Emanuel E. Zelniker

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.

A statistical analysis of the Delogne-Kasa method for fitting circles

Abstract In this paper, we examine the problem of fitting a circle to a set of noisy measurements of points on the circles circumference. Delogne [Proc. IMEKO-Symp. Microwave Measurements, 1972, pp. 117–123] has proposed an estimator which has been shown by Kasa [IEEE Trans. Instrum. Meas. 25 (1976) 8–14] to be convenient for its ease of analysis and computation. Using Chans circular functional model to describe the distribution of points, we perform a statistical analysis of the estimate of the circles centre, assuming independent, identically distributed Gaussian measurement errors. We examine the existence of the mean and variance of the estimator for fixed sample sizes. We find that the mean exists when the number of sample points is greater than 3 and the variance exists when this number is greater than 4. We also derive approximations for the mean and variance for fixed sample sizes when the noise variance is small. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the Cramer–Rao lower bound.

A Unified Bayesian Framework for Adaptive Visual Tracking.

Tracking is regarded as one of the most fundamental tasks in computer vision. It is used in many computer vision applications in fields such as surveillance, robotic navigation and 3D reconstruction to name but a few. Despite decades of research, the goal of fully automatic tracking of arbitrary types of objects in real world conditions is still an open problem. In this paper, we take a step toward the goal of general real-world tracking, and demonstrate a unified generative model for Bayesian multifeature, adaptive target tracking, or AMFT for short (Adaptive Multiple Feature Tracker). We derive a unified generative model for multi-sensory adaptive tracking which cleanly integrates tracking and the modeling of appearance change across multiple features in the same framework. The unified multi-feature observation model ensures that if one feature is not confident, e.g., color after an object crosses into a region of shadow, it is automatically down-weighted in its contribution to the appearance model update. In this way, without pre-training of specific object models, we achieve an extensible tracker for general object types, robust to real-world problems of clutter, appearance/lighting change and target model drift. The standard modeling assumptions made by a non-adaptive generative model are illustrated by the probabilistic graphical model in Figure 1(a). The unknown target state (e.g., location, size, velocity) xt is assumed to change with time t according to some process parameterized by A. At every time t, we make some noisy observations zt of the target xt (e.g., raw image or color histograms). The target is then tracked online by computing the posterior, p(xt |z1:t) over the true target location recursively. In the case of the Kalman filter (KF), all the distributions involved are Gaussian. In the case of the particle filter (PF), all the distributions involved are represented non-parametrically by a set of samples [1]. The true target model, e.g., the appearance or color histogram to search for, is assumed to be part of the parameters H, i.e., it is known and fixed by an operator or initialized by some external process. In many cases however, the true appearance of the target H may change significantly in time, e.g., the appearance changes when a subject moves between shade and sunlight. This is the case for outdoor surveillance applications and is the motivation for this research. Adaptive trackers [2, 3, 4, 6] have been proposed to update the target appearance online in various heuristic ways. We can formalise this more general modeling assumption generatively, by the generalized dynamic Bayesian network illustrated in Figure 1(b). In contrast to Figure 1(a), the true target model which was previously included in the fixed parameters H, is now included as the the initial condition y0 of a dynamic latent variable yt , formalizing the modeling assumption that the target appearance can change over time. In addition to the target state xt , the target appearance yt will therefore be incrementally and recursively updated as part of the process of inferring the latent variables in this model p(xt ,yt |z1:t). The latent space is of course now greatly expanded, and poses a more challenging inference problem than that of Figure 1(a). In Section 2 of the paper, we detail the specific parametric form of the model and an efficient inference algorithm. We evaluate our method (AMFT) against three contemporary trackers: A standard single feature particle filter (PF), mean-shift (MS) [5] and incremental visual tracking (IVT) [4]. The PF and MS trackers are non-adaptive color-based trackers, while IVT aims for pose and illumination change robustness by performing online adaptation in a subspace appearance model. Note that the AMFT, PF and IVT trackers track object scale, but MS does not. We evaluated these methods on a series of challenging video clips exhibiting a wide variety of data and object types for tracking, including far-field indoor and outdoor pedestrians with and without carried objects, vehicle tracking, and near-field indoor face trackH 1 x2 x3

Optimal circle fitting via branch and bound

We examine the problem of fitting a circle to a set of noisy measurements of points from the circles circumference, assuming independent, identically distributed Gaussian measurement errors. We propose an algorithm based on branch and bound to obtain the maximum likelihood estimate and show that this algorithm obtains the optimal estimate. We examine the rate of convergence and determine the computational complexity of the proposed algorithm. We also provide timings and compare them to those of existing techniques for circle fitting proposed in the literature. Finally, we demonstrate that our algorithm is statistically efficient by comparing our results to the Cramer-Rao lower bound.

A statistical analysis of least-squares circle-centre estimation

We examine the problem of fitting a circle to a set of noisy measurement of points on the circles circumference. An estimator based on the standard least-squares techniques has been proposed by Delogne which has been shown by Kasa to be convenient for its ease of analysis and computation. Using Chans circular functional model to describe the distribution of points, we perform a statistical analysis of the circles centre estimation, assuming an independent and identical distributed Gaussian measurement errors. We examine the existence of the mean and variance of the estimator for fixed sample sizes. We find that the mean exists when the number of sample points is greater than 2 and the variance exists when this number is greater than 3. We also derive the approximations for the mean and variance for fixed sample sizes when the noise variance is small. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the Cramer-Rao lower bound. We show this through Monte-Carlo simulations.

Radon transform processing for accurate centreline estimation of thick lines

The accurate fitting of a line to noisy measurements of points along its length is a much studied problem in the literature. In this paper, we interpret the maximum-likelihood estimator (MLE) for line-direction and perpendicular offset estimation in terms of convolution on the RADON Transform of an image which is ideal in a certain sense. We use our convolution-based MLE approach to find good estimates for the parameters of a line in digital images. By interpreting the MLE as a minimal variance estimator, it is possible to show how the conventional Radon Transform can be used to estimate thick (wider than one pixel) line segment parameters, i.e., the direction of the centreline and its perpendicular offset. We compare our new method to the Hough Tranform as well as the Cramer-Rao Lower Bound in synthetic digital images.