Evaluation of Space Filling Curves for Lower-Dimensional Transformation of Image Histogram Sequences

Abstract

Histogram sequences represent high-dimensional time-series converted from images by space filling curves (SFCs). To overcome the high-dimensionality nature of histogram sequences (e.g., 10⁶ dimensions for a 1024×1024 image), we often use lower-dimensional transformations, but the tightness of their lower-bounds is highly affected by the types of SFCs. In this paper we attack a challenging problem of evaluating which SFC shows the better performance when we apply the lower-dimensional transformation to histogram sequences. For this, we first present a concept of spatial locality and propose spatial locality preservation metric (SLPM in short). We then evaluate five well-known SFCs from the perspective of SLPM and verify that the evaluation result concurs with the actual transformation performance. Finally, we empirically validate the accuracy of SLPM by providing that the Hilbert-order with the highest SLPM also shows the best performance in k-NN (k-nearest neighbors) search.