A Bayesian method for fitting parametric and nonparametric modelsto noisy data

We present a simple paradigm for fitting models, parametric and nonparametric, to noisy data, which resolves some of the problems associated with classical MSE algorithms. This is done by considering each point on the model as a possible source for each data point. The paradigm can be used to solve problems which are ill-posed in the classical MSE approach, such as fitting a segment (as opposed to a line). It is shown to be nonbiased and to achieve excellent results for general curves, even in the presence of strong discontinuities. Results are shown for a number of fitting problems, including lines, circles, elliptic arcs, segments, rectangles, and general curves, contaminated by Gaussian and uniform noise     

Robust line fitting in a noisy image by the method of moments

The standard least squared distance method of fitting a line to a set of data points is known to be unreliable when the random noise in the input is significant compared with the data correlated to the line itself. Here, we present a new statistical clustering method based on Legendre moment theory and maximum entropy principle for line fitting in a noisy image. We propose a new approach for estimating the underlying probability density function (p.d.f.) of the data set. The p.d.f. is expanded in terms of Legendre polynomials by means of the Legendre moments. The order of the expansion is selected according to the maximum entropy principle. Then, the points corresponding to the maxima of the p.d.f. will be the true points of the line to be extracted by a chaining algorithm. This approach is directly generalized to multidimensional data. The proposed algorithm was successfully applied to real and simulated noisy line images, with comparison to some well-known methods     

Line fitting in a noisy image

The conventional least-squared-distance method of fitting a line to a set of data points is unreliable when the amount of random noise in the input (such as an image) is significant compared with the amount of data correlated to the line itself. Points which are far away from the line (outliers) are usually just noise, but they contribute the most to the distance averaging, skewing the line from its correct position. The author presents a statistical method of separating the data of interest from random noise, using a maximum-likelihood principle     

Comments on: "Robust line fitting in a noisy image by the method of moments"

Qjidaa and Radouane (1999) presented a method for robust line fitting and experimentally compared it to other methods, including a method suggested by us. The results attributed by Qjidaa and Radouane to our algorithm are incorrect. We apply our algorithm to the data used by Qjidaa and Radouane and demonstrate its robustness and accuracy.     

An Isodata algorithm for straight line fitting

This note describes a method of fitting κ straight lines to a set of data points using an algorithm analogous to the Isodata, or κ-means, clustering technique for partitioning a set of data points into κ compact clusters.     

What's in a set of points? [straight line fitting]

The problem of fitting a straight line to a planar set of points is reconsidered. A parameter space computational approach capable of fitting one or more lines to a set of points is presented. The suggested algorithm handles errors in both coordinates of the data points, even when the error variances vary between coordinates and among points and can be readily made robust to outliers. The algorithm is quite general and allows line fitting according to several useful optimality criteria to be performed within a single computational framework. It is observed that certain extensions of the Hough transform can be turned to be equivalent to well-known M estimators, thus allowing computationally efficient approximate M estimation     

直线拟合算法在车辆监控系统中的研究与实现

在充分研究了GIS和GPS的前提下,运用数值分析、数据结构、MapInfo、VB以及C等相关知识,提出了一个能在实际的车辆监控系统中使得在装置的小内存中能够存储地图信息的有效直线拟合算法.用该算法从MapInfo中获得必要的地图信息并存入装置的内存中,可以在很大程度上节省存储空间,从而使得用小容量的内存保存地图信息成为可能.经实际的车辆监控系统验证,该拟合算法完全可行.并且给出了该算法的类C语言描述.     

直线拟合算法在车辆监控系统中的研究与实现

在充分研究了GIS和GPS的前提下,运用数值分析、数据结构、MapInfo、VB以及C等相关知识,提出了一个能在实际的车辆监控系统中使得在装置的小内存中能够存储地图信息的有效直线拟合算法。用该算法从MapInfo中获得必要的地图信息并存入装置的内存中,可以在很大程度上节省存储空间,从而使得用小容量的内存保存地图信息成为可能。经实际的车辆监控系统验证,该拟合算法完全可行。并且给出了该算法的类C语言描述。     

噪声图像边缘检测方法的研究*

对图像中常见的高斯噪声和椒盐噪声的特性进行了分析,对含有这两种噪声的数字图像的边缘检测方法进行了研究,尤其对基于顺序形态学的噪声图像边缘检测方法进行了深入的分析研究,基于顺序形态学理论提出了针对分别含有高斯噪声和椒盐噪声的图像边缘检测方法。通过仿真验证表明,对于含有以上两种噪声的图像,提出的方法不仅能够去除噪声而且能够提取出准确清晰的边缘。     

A nonparametric procedure for blind image deblurring

Observed images are usually blurred versions of true images, due to imperfections of imaging devices, atmospheric turbulence, out of focus lens, motion blurs, and so forth. The major purpose of image deblurring is to restore the original image from its blurred version. A blurred image can be described by convolution of the original image with a point spread function (psf) that characterizes the blurring mechanism. Thus, one essential problem for image deblurring is to estimate the psf from the observed but blurred image, which turns out to be a challenging task, due to the “ill-posed” nature of the problem. In the literature, most existing image deblurring procedures assume that either the psf is completely known or it has a parametric form. Motivated by some image applications, including handwritten text recognition and calibration of imaging devices, we suggest a method for estimating the psf nonparametrically, in cases when the true image has one or more line edges, which is usually satisfied in the applications mentioned above and which is not a big restriction in some other image applications, because it is often convenient to take pictures of objects with line edges, using the imaging device under study. Both theoretical justifications and numerical studies show that the proposed method works well in applications.     

A method for ray tracing a wide class of generalized cylinders with straight line trajectories

Generalized cylinders with straight line trajectories are discussed for modeling objects of various kinds. For these kinds of generalized cylinders the sweeping cross-section is allowed to change shape, size, and orientation in an arbitrary way as a function of the parameter describing the location of the sweeping cross-section along the trajectory of the generalized cylinder. The sweeping cross-section may even fail to intersect the trajectory of the generalized cylinder for all or a fraction of its range. The only restriction is that the parametric function describing the variation of the sweeping cross-section as a function of the location along the axis should be invertible. For the purpose of rendering the image, the problem of line-surface intersections is reduced to that of curve-curve intersections in a plane. A complete methodology for calculating and rendering ray-traced images of such objects is presented. The method provides for a unification of several special cases discussed in the past and more.     

An Isodata algorithm for straight line fitting

This note describes a method of fitting κ straight lines to a set of data points using an algorithm analogous to the Isodata, or κ-means, clustering technique for partitioning a set of data points into κ compact clusters.     

新的噪声污染灰度图像边缘检测方法

传统的图像边缘检测方法由于引入了各种微分运算,因此用于噪声图像边缘检测时对噪声极度敏感。针对这一问题,提出了一种基于独立分量分析技术的噪声图像边缘检测方法,该算法通过计算数据之间的高阶统计信息,提取特征模板,然后将被高斯噪声污染的灰度图像与这些模板逐个匹配,提取出边缘成分。实验结果表明,基于独立分量分析技术的模板匹配方法自适应强,复杂度低,是一种有效的高斯噪声污染灰度图像边缘检测方法。     

一种两点间直线搜索的输电线检测方法

在无人机应用于输电线巡检背景下,为了方便后续的输电线故障检测与分析,提出了一种两点间直线搜索的输电线检测方法。首先,通过方向可控滤波器对无人机图像进行分割。然后,通过所提出的基于圆搜索(CBS)直线段检测方法进行直线段检测。最后,通过所提出的连接算法进行直线段连接。通过在人造图像上的直线段检测实验,证明该方法是一种有效的直线检测方法。随后,通过在实际场景的无人机图像上进行实验,证明该方法是一种有效的输电线检测方法。     

Proposal of a method to extract straight line and circle using one-dimensional histogram

A new method for fast extraction of straight line and circle is proposed in this study. The method utilizes the Polytope method which is one of minimization algorithms. For the extraction of figures, one-dimensional histogram is used. Basically, main algorithm of the extraction of straight line is the same as those of circle and ellipse. Only the definition of histogram and the evaluation function are changed according as figures. By the comparison with Hough transform, it is understood that the using of memory space is very small and processing time is very short. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

A scalable region-based level set method using adaptive bilateral filter for noisy image segmentation

Image segmentation plays an important role in the computer vision . However, it is extremely challenging due to low resolution, high noise and blurry boundaries. Recently, region-based models have been widely used to segment such images. The existing models often utilized Gaussian filtering to filter images, which caused the loss of edge gradient information. Accordingly, in this paper, a novel local region model based on adaptive bilateral filter is presented for segmenting noisy images. Specifically, we firstly construct a range-based adaptive bilateral filter, in which an image can well be preserved edge structures as well as resisted noise. Secondly, we present a data-driven energy model, which utilizes local information of regions centered at each pixel of image to approximate intensities inside and outside of the circular contour. The estimation approach has improved the accuracy of noisy image segmentation. Thirdly, under the premise of keeping the image original shape, a regularization function is used to accelerate the convergence speed and smoothen the segmentation contour. Experimental results of both synthetic and real images demonstrate that the proposed model is more efficient and robust to noise than the state-of-art region-based models.

     

新的噪声污染灰度图像边缘检测统计方法*

针对传统算子进行边缘检测时易丢失边缘信息和在非边缘处增强噪声的缺陷,提出一种基于非参数变点统计分析的噪声图像边缘检测方法,该统计方法不但不需要图像数字特征的任何先验信息,而且对噪声污染的图像不作任何滤波处理.实验结果表明,提出的算法优于Sobel算子,并能抑制信噪较低的高斯噪声和密度较高的椒盐噪声对分割结果的影响,是一种有效的噪声污染灰度图像边缘检测方法.     

A variation on a nonparametric clustering method

A single modification to a mode-seeking clustering algorithm proposed by Koontz, Narendra, and Fukunaga is shown to generate a novel clustering and to provide an indication of cluster stability. The modified method should provide better clusterings for ``uniform, touching' clusters than the original, although the original should work better than the modified method for ``touching Gaussian' clusters. Suitable ranges for the clustering parameters of both methods are investigated. Since the modification requires changing only one line of the original algorithm, two clusterings can be obtained for the price of one coding.     

针对文物图像的特征线提取方法研究

针对计算机辅助实现文物考古绘图自动化的问题, 提出了一种文物图像的特征线提取方法。首先利用双边滤波器对文物图像进行预处理, 改善了文物图像的主观质量; 运用LoG边缘检测的方法得到图像的边缘路径; 最后采用非均匀B样条得到插值边缘曲线, 并利用高斯滤波器对其平滑处理来提高画笔生成的质量。实验结果表明, 该方法是文物特征线提取的有效方法。