# Satellite image retrieval using low memory locality sensitive hashing in Euclidean space

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## Abstract

This paper presents the use of the Low Memory Locality Sensitive Hashing (LMLSH) technique operating in Euclidean space to build a data structure for the Defense Meteorological Satellite Program (DMSP) satellite imagery database. The LMLSH technique finds satellite image matches in sublinear search time. The texture feature vectors of the images are extracted using pyramid-structured wavelet transform coupled with Gaussian central moment technique. These feature vectors and families of hash functions, drawn randomly and independently from a Gaussian distribution, are used to build hash tables. Given a query, the hash tables are used to pull out the best matches to that query and this is done in a sublinear search time complexity. When tested, our algorithm has proven to be approximately *twenty six* times faster than the Linear Search (LS) algorithm. In addition, the LMLSH algorithm searches about two percent of the entire database randomly to find the possible matches to any given query without loss of accuracy compared to the absolute best matches returned by its LS counterpart.

### Keywords

Item Image Approximate nearest neighbor Exact nearest neighbor Texture feature vector and match set### Parameter notations

**P**Data set containing the texture feature vectors of the images

*N*Number of texture feature vectors in

**P***d*Dimensionality of the texture feature vector

**p**Any vector belonging to

**P**- ℜ
^{d} A

*d*-dimensional vector space such that if**p**∈ ℜ^{ d }then**p**is a*d*-dimensional vector**q**A query vector such that

**q**∈ ℜ^{ d }*L*Number of tables

*m*A prime number representing the number of bins per table

*N*_{gd}(*μ*,*σ*^{2})A Gaussian distribution with mean

*μ*and variance*σ*^{2}**H**_{Gj}A family of hash functions drawn randomly from

*N*_{ gd }(0,*d*^{2}) for table*j**α*Load factor, i.e. expected number of texture feature vectors that project into the same bin

*β*(**q**,*R*)A sphere of radius

*R*centered at**q***δ*The probability that a true nearest neighbor is not reported to a given

**q**- Pr
Probability.

## Notes

### Acknowledgement

We are grateful to National Oceanic and Atmospheric Administration (NOAA)/National Geophysical Data Center in Boulder, Colorado, for providing us with the DMSP satellite imagery database. This work is partially supported by NOAA/National Center for Atmospheric Research Educational Program under Cooperative Agreement No: NA060AR4810187.

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