An Envelope-Based Approach to Rotation-Invariant Boundary Image Matching

The original conference version of this paper mischaracterizes the contributions of the current authors, relative to the contributions of Keogh et al. [11, 12]. We would like to take this opportunity to correct this in this online version, which should be considered the official version of this work.) Boundary image matching identifies similar boundary images using their corresponding time-series, and supporting the rotation invariance is crucial to provide more intuitive matching results. Computing the rotation-invariant distance between image time-series, however, is a very time-consuming process since it requires a lot of Euclidean distance computations for all possible rotations. To solve this problem, in this paper we use a novel notion of envelope-based lower bound proposed by Keogh et al. [12] to reduce the number of distance computations dramatically. With the help of Keogh et al.’s prior work [11, 12], we first explain how to construct a single envelope from a query sequence and how to obtain a lower bound of the rotation-invariant distance using the envelope. We then explain that the single envelope lower bound can reduce a number of distance computations. This single envelope approach, however, may cause bad performance since it may incur a larger lower bound due to considering all possible rotated sequences in a single envelope. To solve this problem, we present a concept of rotation interval, and using the concept of multiple envelopes proposed by Keogh et al. [12] with these rotation intervals, we then generalize the envelope-based lower bound by exploiting multiple envelopes rather than a single envelope. We also propose equi-width and envelope-minimization divisions as the method of determining rotation intervals in the multi-envelope approach. We further present an advanced multi-step matching algorithm that progressively prunes search spaces by dividing the rotation interval in half. Experimental results show that our envelope-based solutions outperform naive solutions by one to three orders of magnitude.