Fitting Voronoi Diagrams to Planar Tesselations

Given a tesselation of the plane, defined by a planar straight-line graph $G$, we want to find a minimal set $S$ of points in the plane, such that the Voronoi diagram associated with $S$ "fits" \ $G$. This is the Generalized Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered recently in \cite{Baner12}. Here we give an algorithm that solves this problem with a number of points that is linear in the size of $G$, assuming that the smallest angle in $G$ is constant.Comment: 14 pages, 8 figures, 1 table. Presented at IWOCA 2013 (Int. Workshop on Combinatorial Algorithms), Rouen, France, July 201

Study of Speaker Recognition Systems

Speaker Recognition is the computing task of validating a user’s claimed identity using characteristics extracted from their voices. This technique is one of the most useful and popular biometric recognition techniques in the world especially related to areas in which security is a major concern. It can be used for authentication, surveillance, forensic speaker recognition and a number of related activities. Speaker recognition can be classified into identification and verification. Speaker identification is the process of determining which registered speaker provides a given utterance. Speaker verification, on the other hand, is the process of accepting or rejecting the identity claim of a speaker. The process of Speaker recognition consists of 2 modules namely: - feature extraction and feature matching. Feature extraction is the process in which we extract a small amount of data from the voice signal that can later be used to represent each speaker. Feature matching involves identification of the unknown speaker by comparing the extracted features from his/her voice input with the ones from a set of known speakers. Our proposed work consists of truncating a recorded voice signal, framing it, passing it through a window function, calculating the Short Term FFT, extracting its features and matching it with a stored template. Cepstral Coefficient Calculation and Mel frequency Cepstral Coefficients (MFCC) are applied for feature extraction purpose. VQLBG (Vector Quantization via Linde-Buzo-Gray), DTW (Dynamic Time Warping) and GMM (Gaussian Mixture Modelling) algorithms are used for generating template and feature matching purpose

Indoor Geo-location And Tracking Of Mobile Autonomous Robot

The field of robotics has always been one of fascination right from the day of Terminator. Even though we still do not have robots that can actually replicate human action and intelligence, progress is being made in the right direction. Robotic applications range from defense to civilian, in public safety and fire fighting. With the increase in urban-warfare robot tracking inside buildings and in cities form a very important application. The numerous applications range from munitions tracking to replacing soldiers for reconnaissance information. Fire fighters use robots for survey of the affected area. Tracking robots has been limited to the local area under consideration. Decision making is inhibited due to limited local knowledge and approximations have to be made. An effective decision making would involve tracking the robot in earth co-ordinates such as latitude and longitude. GPS signal provides us sufficient and reliable data for such decision making. The main drawback of using GPS is that it is unavailable indoors and also there is signal attenuation outdoors. Indoor geolocation forms the basis of tracking robots inside buildings and other places where GPS signals are unavailable. Indoor geolocation has traditionally been the field of wireless networks using techniques such as low frequency RF signals and ultra-wideband antennas. In this thesis we propose a novel method for achieving geolocation and enable tracking. Geolocation and tracking are achieved by a combination of Gyroscope and encoders together referred to as the Inertial Navigation System (INS). Gyroscopes have been widely used in aerospace applications for stabilizing aircrafts. In our case we use gyroscope as means of determining the heading of the robot. Further, commands can be sent to the robot when it is off balance or off-track. Sensors are inherently error prone; hence the process of geolocation is complicated and limited by the imperfect mathematical modeling of input noise. We make use of Kalman Filter for processing erroneous sensor data, as it provides us a robust and stable algorithm. The error characteristics of the sensors are input to the Kalman Filter and filtered data is obtained. We have performed a large set of experiments, both indoors and outdoors to test the reliability of the system. In outdoors we have used the GPS signal to aid the INS measurements. When indoors we utilize the last known position and extrapolate to obtain the GPS co-ordinates

The complexity of finding minimal Voronoĭ covers with applications to machine learning

Abstract Our goal in this paper is to examine the application of Voronoi diagrams, a fundamental concept of computational geometry, to the nearest neighbor algorithm used in machine learning. We consider the question "Given a planar polygonal tessellation T and an integer k, is there a set of k points whose Voronoi diagram contains every edge in T?" We show that this question is NP-hard. We encountered this problem while studying a learning model in which we seek the minimum sized set of training examples needed to teach a given geometric concept to a nearest neighbor learning program. That is, given a concept which can be described by a planar tessellation, we are seeking to construct the smallest set of points whose Voronoi diagram is consistent with the given tessellation. In a sense, this question captures the difficulty of teaching the nearest neighbor algorithm a simple structure, using a minimal number of examples. In addition, we consider the natural inverse to the problem of computing Voronoi diagrams. Given a planar polygonal tessellation T, we describe an algorithm to find a set of points whose Voronoi diagram is T, if such a set exists