Constraints are a natural mechanism for the specification of similarity queries on time-series data. However, to realize the expressive power of constraint programming in this context, one must provide the matching implementation technology for efficient indexing of very large data sets. In this paper, we formalize the intuitive notions of exact and approximate similarity between time-series patterns and data. Our definition of similarity extends the distance metric used in [2, 7] with invariance under a group of transformations. Our main observation is that the resulting, more expressive, set of constraint queries can be supported by a new indexing technique, which preserves all the desirable properties of the indexing scheme proposed in [2, 7].

Abstract — This paper is concerned with the problem of feature point registration and scene recognition from images under weak perspective transformations which are well approximated by affine transformations, and under possible occlusion and/or appearance of new objects. It presents a set of local absolute affine invariants derived from the convex hull of scattered feature points (e.g., fiducial or marking points, corner points, inflection points, etc.) extracted from the image. The affine invariants are constructed from the areas of the triangles formed by connecting three vertices among a set of four consecutive vertices (quadruplets) of the convex hull, and hence do make direct use of the area invariance property associated with the affine transformation. Because they are locally constructed, they are very well suited to handle the occlusion and/or appearance of new objects. These invariants are used to establish the correspondences between the convex hull vertices of a test image with a reference image in order to undo the affine transformation between them. A point matching approach for recognition follows this. The time complexity for registering v feature points on the test image with x feature points of the reference image is of order y@x 2 vA vA. vA The method has been tested on real indoor and outdoor images and performs well. Index Terms—Affine invariants, affine transformations, alignment, convex hull, occlusion, perspective, registration, weak. I.

Similarity search on time-series data sets is of growing importance in data mining. With the increasing amount of data of time-series in many applications, from financial to scientific, it is important to study the methods of retrieving similarity patterns efficiently and user friendly for business decision making. The thesis proposes methods of efficient retrieval of all objects in the time-series database with a shape similar to a search template. The search template can be either a shape or a sequence of data. Two search modules, subsequence search and whole sequence search, are designed and implemented. We study a set of linear transformations that can be used as the basis for similarity queries on time-series data, and design an innovative representation technique which abstracts the shape notion so that the user can interactively query and answer the multi-level similarity patterns. The wavelet analysis technique and the OLAP technique used in knowledge discovery and data warehou...

We present a flexible and efficient method for similarity querying in time-series databases. A sequence S is considered similar to a query sequence Q if the sequences match (up to some tolerance ε) after S is appropriately shifted and scaled. Our method allows the user...

Abstract. After a review of the circle fitting issue, we recall a relatively unknown method derived from a classical geometric result. We propose an improvement of this technique by reweighting the data, iterating the procedure, and choosing at every step as the new inversion point the one diametrically opposite to the previous inversion point. © 2003 SPIE and IS&T. [DOI: 10.1117/1.1525792] 1