Mobile Targets Region-of-Interest via Distributed Pyroelectric Sensor Network: Towards a Robust, Realtime Context Reasoning Fei Hu, Qingquan Sun, Qi Hao Department of Electrical and Computer Engineering, The University of Alabama Tuscaloosa, AL 35487 Email: {fei, qh}@eng.ua.edu,
[email protected]
Abstract—We have established a multi-walker recognition / tracking testbed based on low-cost pyroelectrc sensor network (PSN). In order to identify a region of interest (RoI) in the monitoring area for the detection of any interesting mobile targets, we propose to use Bayesian machine learning and binary signal projection to extract the statistical contextual features from real-time, high-dimensional PSN data. This paper describes our recent results in this area, which include two aspects: (1) we have proposed to use binary principle component analysis (B-PCA) to interpret the relationship between observed sensor data and hidden context patterns. (2) We have conducted comprehensive experiments from real PSN sensor data to verify the context detection accuracy based on B-PCA models. Our results show that B-PCA can better capture context basis than general PCA algorithm 1.
I.
Suppose there are different complex walking scenarios in a pyroelectric sensor network, for example, sometimes only one person walks through a path; sometimes a few people walk by; sometimes the same person walks through the network but with different paths. If we call each of those scenarios as a specific “context”, then how do we identify those different contexts through the analysis of pyroelectric sensor data?
INTRODUCTION
Figure 1. (a) Pyroelectric sensor with Fresnel lens (b) sensor data
We have built an Intelligent Compressive Multi-Walker Recognition and Tracking (iSMART) system [1-3] which uses low-cost pyroelectric sensors ($3 each) to track and recognize mobile targets. Such a system has much lower deployment cost than traditional video-based human tracking system. The latter uses expensive PTZ video cameras, each of which costs more than $1,000 to achieve a high-resolution image capture. Moreover, the video processing algorithms consume much more CPU resources than our pyroelectric sensing system. We attach fresnal lens to each pyroelectric sensor in order to generate rich field of view (FOV). As shown in Figure 1 (a), the lens has certain pattern of holes that can make incoming thermal signals generate different sensing data. To achieve a good detection effect, we put multiple sensors together in a 30 x 20 cm range to form a “cluster”. If a sensor detects the gait of a human, it will generate a “1”, otherwise “0”. Figure 1 (b) shows a 3-sensor data matrix, where the shaded data means “1”, and blank part means “0”.
1 This research has been supported by U.S. National Science Foundation (NSF) IIS # 0915862 and RGC-14242-21451-200. All results presented here do not necessarily reflect NSF’s opinions.
978-1-4244-8168-2/10/$26.00 ©2010 IEEE
Note that here the context identification does not rely on other environmental information (such as GPS-based position data), human daily activity habits, room layout, etc. Instead, because the pyroelectric data (binary sequences) has rich information, we decide to use only the binary data analysis to deduce the hidden context patterns. In this paper, we will report our results on context identification / extraction through a special principle component analysis (PCA), called binary PCA (B-PCA), to find the hidden patterns of the pyroelectric sensor data. Those patterns will be used to identify the context. The reason of using B-PCA is because it is specially optimized for binary data matrix in order to extract the signal projection basis and corresponding basis coefficients. The coefficients indicate different context patterns. The rest of the paper is organized as follows: In section II we briefly summarize other related work in context identification. Section III will explain the math models of BPCA from the physical interpretation of pyroelectric sensor data. Section IV will discuss experimental results. Finally, Section V concludes this paper.
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II. RELATED WORK Context awareness has been used in many computing applications. For example, we can enhance people’s interactions by using some social network context information (such as neighbors, social roles, employment data, etc.) [4]. In mobile computing applications, objects’ mobility information can be used as context data (such as mobility patterns, movement velocity / direction, etc.) to enhance packet delivery performance in wireless networks [5]. For instance, we can deliver more data in the movement direction. A work with certain relevance to our research is the use of video data analysis to search a region of interest (RoI). For instance, in [6, 7] a concept called saliency is proposed to measure how dominant a local image block is different from background pixels. Then the Bayesian framework is proposed to calculate the exact saliency value and context data. Those ideas provide good implications to our research. For example, we may divide the incoming pyroelectric binary data matrix into different small matrices. Then we could use machine learning algorithms or statistical models to calculate whether or not this window of matrix has certain patterns we are interested in (such as the pattern of 2people walking). However, we cannot directly apply the image-based context extraction methods to our case because pyroelectric binary data does not have intuitive image pixel meanings. Therefore, we resort to other methods to extract the context. III. BINARY PCA FOR CONTEXT IDENTIFICATION The context identification problem in our multiwalker scenario could be formatted as the issue of identifying the Hidden Context Patterns (HCPs) given a window of Observed Sensing Data (OSD). Note that typically OSD is high-dimensional binary data matrix since we could take many sensors’ data as observations. Suppose we could use a signal projection method to decompose the OSD into the sum of a series of items. Each item is the multiplication of a basis function (B) and a coefficient (C). Suppose B is common to all scenarios, that is, we always project the OSD to the same bases. As shown in Figure 2, when mapping to the same bases (B), we can easily see that different windows of OSD will have different coefficients vectors (C). We can then use C as the HCP of different scenario. In order to identify the context pattern (C) in an OSD, we could first train the values of B and C for different scenarios that could happen (such as 1-walker case, 2-walker case, Path-1, Path-2, etc.) in a pyroelectric sensor network. We then store the corresponding coefficient vector (C) in the database for later comparison. Then for any new OSD to be identified, we can project it to the same bases (B) and then obtain a C. By comparing C with the context database, we can find out which context this OSD belongs to.
Bases (B)
x Coefficients (C)
=
OSDs (X)
Figure 2. Signal projection to a series of bases and coefficients In this work, we use PCA to project a window of OSD (matrix X) into bases and coefficients. However, general PCA assumes OSD is a real-valued matrix, which may not be able to generate feature-dominant context coefficients C since our OSD is a binary matrix. To solve this issue, we propose to use binary PCA (B-PCA) which is an optimized algorithm of basic PCA. It aims to extract features from binary data with Bernoulli distribution (suppose x is an element of X):
P( x | p ) = p x (1 − p )1− x
(1)
Because in machine learning algorithms exponential family functions have the most popular applications, we introduce log-odds parameter ξ = log (p/1-p) and the logistic function σ (ξ) = 1 / [1 + exp (-ξ)] to change the above Bernoulli to exponential format [8]:
P( x | ξ ) = σ (ξ ) x σ (−ξ )1− x , 1 p , and ξ = Log ( ) here σ (ξ ) = −ξ 1− p 1+ e
(2)
If a pyroelectric sensor network has N sensors and total M time instants of data, we will have an OSD of NxM high-dimensional binary matrix. Random variable X should meet the following probability distribution:
P( X | Θ) = ∏∏ σ (Θ nm ) X nm σ (−Θ nm )1− X nm n
m
(3)
Where Θnm = { ξ(x) } is log-odds matrix of X. By taking Log for all elements of OSD X,, we can get the Log-Likelihood of X as follows:
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L ( X | Θ) =
∑∑ [x n
m
nm
M
Anli = ∑ TnmVlmVim ,
Logσ (Θ nm ) + (1 − x nm ) Logσ (−Θ nm )]
m =1 M
Like general PCA, B-PCA can also reduce a high dimensional data matrix to much more compact format – two small matrices U and V, with an optional bias vector Δ. Assume those matrices are in a low dimension L
