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.

Every time-series has its own linear trend, the directionality of a time-series, and removing the linear trend is crucial to get more intuitive matching results. Supporting the linear detrending in subsequence matching is a challenging problem due to the huge number of all possible subsequences. In this paper we define this problem as the linear detrending subsequence matching and propose its efficient index-based solution. To this end, we first present a notion of LD-windows (LD means linear detrending). Using the LD-windows we then present a lower bounding theorem for the index-based matching solution and show its correctness. We next propose the index building and subsequence matching algorithms. We finally show the superiority of the index-based solution.

This paper proposed an automated segmentation algorithm for MR brain images through the complementary use of T1-weighted, T2-weighted, and PD images. The proposed segmentation algorithm is composed of 3 steps. The first step involves the extraction of cerebrum images by placing a cerebrum mask over the three input images. In the second step, outstanding clusters that represent the inner tissues of the cerebrum are chosen from among the 3-dimensional (3D) clusters. The 3D clusters are determined by intersecting densely distributed parts of a 2D histogram in 3D space formed using three optimal scale images. The optimal scale image results from applying scale-space filtering to each 2D histogram and a searching graph structure. As a result, the optimal scale image can accurately describe the shape of the densely distributed pixel parts in the 2D histogram. In the final step, the cerebrum images are segmented by the FCM (Fuzzy c-means) algorithm using the outstanding cluster center value as the initial center value. The ability of the proposed segmentation algorithm to calculate the cluster center value accurately then compensates for the current limitation of the FCM algorithm, which is unduly restricted by the initial center value used. In addition, the proposed algorithm, which includes a multi spectral analysis, can achieve better segmentation results than a single spectral analysis.