Efficient entry point encoding and decoding algorithms on 2D Hilbert space filling curve

The Hilbert curve is an important method for mapping high-dimensional spatial information into one-dimensional spatial information while preserving the locality in the high-dimensional space. Entry points of a Hilbert curve can be used for image compression, dimensionality reduction, corrupted image detection and many other applications. As far as we know, there is no specific algorithms developed for entry points. To address this issue, in this paper we present an efficient entry point encoding algorithm (EP-HE) and a corresponding decoding algorithm (EP-HD). These two algorithms are efficient by exploiting the m consecutive 0s in the rear part of an entry point. We further found that the outputs of these two algorithms are a certain multiple of a certain bit of s, where s is the starting state of these m levels. Therefore, the results of these m levels can be directly calculated without iteratively encoding and decoding. The experimental results show that these two algorithms outperform their counterparts in terms of processing entry points.