Given a set of n points in d-dimensional Euclidean space, S E d , and a query point q 2 E d , we wish to determine the nearest neighbor of q, that is, the point of S whose Euclidean distance to q is minimum. The goal is to preprocess the point set S, such that queries can be answered as eeciently as possible. We assume that the dimension d is a constant independent of n. Although reasonably goo...

Similarity search in multimedia databases requires an efficient support of nearest-neighbor search on a large set of high-dimensional points as a basic operation for query processing. As recent theoretical results show, state of the art approaches to nearest-neighbor search are not efficient in higher dimensions. In our new approach, we therefore precompute the result of any nearest-neighbor se...

Both a new iterative grid-search technique and the iterative Fourier-transform algorithm are used to illuminate the relationships among the ambiguous images nearest a given object, error metric minima, and stagnation points of phase-retrieval algorithms. Analytic expressions for the subspace of ambiguous solutions to the phase-retrieval problem are derived for 2 X 2 and 3 X 2 objects. Monte Car...

A reverse k nearest neighbor (RkNN) query retrieves all the data points that have q as one of their k closest points. In recent years, considerable research has been conducted into monitoring reverse k nearest neighbor queries. In this paper, we study the problem of continuous reverse nearest neighbor queries where both the query object q and data objects are moving. Existing state-of-the-art t...

Background: Outlier detection is an important factor in data mining since it is used in various real time applications. Outlier is an extreme points that are not related to any of the class. Dealing with dimensions is the great challenge, due to “curse of dimensionality”, for effective outlier detection. In a high dimensional data space, it is difficult to detect most related points and most un...

For an arbitrary point of a homogeneous Poisson point process in a d-dimen-siona! Euclidean space, consider the number of Poisson points that have that given point as their r-th nearest neighbor (r = 1,2,...). It is shown that as d tends to infinity, these nearest neighbor counts (r = 1,2,...) are tid asymptotically Poisson with mean 1. The proof relies on Renyi's characterization of Poisson pr...

Given a set P of n points in the plane, we wish to find a set Q ⊂ P of k points for which the convex hull conv(Q) has the minimum area. We solve this, and the related problem of finding a minimum area convex k-gon, in time O(n log n) and space O(n log n) for fixed k, almost matching known bounds for the minimum area triangle problem. Our algorithm is based on finding a certain number of nearest...

In this paper, a simple, efficient, and parameter free algorithm, DISCUR, is proposed to reconstruct curves from unorganized sample points. The proposed algorithm can reconstruct multiple simple curves that may be open, closed, and/or with sharp corners. The criteria for the curve reconstruction are based on two observations we have made concerning the human visual system: (1) two closest neigh...

In this paper, we propose a novel classification method, called the nearest feature line (NFL), for face recognition. Any two feature points of the same class (person) are generalized by the feature line (FL) passing through the two points. The derived FL can capture more variations of face images than the original points and thus expands the capacity of the available database. The classificati...

Given the influences of illumination, imaging angle, and geometric distortion, among others, false matching points still occur in all image registration algorithms. Therefore, false matching points detection is an important step in remote sensing image registration. Random Sample Consensus (RANSAC) is typically used to detect false matching points. However, RANSAC method cannot detect all false...