information redundancy effectively, a new construction method was presented by inducting the relation formula of real-complex moments. Also some concepts as moment invariants polynomial and moment invariants polynomial space were discussed so as to characterize its algebra structure. Lastly, the author listed overall practical moment invariants based on 3-order moments without informational redundancy. Compared with the typical construction approaches: algebraic theoretic construction method and triangle function construction method, this algorithm is more brief and effective, and also more suitable for discovering information redundancy. Moreover, these new moment invariants are robust and perform well in image description.

Key words: geometric moment invariants, affine moment invariants, complex moment, linear space of moment invariants

摘要： 为了更简洁高效地构造指定要求的不变矩，并判断矩组信息冗余性，推导了实复矩反演关系公式并提出了Hu不变矩构造定理。不变矩多项式和不变矩多项式空间概念的引入，可以赋予不变矩多项式空间代数结构特征。结合组合计数定理，列出了工程上非常实用且没有信息冗余的全部3阶4次不变矩，这是对7个经典Hu不变矩的推广。实验表明,与Hu不变矩的代数不变量构造方法和三角函数系构造方法相比，该构造方法更简洁高效且具有一般性，也更适合判断矩组信息冗余。所构造新不变矩具有较好的鲁棒性，用于图像描述取得了较好效果。

关键词: 几何不变矩, 仿射不变矩, 复数矩, 不变矩多项式空间