Peter J. Kootsookos

Detection and vectorization of roads from lidar data

A method for the automatic detection and vectorization of roads from lidar data is presented. To extract roads from a lidar point cloud, a hierarchical classification technique is used to classify the lidar points progressively into road and non-road points. During the classification process, both intensity and height values are initially used. Due to the homogeneous and consistent nature of roads, a local point density is introduced to finalize the classification. The resultant binary classification is then vectorized by convolving a complex-valued disk named the Phase Coded Disk (PCD) with the image to provide three separate pieces of information about the road. The centerline and width of the road are obtained from the resultant magnitude image while the direction is determined from the corresponding phase image, thus completing the vectorized road model. All algorithms used are described and applied to two urban test sites. Completeness values of 0.88 and 0.79 and correctness values of 0.67 and 0.80 were achieved for the classification phase of the process. The vectorization of the classified results yielded RMS values of 1.56 m and 1.66 m, completeness values of 0.84 and 0.81 and correctness values of 0.75 and 0.80 for two different data sets.

FIR approximation of fractional sample delay systems

This brief examines the approximation of fractional delays by FIR systems using various techniques which have previously been reported in the literature. In particular, the equivalence of the time-domain Lagrangian interpolation, the frequency-domain maximally flat error criterion and the window method is shown, provided maximal flatness is specified at /spl omega//sub 0/=0 and the window used is a scaled binomial function. The first of these has been known before, the second equivalence is new.

Threshold behavior of the maximum likelihood estimator of frequency

We present accurate simplifications of the Rife and Boorstyn (1974) performance equations for the maximum likelihood estimator of frequency. The simplicity of the result allows quick calculation of the onset of threshold as a function of sample size and signal to noise ratio (SNR). The accuracy of the new expression is demonstrated via simulation. >

Evaluation of HMM training algorithms for letter hand gesture recognition

The paper introduces an application using computer vision for letter hand gesture recognition. A digital camera records a video stream of hand gestures. The hand is automatically segmented, the position of the hand centroid is calculated in each frame, and a trajectory of the hand is determined. After smoothing the trajectory, a sequence of angles of motion along the trajectory is calculated and quantized to form a discrete observation sequence. Hidden Markov models (HMMs) are used to recognize the letters. Baum Welch and Viterbi path counting algorithms are applied for training the HMMs. Our system recognizes all 26 letters from A to Z and the database contains 30 example videos of each letter gesture. We achieve an average recognition rate of about 90 percent. A motivation for the development of this system is to provide an alternate text input mechanism for camera enabled handheld devices, such as video mobile phones and PDAs.

Analysis of the variance threshold of Kay's weighted linear predictor frequency estimator

A theoretical approximation for the variance of Kays weighted linear predictor frequency estimator is derived. From this expression, an inequality describing the variance threshold of the estimator is found. The window weights are then optimized to improve the variance. Numerical simulations demonstrate that the variance approximations are valid for medium to high signal-to-noise ratios or for large numbers of samples. >

The circular nature of discrete-time frequency estimates

It is shown that the conventional (linear) definitions of mean and variance can yield absurd results when applied to data defined on a circular domain. Appropriate definitions for the mean, variance, and moments of circular data are given, and these concepts are applied to reformulate a recently proposed frequency estimator to avoid bias and elevated threshold effects. The maximum likelihood frequency estimator is shown to be equivalent to least-squares regression on phase estimates. These results demonstrate the importance of appreciating the true circular nature of many quantities commonly encountered in digital signal processing.<<ETX>>

A unified approach to the STFT, TFDs, and instantaneous frequency

Cohens class of time-frequency representations (TFRs) is reformulated into a discrete-time, discrete-frequency, computer-implementable form. It is shown how, in this form, many of the properties of the continuous-time, continuous-frequency formulation are either lost or altered. Intuitions applicable in the continuous-time case do not necessarily carry over to the discrete-time case examined. The properties of the discrete variable formulation examined are the presence and form of cross-terms, instantaneous frequency estimation, and relationships between Cohens class of TFRs. A parameterized class of distributions which is a blending between the short-time Fourier transform (STFT) and the Wigner-Ville distribution. The two main conclusions are that all TFRs of Cohens class implementable in the given form (which includes all commonly used TFRs) possess cross-terms and that instantaneous frequency estimation using periodic moments of these TFRs is purposeless, since simpler methods obtain the same result. >

Time-frequency signal analysis and instantaneous frequency estimation: methodology, relationships and implementations

A procedure is described for the time-frequency analysis of signals, based on time-frequency distributions (TFDs) and instantaneous frequency (IF) estimation. First, a suitable TFD is used to determine the number of signal components. Then, if the signal is monocomponent, the IF law can be estimated directly. For multicomponent signals, two-dimensional windowing in the time-frequency domain (a form of time-varying filtering) is used to isolate each component; IF estimation is then applied to the individual components. The periodic first moment of a TFD is used to estimate the IF. A suitable definition and of the periodic first moment is proposed, and the relationship of these estimators to others based on the central finite difference of the phase of the analytic signal is given. A TFD such as the Wigner-Ville distribution can be used to represent both IF and amplitude variations in the individual signal components at each stage of the analysis.<<ETX>>

The Nehari shuffle: FIR(q) filter design with guaranteed error bounds

An approach to the problem of designing a finite impulse response filter of specified length q which approximates in uniform frequency (L/sub infinity /) norm a given desired (possibly infinite impulse response) causal, stable filter transfer function is presented. An algorithm-independent lower bound on the achievable approximation error is derived, and an approximation method that involves the solution of a fixed number of all-pass (Nehari) extension problems (and is therefore called the Nehari shuffle) is presented. Upper and lower bounds on the approximation error are derived for the algorithm. Examples indicate that the method closely approaches the derived global lower bound. The method is compared with the Preuss (complex Remez exchange) algorithm in some examples. >

Effect of initial HMM choices in multiple sequence training for gesture recognition

We present several ways to initialize and train hidden Markov models (HMMs) for gesture recognition. These include using a single initial model for training (re-estimation), multiple random initial models, and initial models directly computed from physical considerations. Each of the initial models is trained on multiple observation sequences using both Baum-Welch and the Viterbi path counting algorithm on three different model structures: fully connected (or ergodic), left-right, and left-right banded. After performing many recognition trials on our video database of 780 letter gestures, results show that a) the simpler the structure is, the less the effect of the initial model, b) the direct computation method for designing the initial model is effective and provides insight into HMM learning, and c) Viterbi path counting performs best overall and depends much less on the initial model than does Baum-Welch training.