| Summary: | Trademark orthogonal representation is an important research field in artificial intelligence technology and has extensive applications in trademark retrieval and recognition. However, the Gibbs phenomenon arises when complex trademark shapes are represented by using traditional methods, such as continuous orthogonal function and wavelet. In order to represent the complex trademark without Gibbs phenomenon, a novel method named hierarchical V-system (HV system) is proposed in this study, which is generated by V-system of multi-degree k (k = 0, 1, 2, 3). The hierarchical structure brings more detailed shape representation information. We show that the proposed method in this paper can represent the trademark shapes with fewer finite terms and obtain accurate representation result. This study also proposes the normalized descriptors of hierarchical V-system (HV descriptors). Furthermore, we demonstrate that the HV descriptors satisfy the invariance in rotation, translation, and scale transform. The experimental results show that the hierarchical V-system method can give reasonable descriptors for representing complex trademark without Gibbs phenomenon.
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