The success of time series data mining applications, such as query by content, clustering, and classification, is greatly determined by the performance of the algorithm used for the determination of similarity between two time series. The previous research on time series matching has mainly focused on whole sequence matching and sequence-to-subsequence matching. Relatively, very little work has been done on subsequence-tosubsequence matching, where two time series are considered similar if they contain similar subsequences or patterns in the same time order. This paper presents an effective approach capable of handling whole sequence, sequence-to-subsequence and subsequence-to-subsequence matching. The proposed approach derives its strength from the novel two stage segmentation algorithm, which facilitates aligning the two time series by retaining perceptually important points in both time series as break points.
The algorithm used for the segmentation of an image, and scheme used for the representation of the segmentation result are mostly selected based on the final image analysis or interpretation objective. The boundary based image segmentation and representation system developed by Nabors segments and stores the result as a graph-tree hierarchical structure that is capable of supporting diverse applications. This paper shows that Nabors' hierarchical representation of curves is not invariant to rotation, and proposes an enhanced representation which retains its structure and remains invariant under rotation. The curve matching algorithm which matches two curves based on their hierarchical representation makes it easy to determine if a curve is a section of a larger curve. The potential of the representation is illustrated by developing image registration and image stitching methods based on the new representation.
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