An adaptive observer framework for accurate feature depth estimation using an uncalibrated monocular camera

This paper presents a novel solution to the problem of depth estimation using a monocular camera undergoing known motion. Such problems arise in machine vision where the position of an object moving in three-dimensional space has to be identified by tracking motion of its projected feature on the two-dimensional image plane. The camera is assumed to be uncalibrated, and an adaptive observer yielding asymptotic estimates of focal length and feature depth is developed that precludes prior knowledge of scene geometry and is simpler than alternative designs. Experimental results using real camera imagery are obtained with the current scheme as well as the extended Kalman filter, and performance of the proposed observer is shown to be better than the extended Kalman filter-based framework.     

Interpolated corrected curvature measures for polygonal surfaces

A consistent and yet practically accurate definition of curvature onto polyhedral meshes remains an open problem. We propose a new framework to define curvature measures, based on the Corrected Normal Current, which generalizes the normal cycle: it uncouples the positional information of the polyhedral mesh from its geometric normal vector field, and the user can freely choose the corrected normal vector field at vertices for curvature computations. A smooth surface is then built in the Grassmannian ℝ³ × 𝕊² by simply interpolating the given normal vector field. Curvature measures are then computed using the usual Lipschitz–Killing forms, and we provide closed-form formulas per triangle. We prove a stability result with respect to perturbations of positions and normals. Our approach provides a natural scale-space for all curvature estimations, where the scale is given by the radius of the measuring ball. We show on experiments how this method outperforms state-of-the-art methods on clean and noisy data, and even achieves pointwise convergence on difficult polyhedral meshes like digital surfaces. The framework is also well suited to curvature computations using normal map information.     

Hybrid regression and isophote curvature for accurate eye center localization

Multimedia Tools and Applications - The eye center localization is a crucial requirement for various human-computer interaction applications such as eye gaze estimation and eye tracking. However,...     

Recursive estimation methods for discrete systems

In system identification, the error evolution is composed of two decoupled parts: one is the identifying information on the current estimation residual, while the other is past arithmetic errors. Previous recursive algorithms only considered how to update current prediction errors. Up to now, research has mostly been based on recursive least-squares (RLS) methods. In this note, a general recursive identification method is proposed for discrete systems. Using this new algorithm, a recursive empirical frequency-domain optimal parameter (REFOP) estimate is established. The REFOP method has the advantage of resisting disturbance noise. Some simulations are included to illustrate the new method's reliability.     

A framework for real-time discrete event control

The TTM/RTTL (timed transition model with real-time temporal logic) framework is presented for modeling, specifying, and analyzing real-time discrete-event systems. TTMs are used to represent the process of the plant and its controller. RTTL is the assertion language for specifying plant behavior and verifying that a controller satisfies the specification. The framework adapts features from the program verification literature which are useful for posing problems of interest to the control engineer, such as modular synthesis and design. Examples are used to illustrate the ideas presented. The authors' published analytical results are summarized and referenced     

Exact and interpolatory quadratures for curvature tensor estimation

The computation of the curvature of smooth surfaces has a long history in differential geometry and is essential for many geometric modeling applications such as feature detection. We present a novel approach to calculate the mean curvature from arbitrary normal curvatures. Then, we demonstrate how the same method can be used to obtain new formulae to compute the Gaussian curvature and the curvature tensor. The idea is to compute the curvature integrals by a weighted sum by making use of the periodic structure of the normal curvatures to make the quadratures exact. Finally, we derive an approximation formula for the curvature of discrete data like meshes and show its convergence if quadratically converging normals are available.     

基于离散曲率的点云光顺算法

通过对三维激光扫描仪扫描测量数据的误差来源进行分析,设计了一种基于离散曲率的点云光顺处理的快速算法,该算法以曲率特征为索引,能够快速判别点云数据的特征点,对非特征点采用[w]邻域内[X,Y]两个方向拟合三次B样条曲线做光顺处理。最后通过实例证明了所提方法的有效性。     

基于离散曲率熵的徘徊行为检测

针对公共重点区域的智能监视问题,提出了一种新的徘徊行为异常检测方法。该方法利用视频目标跟踪算法得到可疑行人的运动轨迹,通过曲线拟合对运动目标的离散点轨迹进行平滑,计算离散点的离散曲率,计算感兴趣区域内运动目标轨迹点的离散曲率的熵及方差,通过离散熵阈值比较进行徘徊行为判断,该方法只需计算运动目标的轨迹,无需建立样本库,实验证明了该方法的有效性、实时性。     

Consistent curvature estimators on discrete black-and-white images

Translated from Kibernetika, No. 6, pp. 103–110, November–December, 1990.     

A curvature estimation for pen input segmentation in sketch-based modeling

A proper segmentation of pen marking enhances shape recognition and enables a natural interface for sketch-based modeling from simple line drawing tools to 3D solid modeling applications; user input is otherwise restricted to draw only one segment per one stroke. In general, the pen marking segmentation is achieved by detecting the points of high curvature-called, segmenting points-and splitting the pen marking at those points. This paper presents a curvature estimation method, which considers only local shape information. The proposed method can therefore estimate curvature on-the-fly while user is drawing on a pen-input display, such as tablet PCs.     

An accurate estimation algorithm for big data streams

Sketch is a memory-efficient data structure, and is used to store and query the frequency of any item in a given multiset. As it can achieve fast query and update, it has been applied to various fields. Different sketches have different advantages and disadvantages. Sketches are originally proposed for estimation of flow size in network measurement. The key factor of sketches for network measurement is the insertion speed and accuracy. In this paper, we propose a new sketch, which can significantly improve the insertion speed while improving the accuracy. Our key methods include on-chip/off-chip separation and partial update algorithm. Extensive experimental results show that our sketch significantly outperforms the state-of-the-art both in terms of accuracy and speed.     

Comparison of discrete Hodge star operators for surfaces

We investigate the performance of various discrete Hodge star operators for discrete exterior calculus (DEC) using circumcentric and barycentric dual meshes. The performance is evaluated through the DEC solution of Darcy and incompressible Navier–Stokes flows over surfaces. While the circumcentric Hodge operators may be favorable due to their diagonal structure, the barycentric (geometric) and the Galerkin Hodge operators have the advantage of admitting arbitrary simplicial meshes. Numerical experiments reveal that the barycentric and the Galerkin Hodge operators retain the numerical convergence order attained through the circumcentric (diagonal) Hodge operators. Furthermore, when the barycentric or the Galerkin Hodge operators are employed, a super-convergence behavior is observed for the incompressible flow solution over unstructured simplicial surface meshes generated by successive subdivision of coarser meshes. Insofar as the computational cost is concerned, the Darcy flow solutions exhibit a moderate increase in the solution time when using the barycentric or the Galerkin Hodge operators due to a modest decrease in the linear system sparsity. On the other hand, for the incompressible flow simulations, both the solution time and the linear system sparsity do not change for either the circumcentric or the barycentric and the Galerkin Hodge operators.     

Tricubic interpolation of discrete surfaces for binary volumes

Binary-defined 3D objects are common in volume graphics and medical imaging as a result of voxelization algorithms, segmentation methods, and binary operations such as clipping. Traditionally, renderings of binary objects suffer from severe image quality problems, especially when one tries to zoom-in and render the binary data from up close. We present a new rendering technique for discrete binary surfaces. The technique is based on distance-based normal estimation, an accelerated ray casting, and a tricubic interpolator. We demonstrate the quality achieved by our method and report on its interactive rendering speed.     

Efficient source enumeration for accurate direction-of-arrival estimation in threshold region

Estimation of the number of signals impinging on an array of sensors, also known as source enumeration, is usually required prior to direction-of-arrival (DOA) estimation. In challenging scenarios such as the presence of closely-spaced sources and/or high level of noise, using the true source number for nonlinear parameter estimation leads to the threshold effect which is characterized by an abnormally large mean square error (MSE). In cases that sources have distinct powers and/or are closely spaced, the error distribution among parameter estimates of different sources is unbalanced. In other words, some estimates have small errors while others may be quite inaccurate with large errors. In practice, we will be only interested in the former and have no concern on the latter. To formulate this idea, the concept of effective source number (ESN) is proposed in the context of joint source enumeration and DOA estimation. The ESN refers to the actual number of sources that are visible at a given noise level by a parameter estimator. Given the numbers of sensors and snapshots, number of sources, source parameters and noise level, a Monte Carlo method is designed to determine the ESN, which is the maximum number of available accurate estimates. The ESN has a theoretical value in that it is useful for judging what makes a good source enumerator in the threshold region and can be employed as a performance benchmark of various source enumerators. Since the number of sources is often unknown, its estimate by a source enumerator is used for DOA estimation. In an effort to automatically remove inaccurate estimates while keeping as many accurate estimates as possible, we define the matched source number (MSN) as the one which in conjunction with a parameter estimator results in the smallest MSE of the parameter estimates. We also heuristically devise a detection scheme that attains the MSN for ESPRIT based on the combination of state-of-the-art source enumerators.     

A Fast algorithm for active contours and curvature estimation

A model for representing image contours in a form that allows interaction with higher level processes has been proposed by Kass et al. (in Proceedings of First International Conference on Computer Vision, London, 1987, pp. 259–269). This active contour model is defined by an energy functional, and a solution is found using techniques of variational calculus. Amini et al. (in Proceedings, Second International Conference on Computer Vision, 1988, pp. 95–99) have pointed out some of the problems with this approach, including numerical instability and a tendency for points to bunch up on strong portions of an edge contour. They proposed an algorithm for the active contour model using dynamic programming. This approach is more stable and allows the inclusion of hard constraints in addition to the soft constraints inherent in the formulation of the functional; however, it is slow, having complexity O(nm³), where n is the number of points in the contour and m is the size of the neighborhood in which a point can move during a single iteration. In this paper we summarize the strengths and weaknesses of the previous approaches and present a greedy algorithm which has performance comparable to the dynamic programming and variational calculus approaches. It retains the improvements of stability, flexibility, and inclusion of hard constraints introduced by dynamic programming but is more than an order of magnitude faster than that approach, being O(nm). A different formulation is used for the continuity term than that of the previous authors so that points in the contour are more evenly spaced. The even spacing also makes the estimation of curvature more accurate. Because the concept of curvature is basic to the formulation of the contour functional, several curvature approximation methods for discrete curves are presented and evaluated as to efficiency of computation, accuracy of the estimation, and presence of anomalies.     

State estimation in discrete m-D systems

In this study observers and stochastic state estimation form- D systems are considered. The analysis uses a wave advance process model in transporting the existing 1-D results to them-D setting. A constrained minimization technique is used to compute the optimal state estimator which preserves quarter plane causality. The optimal state estimator, without the quarter plane causality constraint, is also determined. A comparison then yields insight into the tradeoff between quarter plane causality and estimator performance.