幾種輪廓曲率估計(jì)角點(diǎn)檢測(cè)算法研究
發(fā)布時(shí)間：2018-09-09 10:31
【摘要】：角點(diǎn)是圖像中穩(wěn)定的稀疏特征,包含著圖像重要的結(jié)構(gòu)信息,當(dāng)前在圖像處理、計(jì)算機(jī)視覺和模式識(shí)別等領(lǐng)域中對(duì)角點(diǎn)檢測(cè)算法的分析與研究都是基本的課題之一,角點(diǎn)檢測(cè)對(duì)諸如圖像匹配與配準(zhǔn)、目標(biāo)識(shí)別與追蹤、運(yùn)動(dòng)估計(jì)和三維場(chǎng)景重建等任務(wù)的處理都扮演著非常重要的作用。本文從研究輪廓曲線的離散曲率開始,通過相關(guān)理論分析,設(shè)計(jì)和構(gòu)建了三種能較好反映平面曲線曲率概念和性質(zhì)的曲率估計(jì)方案:(1)角度估計(jì)子(兩個(gè));(2)連續(xù)曲率估計(jì)子;(3)點(diǎn)到切線相對(duì)距離累加和估計(jì)子。論文的主要研究工作和創(chuàng)新點(diǎn)具體如下:(1)角度是輪廓曲線離散曲率的一種重要反映,針對(duì)已有的利用角度進(jìn)行角點(diǎn)檢測(cè)的RJ73算法中支持域的選擇存在一些缺點(diǎn)的問題,我們提出了一種新的用于角度估計(jì)的方法(Arc length-based Angle Estimator,簡(jiǎn)稱AAE)。AAE方法首先將從灰度圖像中提取的邊緣輪廓線弧長(zhǎng)參數(shù)化為兩條參數(shù)曲線,然后通過相關(guān)理論分析將對(duì)邊緣輪廓線的角度估計(jì)問題轉(zhuǎn)化為弧長(zhǎng)參數(shù)曲線的斜率估計(jì)問題,最后通過(加權(quán))最小二乘擬合技術(shù)(Weighted Least Square,簡(jiǎn)稱WLS)來(lái)給出斜率估計(jì)問題的解決方案。(2)AAE方法是通過將輪廓曲線的角度估計(jì)問題轉(zhuǎn)化為弧長(zhǎng)參數(shù)曲線的斜率估計(jì)給出了一種新的角度估計(jì)方案。我們也可以不進(jìn)行輪廓曲線的參數(shù)化而是直接估計(jì)曲線上任一點(diǎn)處的角度,采用的方法是將目標(biāo)點(diǎn)前、后支持域內(nèi)的點(diǎn)近似看作兩條直線段,將這兩條直線段的夾角視為目標(biāo)點(diǎn)處的角度值。為了計(jì)算兩條直線段的夾角,需要計(jì)算兩條直線段的方向向量,而這兩個(gè)方向向量中的任一個(gè)可以近似看作由相應(yīng)半支持域內(nèi)的點(diǎn)構(gòu)建的協(xié)方差矩陣的特征向量,在此基礎(chǔ)上給出了另外一種新的利用協(xié)方差矩陣特征向量來(lái)估計(jì)輪廓曲線角度的方案EAE(Eigenvector-based Angle Estimator,簡(jiǎn)稱EAE)。(3)論文將離散曲線以弧長(zhǎng)為參數(shù)得到兩條對(duì)應(yīng)的參數(shù)離散曲線,然后對(duì)離散數(shù)字曲線分別用Chebyshev多項(xiàng)式進(jìn)行擬合,得到相對(duì)應(yīng)的連續(xù)可微曲線,并采用最小二乘擬合技術(shù)來(lái)求解Chebyshev多項(xiàng)式中的各待定系數(shù)。這樣對(duì)當(dāng)前點(diǎn)的曲率估計(jì)轉(zhuǎn)化為對(duì)擬合曲線在對(duì)應(yīng)參數(shù)點(diǎn)處的求導(dǎo)問題,我們就可以獲得離散數(shù)字曲線上每一點(diǎn)的連續(xù)曲率估計(jì)。(4)通過直觀的觀察發(fā)現(xiàn),對(duì)于輪廓曲線上一點(diǎn)而言,該點(diǎn)處曲率值越大,其附近點(diǎn)到該點(diǎn)處切線的距離相對(duì)也越大。在此發(fā)現(xiàn)的基礎(chǔ)上,我們提出了一種新的度量離散曲率的方法。對(duì)于一般的離散數(shù)字輪廓曲線段,首先用二次多項(xiàng)式做最小二乘擬合來(lái)求取當(dāng)前目標(biāo)點(diǎn)處的切線方程,然后計(jì)算目標(biāo)點(diǎn)支持域內(nèi)所有點(diǎn)到該切線的相對(duì)距離累加和,這個(gè)相對(duì)距離累加和可作為數(shù)字曲線曲率的一種離散估計(jì)。
[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.
【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：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.
【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TP391.41
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相關(guān)期刊論文 前10條
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