A computational approach to edge detection

This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.     

新型边缘检测法

灰度图阈值法、跟踪法、小波变换法是边缘检测的常用方法,这些方法所获得的边缘线出现断点,而且掺杂噪声,效果不很理想.给出了一种新型边缘检测方法:连续点过滤和多尺度边缘跟踪相结合.连续点过滤的边缘检测法可以获得较好的边缘,在此基础上利用多尺度的跟踪法,解决了检测图像的边缘断点问题,使得图像的边缘线更加确切和平滑.经实验验证,该方法比普通的方法在边缘精确性上有较大提高.     

A bayesian approach to edge detection in images

New statistical techniques for the edge detection problem in images are developed. The image is modeled by signal and noise, which are independent, additive, Gaussian, and autoregressive in two dimensions. The optimal solution, in terms of statistical decision theory, leads to a test that decides among multiple, composite, overlapping hypotheses. A redefinition of the problem, involving nonoverlapping hypotheses, allows the formulation of a computationally attractive scheme. Results are presented with both simulated data and real satellite images. A comparison with standard gradient techniques is made.     

A geometric approach to nonlinear fault detection and isolation

We present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems. A necessary condition for the problem to be solvable is derived in terms of an unobservability distribution, which is computable by means of suitable algorithms. The existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an “observable” quotient subsystem unaffected by all fault signals but one. For this subsystem, a fault detection filter is designed     

A geometric approach to fault detection and isolation for bilinearsystems

In this paper, a geometric approach to the synthesis of a residual generator for fault detection and isolation (FDI) in bilinear systems is considered. A necessary and sufficient condition to solve the so-called fundamental problem of residual generation is obtained. The proposed approach resorts to extensions of the notions of (C, A)-invariant and unobservability subspaces, and it yields a constructive design method     

A geometric approach to the synthesis of failure detection filters

A geometric formulation of Beard's failure detection filter problem is stated using the concepts of(C, A)-invariant and unobservability subspaces. The notions of output separable and mutually detectable families of subspaces introduced by Beard are also clarified. It is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum. Moreover, it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions. Finally, the complete duality between a generalization of Beard's detection filter problem and the restricted control decoupling problem is illustrated.     

A gravitational approach to edge detection based on triangular norms

We study the method of Sun et al. for edge detection based on the Law of Universal Gravity. We analyze the effect of the substitution of the product operation by other triangular norms in the calculation of the gravitational forces. We treat edges as fuzzy sets for which membership degrees are extracted from the resulting gravitational force on each pixel. We consider several prototypical triangular norms and experimentally show that their features determine the kind of edges detected. The new method is tested on the Berkeley Segmentation Dataset, showing to be competitive compared to the Canny method.     

一种基于统计的图像边缘检测方法*

提出了一种基于统计的图像边缘检测方法.它首先通过计算图像中每一点的梯度向量以及方差-协方差矩阵,然后对每一点的梯度向量进行非极大值抑制,最后使用统计的方法求出局部标准化梯度阈值来检测图像的真实边缘.通过与经典的边缘算子相比较,该方法不仅能很好地检测出图像的真实边缘,而且有效地抑制了虚假边缘的产生,取得了良好的效果.     

A pseudo top-hat mathematical morphological approach to edge detection in dark regions

Edge detection is an important pre-processing step in image segmentation. Conventionally, edges are detected according to gradient property, then processed by the thresholding technique. By such an approach, fine edge details in dark region of the image are eliminated. It is annoying sometimes as they are as useful as those in bright region, although this is caused by unevenly distributed lighting in many machine vision applications. In this paper, a novel mathematical morphological edge detection algorithm, based on pseudo top-hat transformation which is derived from top-hat transformation, is proposed to preserve these edge details as well as prominent ones. The algorithm is also presented in detail. Comprehensive experimental results show that the proposed algorithm is efficient for edge details extraction in place of shading while preserving distinguish features.     

基于非线性滤波的万有引力边缘检测方法

将非线性滤波算子融入到万有引力边缘检测算法中,提出了一种新的边缘检测方法。通过计算图像中每个像素点的非线性梯度值,构造以该梯度值为自变量的归一化函数,用该函数值代替中心像素点灰度值对图像进行万有引力边缘检测。实验结果表明,同传统的边缘检测算法相比,此方法不仅边缘定位准确,而且对于各种噪声图像也具有良好的边缘检测效果。     

A geometric approach to nonlinear fault detection and isolation in a hybrid three-cell converter

In this paper, the problem of fault detection and isolation in a three-cell converter is investigated using a nonlinear geometric approach. This powerful method based on the unobservability distribution is used to detect and isolate the faulty cell in the three-cell converter. First, a model describing the faults in the cells is presented. The geometric approach is then applied on this faulty model to generate residual signals based on a sliding-mode observer that allows the detection of faults in the three-cell converter. Numerical results show the effectiveness of the proposed sliding-mode residual generators for fault detection and isolation in the three-cell converter.     

A geometric approach to boundary-conformed toolpath generation

Isoparametric or streamline-like toolpath generation is an important method for CNC surface machining. For a trimmed surface, the generation of such a toolpath is not straightforward because by simply following the isoparametric curves of the parametric surface to generate the toolpath, the resulting toolpath may no longer conform to the trimmed boundary of the surface. Various methods have been proposed to solve this problem. Some methods work well for single surface machining, but may not be feasible for multi-patch surface machining. A new geometric approach to the problem of multi-patch machining is proposed in this paper. The new method works by generating bisectors to partition the region into smaller subregions, and generates the toolpath by offsetting the subregion boundary by using a special offset function. As this new method does not rely on processing on the parametric domain of the surface patches, it can be used for both NURBS and subdivision surfaces. Examples are given to demonstrate the capability of the new method, and to show that the new method compares favorably with existing techniques.     

A geometric approach to non-parametric density estimation

A novel non-parametric density estimator is developed based on geometric principles. A penalised centroidal Voronoi tessellation forms the basis of the estimator, which allows the data to self-organise in order to minimise estimate bias and variance. This approach is a marked departure from usual methods based on local averaging, and has the advantage of being naturally adaptive to local sample density (scale-invariance). The estimator does not require the introduction of a plug-in kernel, thus avoiding assumptions of symmetricity and morphology. A numerical experiment is conducted to illustrate the behaviour of the estimator, and it's characteristics are discussed.     

A geometric approach to leveraging weak learners

AdaBoost is a popular and effective leveraging procedure for improving the hypotheses generated by weak learning algorithms. AdaBoost and many other leveraging algorithms can be viewed as performing a constrained gradient descent over a potential function. At each iteration the distribution over the sample given to the weak learner is proportional to the direction of steepest descent. We introduce a new leveraging algorithm based on a natural potential function. For this potential function, the direction of steepest descent can have negative components. Therefore, we provide two techniques for obtaining suitable distributions from these directions of steepest descent. The resulting algorithms have bounds that are incomparable to AdaBoost's. The analysis suggests that our algorithm is likely to perform better than AdaBoost on noisy data and with weak learners returning low confidence hypotheses. Modest experiments confirm that our algorithm can perform better than AdaBoost in these situations.     

A geometric approach to remote eye tracking

This paper presents a principled analysis of various combinations of image features to determine their suitability for remote eye tracking. It begins by reviewing the basic theory underlying the connection between eye image and gaze direction. Then a set of approaches is proposed based on different combinations of well-known features and their behaviour is evaluated, taking into account various additional criteria such as free head movement, and minimum hardware and calibration requirements. The paper proposes a final method based on multiple glints and the pupil centre; the method is evaluated experimentally. Future trends in eye tracking technology are also discussed.     

A computer-aided geometric approach to inverse kinematics

This paper presents a geometric approach to solving the inverse kinematics for three-joint placeable robotic manipulators. The distinct feature of this approach is that it uses geometric variables such as length, area ratio, and Pythagoras difference to find the closed form solutions. It is proved here that for any three-joint placeable manipulator there exists a geometric variable that keeps constant during the evolution of the manipulator. With this invariant, a characteristic equation of the manipulator can be derived and can be transformed into a polynomial equation with degree up to four. Therefore the closed form solution of the three-joint placeable manipulator can be obtained. A characteristic equation of the three-revolute-joint manipulator produced by this approach with the assistance of Maple is listed in the Appendix. The possible application of this geometric approach to a six-joint manipulator is also discussed in the paper. © 1998 John Wiley & Sons, Inc. 15: 131–143, 1998     

A geometric approach to shape from defocus

We introduce a novel approach to shape from defocus, i.e., the problem of inferring the three-dimensional (3D) geometry of a scene from a collection of defocused images. Typically, in shape from defocus, the task of extracting geometry also requires deblurring the given images. A common approach to bypass this task relies on approximating the scene locally by a plane parallel to the image (the so-called equifocal assumption). We show that this approximation is indeed not necessary, as one can estimate 3D geometry while avoiding deblurring without strong assumptions on the scene. Solving the problem of shape from defocus requires modeling how light interacts with the optics before reaching the imaging surface. This interaction is described by the so-called point spread function (PSF). When the form of the PSF is known, we propose an optimal method to infer 3D geometry from defocused images that involves computing orthogonal operators which are regularized via functional singular value decomposition. When the form of the PSF is unknown, we propose a simple and efficient method that first learns a set of projection operators from blurred images and then uses these operators to estimate the 3D geometry of the scene from novel blurred images. Our experiments on both real and synthetic images show that the performance of the algorithm is relatively insensitive to the form of the PSF Our general approach is to minimize the Euclidean norm of the difference between the estimated images and the observed images. The method is geometric in that we reduce the minimization to performing projections onto linear subspaces, by using inner product structures on both infinite and finite-dimensional Hilbert spaces. Both proposed algorithms involve only simple matrix-vector multiplications which can be implemented in real-time.