几种轮廓曲率估计角点检测算法研究
发布时间：2018-09-09 10:31
【摘要】：角点是图像中稳定的稀疏特征,包含着图像重要的结构信息,当前在图像处理、计算机视觉和模式识别等领域中对角点检测算法的分析与研究都是基本的课题之一,角点检测对诸如图像匹配与配准、目标识别与追踪、运动估计和三维场景重建等任务的处理都扮演着非常重要的作用。本文从研究轮廓曲线的离散曲率开始,通过相关理论分析,设计和构建了三种能较好反映平面曲线曲率概念和性质的曲率估计方案:(1)角度估计子(两个);(2)连续曲率估计子;(3)点到切线相对距离累加和估计子。论文的主要研究工作和创新点具体如下:(1)角度是轮廓曲线离散曲率的一种重要反映,针对已有的利用角度进行角点检测的RJ73算法中支持域的选择存在一些缺点的问题,我们提出了一种新的用于角度估计的方法(Arc length-based Angle Estimator,简称AAE)。AAE方法首先将从灰度图像中提取的边缘轮廓线弧长参数化为两条参数曲线,然后通过相关理论分析将对边缘轮廓线的角度估计问题转化为弧长参数曲线的斜率估计问题,最后通过(加权)最小二乘拟合技术(Weighted Least Square,简称WLS)来给出斜率估计问题的解决方案。(2)AAE方法是通过将轮廓曲线的角度估计问题转化为弧长参数曲线的斜率估计给出了一种新的角度估计方案。我们也可以不进行轮廓曲线的参数化而是直接估计曲线上任一点处的角度,采用的方法是将目标点前、后支持域内的点近似看作两条直线段,将这两条直线段的夹角视为目标点处的角度值。为了计算两条直线段的夹角,需要计算两条直线段的方向向量,而这两个方向向量中的任一个可以近似看作由相应半支持域内的点构建的协方差矩阵的特征向量,在此基础上给出了另外一种新的利用协方差矩阵特征向量来估计轮廓曲线角度的方案EAE(Eigenvector-based Angle Estimator,简称EAE)。(3)论文将离散曲线以弧长为参数得到两条对应的参数离散曲线,然后对离散数字曲线分别用Chebyshev多项式进行拟合,得到相对应的连续可微曲线,并采用最小二乘拟合技术来求解Chebyshev多项式中的各待定系数。这样对当前点的曲率估计转化为对拟合曲线在对应参数点处的求导问题,我们就可以获得离散数字曲线上每一点的连续曲率估计。(4)通过直观的观察发现,对于轮廓曲线上一点而言,该点处曲率值越大,其附近点到该点处切线的距离相对也越大。在此发现的基础上,我们提出了一种新的度量离散曲率的方法。对于一般的离散数字轮廓曲线段,首先用二次多项式做最小二乘拟合来求取当前目标点处的切线方程,然后计算目标点支持域内所有点到该切线的相对距离累加和,这个相对距离累加和可作为数字曲线曲率的一种离散估计。
[Abstract]:Corner is a stable sparse feature in image, which contains important structural information of image. At present, the analysis and research of diagonal detection algorithms in the fields of image processing, computer vision and pattern recognition are one of the basic topics. Corner detection plays an important role in processing tasks such as image matching and registration, target recognition and tracking, motion estimation and 3D scene reconstruction. In this paper, the discrete curvature of contour curve is studied. Three curvature estimation schemes are designed and constructed, which can better reflect the concept and properties of planar curve curvature: (1) angle estimator (two); (2) continuous curvature estimators, (3) point to tangent relative distance accumulators and estimators. The main research work and innovation of this paper are as follows: (1) Angle is an important reflection of discrete curvature of contour curve. There are some shortcomings in the selection of support domain in the existing RJ73 algorithm which uses angle to detect corners. In this paper, we propose a new method for angle estimation (Arc length-based Angle Estimator, AAE) .AAE, which firstly transforms the arc length of edge contour from gray image into two parameter curves. Then the angle estimation problem of the edge contour is transformed into the slope estimation problem of arc length parameter curve through the relevant theoretical analysis. Finally, the (weighted) least square fitting technique (Weighted Least Square, is used to give a solution to the slope estimation problem. (2) the AAE method transforms the angle estimation problem of contour curve into the slope estimation of arc length parameter curve. A new angle estimation scheme is proposed. Instead of parameterizing the contour curve, we can directly estimate the angle at any point on the curve. The method is to approximate the points in the support domain as two straight lines before and after the target point. The angle between these two straight lines is regarded as the angle value at the target point. In order to calculate the angle of two straight line segments, we need to calculate the direction vector of two straight line segments, and any of these two direction vectors can be approximately regarded as the eigenvector of the covariance matrix constructed by points in the corresponding semi-support domain. On this basis, another new scheme, EAE (Eigenvector-based Angle Estimator, EAE). (3), which uses the eigenvector of covariance matrix to estimate the angle of contour curve, is presented. In this paper, two corresponding discrete curves are obtained by using arc length as a parameter. Then the discrete digital curves are fitted with Chebyshev polynomials, and the corresponding continuous differentiable curves are obtained, and the least square fitting technique is used to solve the undetermined coefficients in the Chebyshev polynomials. In this way, the curvature estimation of the current point is transformed into the derivation of the fitting curve at the corresponding parameter points, and we can obtain the continuous curvature estimation of each point on the discrete digital curve. (4) by visual observation, we find that, For the point on the contour curve, the greater the curvature value of the point, the greater the distance from the point near the point to the tangent line at the point. Based on these findings, we propose a new method to measure discrete curvature. For the general discrete digital contour curve segment, the tangent equation at the current target point is obtained by least square fitting with quadratic polynomial, and then the cumulative sum of relative distance between all points in the support domain and the tangent line is calculated. The cumulative relative distance can be used as a discrete estimate of the curvature of a digital curve.
【学位授予单位】：重庆大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.41
[Abstract]:Corner is a stable sparse feature in image, which contains important structural information of image. At present, the analysis and research of diagonal detection algorithms in the fields of image processing, computer vision and pattern recognition are one of the basic topics. Corner detection plays an important role in processing tasks such as image matching and registration, target recognition and tracking, motion estimation and 3D scene reconstruction. In this paper, the discrete curvature of contour curve is studied. Three curvature estimation schemes are designed and constructed, which can better reflect the concept and properties of planar curve curvature: (1) angle estimator (two); (2) continuous curvature estimators, (3) point to tangent relative distance accumulators and estimators. The main research work and innovation of this paper are as follows: (1) Angle is an important reflection of discrete curvature of contour curve. There are some shortcomings in the selection of support domain in the existing RJ73 algorithm which uses angle to detect corners. In this paper, we propose a new method for angle estimation (Arc length-based Angle Estimator, AAE) .AAE, which firstly transforms the arc length of edge contour from gray image into two parameter curves. Then the angle estimation problem of the edge contour is transformed into the slope estimation problem of arc length parameter curve through the relevant theoretical analysis. Finally, the (weighted) least square fitting technique (Weighted Least Square, is used to give a solution to the slope estimation problem. (2) the AAE method transforms the angle estimation problem of contour curve into the slope estimation of arc length parameter curve. A new angle estimation scheme is proposed. Instead of parameterizing the contour curve, we can directly estimate the angle at any point on the curve. The method is to approximate the points in the support domain as two straight lines before and after the target point. The angle between these two straight lines is regarded as the angle value at the target point. In order to calculate the angle of two straight line segments, we need to calculate the direction vector of two straight line segments, and any of these two direction vectors can be approximately regarded as the eigenvector of the covariance matrix constructed by points in the corresponding semi-support domain. On this basis, another new scheme, EAE (Eigenvector-based Angle Estimator, EAE). (3), which uses the eigenvector of covariance matrix to estimate the angle of contour curve, is presented. In this paper, two corresponding discrete curves are obtained by using arc length as a parameter. Then the discrete digital curves are fitted with Chebyshev polynomials, and the corresponding continuous differentiable curves are obtained, and the least square fitting technique is used to solve the undetermined coefficients in the Chebyshev polynomials. In this way, the curvature estimation of the current point is transformed into the derivation of the fitting curve at the corresponding parameter points, and we can obtain the continuous curvature estimation of each point on the discrete digital curve. (4) by visual observation, we find that, For the point on the contour curve, the greater the curvature value of the point, the greater the distance from the point near the point to the tangent line at the point. Based on these findings, we propose a new method to measure discrete curvature. For the general discrete digital contour curve segment, the tangent equation at the current target point is obtained by least square fitting with quadratic polynomial, and then the cumulative sum of relative distance between all points in the support domain and the tangent line is calculated. The cumulative relative distance can be used as a discrete estimate of the curvature of a digital curve.
【学位授予单位】：重庆大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.41
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