This paper studies the representation of the set of zeros with multiplicities for an ideal generated by a given set of multivariate polynomials in terms of triangular regular sequences, whose dimensions and degrees can be read out directly. A new algebro-geometric approach is proposed that enables one to decompose any polynomial ideal into finitely many triangular regular sequences of polynomials such that certain implicit relations between the Hilbert polynomials and explicit relations between the sets of zeros of the ideals generated by the regular sequences are preserved. The decomposition algorithms make use of the properties and computations of W-characteristic sets of polynomial ideals and perform simultaneous sum-and-quotient operation, a key technique that is used implicitly in the recursive process of computing Hilbert polynomials. The present work elaborates and reveals inherent connections between some commonly used concepts in the algorithmic theories of triangular sets, Gröbner bases, and Hilbert polynomials. Examples are provided to illustrate the computational aspects and differences of our approach from that of pseudo-division-based triangular decomposition.

With the development of artificial intelligence, computer vision technology has been widely used in the fields of security monitoring, automatic driving and wisdom city. However, there has not been a research on the detection of the meridians in human bodies by using the computer vision technology. In order to promote the use of the computer vision technology in human meridian detection, this paper first releases a dataset based on human meridians, which makes up for the gap in the field of human meridian detection using image processing technology. Moreover, the human meridian detection dataset is manually annotated and proofread by experienced Traditional Chinese Medicine (TCM) practitioners according to the position and direction of the human meridians, so that the annotated human meridians are as accurate as possible. The released human meridian dataset label’s 12 meridians, including spleen meridian, pericardium meridian, stomach meridian, lung meridian, heart meridian, kidney meridian, gallbladder meridian, liver meridian, triple energizer meridian, bladder meridian, large intestine meridian and small intestine meridian. A total of 296 acupoints were labeled. At last, this paper proposes a method for data augmentation, especially for datasets with a small amount of data, wherein the data amount can be augmented by enhancing the underlying edge visual features of the data. Experimental results show that human meridians can be detected by using image processing technology, and the proposed method for data augmentation can effectively improve the detection accuracy of human meridians. The dataset can be downloaded from https://www.zksylf.com/col.jsp?id=127 .