In computer science, geometric hashing is a method for efficiently finding two-dimensional objects represented by discrete points that have undergone an affine transformation, though extensions exist to other object representations and transformations. In an off-line step, the objects are encoded by treating each pair of points as a geometric basis. The remaining points can be represented in an invariant fashion with respect to this basis using two parameters. For each point, its quantized transformed coordinates are stored in the hash table as a key, and indices of the basis points as a value. Then a new pair of basis points is selected, and the process is repeated. In the on-line (recognition) step, randomly selected pairs of data points are considered as candidate bases. For each candidate basis, the remaining data points are encoded according to the basis and possible correspondences from the object are found in the previously constructed table. The candidate basis is accepted if a sufficiently large number of the data points index a consistent object basis.
Geometric hashing was originally suggested in computer vision for object recognition in 2D and 3D,[1] but later was applied to different problems such as structural alignment of proteins.[2][3]
^A.S. Mian, M. Bennamoun, and R. Owens, Three-dimensional model-based object recognition and segmentation in cluttered scenes., IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, Oct. 2006, pp. 1584-601.
^Moll, Mark; Bryant, Drew H.; Kavraki, Lydia E. (2010-11-11). "The LabelHash algorithm for substructure matching". BMC Bioinformatics. 11: 555. doi:10.1186/1471-2105-11-555. ISSN 1471-2105. PMC 2996407. PMID 21070651.
^Nussinov, R.; Wolfson, H. J. (1991-12-01). "Efficient detection of three-dimensional structural motifs in biological macromolecules by computer vision techniques". Proceedings of the National Academy of Sciences of the United States of America. 88 (23): 10495–10499. doi:10.1073/pnas.88.23.10495. ISSN 0027-8424. PMC 52955. PMID 1961713.
In computer science, geometrichashing is a method for efficiently finding two-dimensional objects represented by discrete points that have undergone...
hashing is known as geometrichashing or the grid method. In these applications, the set of all inputs is some sort of metric space, and the hashing function...
between every point in a grid and a discrete collection of points. Geometrichashing: a method for efficiently finding two-dimensional objects represented...
Perceptual hashing is the use of a fingerprinting algorithm that produces a snippet, hash, or fingerprint of various forms of multimedia. A perceptual hash is...
eigenvectors of the templates (called eigenfaces) Modelbases are a collection of geometric models of the objects that should be recognized a search is used to find...
Fowler–Noll–Vo hash function: fast with low collision rate Pearson hashing: computes 8 bit value only, optimized for 8 bit computers Zobrist hashing: used in...
In machine learning, feature hashing, also known as the hashing trick (by analogy to the kernel trick), is a fast and space-efficient way of vectorizing...
families are known (for hashing integers, vectors, strings), and their evaluation is often very efficient. Universal hashing has numerous uses in computer...
dynamic arrays based on geometric expansion waste linear (Ω(n)) space, where n is the number of elements in the array, hashed array trees waste only order...
Hogg; Michael Blanton (2006-09-28). "Making the Sky Searchable: Fast GeometricHashing for Automated Astrometry" (PDF). [cosmo]. W. M. Smart (1977). "XII...
... To the untrained eye, the reflectors looked extremely odd, a geometricalhash of lightweight sticks and sharp angles made of metal foil. .. photographs...
bits are required for a valid header, since this requires only a single hashing operation. The Hashcash system has the advantage over micropayment proposals...
In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing...
alignments Zuker 1991 Bachar et al. Structure, topology independent Uses geometrichashing for the topology independent comparison of proteins Bachar et al....
Association for Computing Machinery for his work on locality-sensitive hashing. In 2012 his work co-developing the sparse Fourier transform was named...
node, bearing the weight of hardware expenses and network bandwidth. Geometric Method (GM) was invented by Meni Rosenfeld. It is based on the same "score"...
by the algorithm, such as the pairwise independence used in universal hashing the use of expander graphs (or dispersers in general) to amplify a limited...
a.size ← a.size + 1 As n elements are inserted, the capacities form a geometric progression. Expanding the array by any constant proportion a ensures...
as on a ruler or number line Congruence notation in geometry — as on a geometric figure Graphed points — as on a graph Hatch marks are frequently used...
arranged in order of decreasing probability, and these probabilities are geometrically distributed, the cost of linear search is only O(1). Linear search is...
among the first geometric problems that were treated at the origins of the systematic study of the computational complexity of geometric algorithms. Randomized...
probability. Unfortunately, we do not have linear perfect hashing, so we have to use an almost linear hash function, i.e. a function h such that: h ( x + y )...
In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one...