Mining of spatial data is an enabling technology for mobile services, Internet-connected cars and the Internet of Things. But the very distinctiveness of spatial data that drives utility can cost user privacy. Past work has focused upon points and trajectories for differentially private release. In this work, we continue the tradition of privacy-preserving spatial analytics, focusing not on point or path data, but on planar spatial regions. Such data represent the area of a user’s most frequent visitation—such as “around home and nearby shops”. Specifically we consider the differentially private release of data structures that support range queries for counting users’ spatial regions. Counting planar regions leads to unique challenges not faced in existing work. A user’s spatial region that straddles multiple data structure cells can lead to duplicate counting at query time. We provably avoid this pitfall by leveraging the Euler characteristic for the first time with differential privacy. To address the increased sensitivity of range queries to spatial region data, we calibrate privacy-preserving noise using bounded user region size and a constrained inference that uses robust least absolute deviations. Our novel constrained inference reduces noise and promotes covertness by (privately) imposing consistency. We provide a full end-to-end theoretical analysis of both differential privacy and high-probability utility for our approach using concentration bounds. A comprehensive experimental study on several real-world datasets establishes practical validity.
A key challenge in aggregation is the distinct counting @cite_14 @cite_7 @cite_20 @cite_3 @cite_53 or multiple-counting problem @cite_36 @cite_46 . In contrast to point objects, a spatial body can span more than one cell in a partitioned space, inhibiting the ability of regular histograms to form accurate counts. Euler histograms @cite_45 are designed to address this problem for convex bodies @cite_36 @cite_46 , by appealing to Euler's formula from graph theory @cite_39 . A variation of Euler histogram has been studied for trajectory data to address aggregate queries on moving objects @cite_19 . In that work, Euler histograms were used in a distributed setting (motivating a distributed Euler histogram), to tackle the duplicate (distinct) entry problem rather than duplicate (distinct) counting. The Euler-histogram tree @cite_23 has been studied as a tree-based data structure for counting vehicle trajectories using the approach first developed in @cite_52 to address the distinct counting problem for reducing storage requirements.
@cite_14 @cite_7 @cite_36 @cite_53 @cite_52 @cite_3 @cite_39 @cite_19 @cite_45 @cite_23 @cite_46 @cite_20
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This work addresses the problem of aggregation of trajectories data. Specifically, we propose a tree-based data structure for counting vehicle trajectories by mapping them into a set of spatial histograms with different granularities. We also present an approach for processing spatio-temporal range queries by aggregating the histograms in the query rectangles. The proposed methodology can be used for preserving the privacy of vehicle drivers by maintaining aggregated trajectory data. In addition, as we show, it can be used to handle the well-known distinct counting problem. Experimental results show that the new data structure achieves a high level of accuracy in query results and consistently outperforms the leading histogram-based approach. Due to the high uptake of location-based services (LBSs), large spatio-temporal datasets of moving objects' trajectories are being created every day. An important task in spatial data analytics is to service range queries by returning trajectory counts within a queried region. The question of how to keep an individual user's data private whilst enabling spatial data analytics by third parties has become an urgent research direction. Indeed, it is increasingly becoming a concern for users. To preserve privacy we discard individual trajectories and aggregate counts over a spatial and temporal partition. However the privacy gained comes at a cost to utility: trajectories passing through multiple cells and re-entering a query region, lead to inaccurate query responses. This is known as the distinct counting problem. We propose the Connection Aware Spatial Euler (CASE) histogram to address this long-standing problem. The CASE histogram maintains the connectivity of a moving object path, but does not require the ID of an object to distinguish multiple entries into an arbitrary query region. Our approach is to process trajectories offline into aggregate counts which are sent to third parties, rather than the original trajectories. We also explore modifications of our aggregate counting approach that preserve differential privacy. Theoretically and experimentally we demonstrate that our method provides a high level of accuracy compared to the best known methods for the distinct counting problem, whilst preserving privacy. We conduct our experiments on both synthetic and real datasets over two competitive Euler histogram-based methods presented in the literature. Our methods enjoy improvements to accuracy from 10 up to 70 depending on trip data and query region size, with the greatest increase seen on the Microsoft T-Drive real dataset, representing a more than tripling of accuracy. We present a framework for robustly estimating registration between a 3D volume image and a 2D projection image and evaluate its precision and robustness in spine interventions for vertebral localization in the presence of anatomical deformation. The framework employs a normalized gradient information similarity metric and multi-start covariance matrix adaptation evolution strategy optimization with local-restarts, which provided improved robustness against deformation and content mismatch. The parallelized implementation allowed orders-of-magnitude acceleration in computation time and improved the robustness of registration via multi-start global optimization. Experiments involved a cadaver specimen and two CT datasets (supine and prone) and 36 C-arm fluoroscopy images acquired with the specimen in four positions (supine, prone, supine with lordosis, prone with kyphosis), three regions (thoracic, abdominal, and lumbar), and three levels of geometric magnification (1.7, 2.0, 2.4). Registration accuracy was evaluated in terms of projection distance error (PDE) between the estimated and true target points in the projection image, including 14 400 random trials (200 trials on the 72 registration scenarios) with initialization error up to ±200 mm and ±10°. The resulting median PDE was better than 0.1 mm in all cases, depending somewhat on the resolution of input CT and fluoroscopy images. The cadaver experiments illustrated the tradeoff between robustness and computation time, yielding a success rate of 99.993 in vertebral labeling (with 'success' defined as PDE <5 mm) using 1,718 664 ± 96 582 function evaluations computed in 54.0 ± 3.5 s on a mid-range GPU (nVidia, GeForce GTX690). Parameters yielding a faster search (e.g., fewer multi-starts) reduced robustness under conditions of large deformation and poor initialization (99.535 success for the same data registered in 13.1 s), but given good initialization (e.g., ±5 mm, assuming a robust initial run) the same registration could be solved with 99.993 success in 6.3 s. The ability to register CT to fluoroscopy in a manner robust to patient deformation could be valuable in applications such as radiation therapy, interventional radiology, and an assistant to target localization (e.g., vertebral labeling) in image-guided spine surgery. Studying trajectories of individuals has received growing interest. The aggregated movement behaviour of people provides important insights about their habits, interests, and lifestyles. Understanding and utilizing trajectory data is a crucial part of many applications such as location based services, urban planning, and traffic monitoring systems. Spatial histograms and spatial range queries are key components in such applications to efficiently store and answer queries on trajectory data. A spatial histogram maintains the sequentiality of location points in a trajectory by a strong sequential dependency among histogram cells. This dependency is an essential property in answering spatial range queries. However, the trajectories of individuals are unique and even aggregating them in spatial histograms cannot completely ensure an individual's privacy. A key technique to ensure privacy for data publishing ϵ-differential privacy as it provides a strong guarantee on an individual's provided data. Our work is the first that guarantees ϵ-differential privacy for spatial histograms on trajectories, while ensuring the sequentiality of trajectory data, i.e., its consistency. Consistency is key for any database and our proposed mechanism, PriSH, synthesizes a spatial histogram and ensures the consistency of published histogram with respect to the strong dependency constraint. In extensive experiments on real and synthetic datasets, we show that (1) PriSH is highly scalable with the dataset size and granularity of the space decomposition, (2) the distribution of aggregate trajectory information in the synthesized histogram accurately preserves the distribution of original histogram, and (3) the output has high accuracy in answering arbitrary spatial range queries.