Arindam Karmakar

Minimum-width rectangular annulus

In this paper, we identify a minimum width rectangular annulus that encloses a given set of n points in a plane. We propose an O(n^2logn) time and O(n) space algorithm for this problem. To the best of our knowledge this is the first sub-cubic algorithm for a rectangular annulus for arbitrary orientation.

k-enclosing axis-parallel square

Let P be a set of n points in the plane. Here we present an efficient algorithm to compute the smallest square containing at least k points of P for large values of k. The worst case time complexity of the algorithm is O(n + (n - k) log2(n - k)) using O(n) space which is the best known bound for worst case time complexity.

Constrained minimum enclosing circle with center on a query line segment

In this paper, we will study the problem of locating the center of smallest enclosing circle of a set P of n points, where the center is constrained to lie on a query line segment. The preprocessing time and space complexities of our proposed algorithm are O(n logn) and O(n) respectively; the query time complexity is O(log2n). We will use this method for solving the following problem proposed by Bose and Wang [3] – given r simple polygons with a total of m vertices along with the point set P, compute the smallest enclosing circle of P whose center lies in one of the r polygons. This can be solved in O( nlogn+mlog2n) time using our method in a much simpler way than [3]; the time complexity of the problem is also being improved.

Path planning algorithms for mobile anchors towards range-free localization

The objective of path planning for a mobile anchor is to find the path of minimum length that the anchor traverses to localize all sensors. The challenge is to design a movement strategy which reduces path length while meeting the requirements of a good range-free localization technique. A novel deterministic movement strategy is proposed in this paper that reduces path length and uses an existing range-free localization scheme which yields good positional accuracy. The mobile anchor moves in a hexagonal pattern to localize all the sensors which form a connected network. We compare performance of our algorithm with an existing path planning algorithm in terms of both path length and localization accuracy. Simulation results show that even in presence of irregular radio propagation, our algorithm achieves full localization. We have proposed another movement strategy for a mobile anchor using same hexagonal pattern to localize all the sensors lying in a rectangular region. Improvement in path length is shown theoretically compared to existing path planning schemes. Proposed a distributed range-free movement strategy for mobile anchor to localization sensors in a connected network.Improvements in terms of both path length and localization accuracy are shown.Proposed another movement strategy for mobile anchor, localizes all the sensors lying in a rectangular region.Improvement of path length is shown theoretically compared to the existing methods.

Determining Duty Cycle and Beacon Interval with Energy Efficiency and QoS for Low Traffic IEEE 802.15.4/ZigBee Wireless Sensor Networks

Wireless Sensor Networks (WSNs) are becoming integral part of today’s world due to their wide range of applications. WSNs are used in industrial applications such as factory automation and control, environmental monitoring etc. which are of low data rate but demand Quality of Service (QoS) in terms of reliability and timeliness along with energy efficiency. A WSN’s lifetime depends on the rate of consumption of energy by the sensors. One way to save energy is the judicious use of active and inactive periods in the duty cycle based Medium Access Control (MAC) protocols. The slotted IEEE 802.15.4 MAC protocol provides for it. The duty cycle mechanism however has the potential to affect the performance of the network in terms of QoS due to possible higher packet collision rate in the active periods with reduction in duty cycle. For such applications an appropriate selection of duty cycle that maintains the required QoS is vital while ensuring longevity of the network. Another important MAC parameter that has a role in the performance of WSNs based on IEEE 802.15.4/ ZigBee is the length of the Beacon Interval (BI). In this paper we present the results of our simulation experiments for determining appropriate Duty Cycle and Beacon Interval that maximizes energy efficiency while ensuring the QoS requirements of the application.

Comprehensive Representation and Efficient Extraction of Spatial Information for Human Activity Recognition from Video Data

Of late, human activity recognition (HAR) in video has generated much interest. A fundamental step is to develop a computational representation of interactions. Human body is often abstracted using minimum bounding rectangles (MBRs) and approximated as a set of MBRs corresponding to different body parts. Such approximations assume each MBR as an independent entity. This defeats the idea that these are parts of the whole body. A representation schema for interaction between entities, each of which is considered as set of related rectangles or what is referred to as extended objects holds promise. We propose an efficient representation schema for extended objects together with a simple recursive algorithm to extract spatial information. We evaluate our approach and demonstrate that, for HAR, the spatial information thus extracted leads to better models compared to CORE9 [1] a compact and comprehensive representation schema for video understanding.

Computation of non-dominated points using compact voronoi diagrams

We discuss in this paper a method of finding skyline or non-dominated points in a set P of n points with respect to a set S of m sites. A point pi∈P is non-dominated if and only if for each pj∈P,

Efficient extraction of spatial relations for extended objects vis-à-vis human activity recognition in video

j \not= i

An Analytical Model for IEEE 802. 15. 4/ ZigBee Wireless Sensor Networks with Duty Cycle Mechanism for Performance Prediction and Configuration of MAC Parameters to Achieve QoS and Energy Efficiency

, there exists at least one point s∈S that is closer to pi than pj. We reduce this problem of determining non-dominated points to the problem of finding sites that have non-empty cells in an additively weighted Voronoi diagram under convex distance function. The weights of the said Voronoi diagram are derived from the co-ordinates of the points of P and the convex distance function is derived from S. In the 2-dimensional plane, this reduction gives a O((m+n)logm+n logn)-time randomized incremental algorithm to find the non-dominated points.

On the Construction of a Generalized Voronoi Inverse of a Rectangular Tessellation

Human activity recognition (HAR) deals with recognition of activities or interactions that include humans within a video. Entities occurring in a video frame can be abstracted in variety of ways, ranging from the detailed silhouette of the entity to the very basic axis-aligned minimum bounding rectangles (MBR). On one end of the spectrum, using a detailed silhouette is not only demanding in terms of storage and computational resources but is also easily susceptible to noise. On the other end of the spectrum, MBRs require less storage, computation and abstracts out noise and video specific details. However, for abstraction of human bodies in a video an MBR does not offer an adequate solution because in addition to abstracting away noise, it also abstracts out important details such as the posture of the human body. For a more precise description, which offers a reasonable tradeoff between efficiency and noise elimination, a human body can be abstracted using a set of MBRs corresponding to different body parts. However, for a representation of activities as relations between interacting objects, a simplistic approximation assuming each MBR to be an independent entity leads to computation of redundant relations. In this paper, we explore a representation schema for interaction between entities that are considered as sets of rectangles, also referred to as extended objects. We further show that, given the representation schema, a simple recursive algorithm can be used to opportunistically extract topological, directional and distance information in O(nlogn) time. We evaluate our representation schema for HAR on the Mind’s Eye dataset (http://www.visint.org), the UT-Interaction (Ryoo and Aggarwal 2010) dataset and the SBU Kinect Interaction dataset (Yun et al. 2012).