Abstract
Regular expressions are a fundamental technique for pattern matching in textual data and for lexical analysis in compiler design. They are ubiquitous in most systems used today, including operating systems (e.g. grep, awk), computer languages (e.g. Perl, Java, Python), and web search engines (e.g. Google). However, this highly useful way of exploring and mining data has thus far eluded non-textual datasets, such as images and 3D geometric data. Shape-based searching of 3D objects continues to be a core problem in computer vision . We propose a novel extension of traditional finite-automata-based methods to find multi-dimensional objects in spatial data sets. Our approach extends regular expressions and finite automata to multi-dimensional pattern models. While we demonstrate the effectiveness and efficiency of our approach for finding target objects in 3D LiDAR image data sets using an implicit geometry representation of the data, it is important to note that the proposed technique can be applied to any general data set of vertices in 3D space. Non-geometric information, such as material and spectral characteristics from hyperspectral image data can also be discretized and encoded into our approach.
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- 1.
Implicit geometry representation of point cloud data may be based on a number of metrics, including population, distance, and validity, see, e.g. [15]. The data presented in this paper uses a simple population metric for voxelization of the point cloud data.
- 2.
While each string in a regular language is a finite string, a regular language itself may be infinite.
- 3.
The reader is referred to [19] for further details.
- 4.
In practice the Kleene operation is rarely helpful to express a pattern, since objects of interest are never infinitely extensible.
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Acknowledgements
This research was supported in part by the U.S. Air Force Office of Scientific Research (AFOSR) under Grant no. FA9550-15-1-0286 and by the U.S. National Geospatial-Intelligence Agency (NGA) under Contract HM1582-10-C-0011, public release number PA Case 13-192.
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Torgersen, T.C., Pauca, V.P., Plemmons, R.J., Nikic, D., Wu, J., Rand, R. (2018). Multi-Dimensional Regular Expressions for Object Detection with LiDAR Imaging. In: Tai, XC., Bae, E., Lysaker, M. (eds) Imaging, Vision and Learning Based on Optimization and PDEs. IVLOPDE 2016. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-91274-5_7
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