Consistent gradient operators

We propose optimal gradient operators based on a newly derived consistency criterion. This criterion is based on an orthogonal decomposition of the difference between a continuous gradient and discrete gradients into the intrinsic smoothing effect and the self-inconsistency involved in the operator. We show that consistency assures the exactness of gradient direction of a locally 1D pattern in spite of its orientation, spectral composition, and sub-pixel translation. Stressing that inconsistency reduction is of primary importance, we derive an iterative algorithm which leads to accurate gradient operators of arbitrary size. We compute the optimum 3×3, 4×4, and 5×5 operators, compare them with conventional operators and examine the performance for one synthetic and several real images. The results indicate that the proposed operators are superior with respect to accuracy, bandwidth and isotropy     

基于改进高斯-拉普拉斯算子的噪声图像边缘检测方法

针对现有梯度算子在图像边缘检测中存在的对噪声比较敏感的问题,提出了一种基于改进高斯-拉普拉斯算子的图像边缘检测方法。噪声图像中的边缘检测是一项关键任务,然而目前常用的几种梯度算子,包括已经提出的高斯-拉普拉斯算子都没能取得理想效果。提出的方法对传统的拉普拉斯边缘检测算子做了改进,并与高斯滤波器相结合。首先,应用高斯滤波器来平滑图像,抑制噪声。然后基于拉普拉斯梯度边缘检测器进行边缘检测。最后在标准图像上进行评估,评估结果显示,提出的边缘检测方法所获得的峰值信噪比(PSNR)和均方误差(MSE)均优于其他几种对比方法。     

Improving angular error via systematically designed near-circular Gaussian-based feature extraction operators

In image filtering, the ‘circularity’ of an operator is an important factor affecting its accuracy. For example, circular differential edge operators are effective in minimising the angular error in the estimation of image gradient direction. We present a general approach to the computation of scalable circular low-level image processing operators that is based on the finite element method. We show that the use of Gaussian basis functions within the finite element method provides a framework for a systematic and efficient design procedure for operators that are scalable to near-circular neighbourhoods through the use of an explicit scale parameter. The general design technique may be applied to a range of operators. Here we evaluate the approach for the design of the image gradient operator. We illustrate that this design procedure significantly reduces angular error in comparison to other well-known gradient approximation methods.     

A new adaptive framework for unbiased orientation estimation in textured images

This paper focuses on directional texture analysis. We propose a new approach for orientation estimation. This approach hinges on two classes of convolution masks, i.e. the gradient and the valleyness operators. We provide a framework for their optimization regarding bias reduction and noise robustness.As the gradient and the valleyness operators are complementary, we propose a combination named GV-JOE. This combination consists in using the gradient on inflexion pixels, the valleyness on crests and valleys, and a linear mixture of both elsewhere. We implement an adaptive selection of the size of our operators, in order to take into account the variations of the texture scale in the image.We apply our approach both on synthetic and natural textures. These experiments show that, when used separately, both classes of operators are more accurate than classical derivative approaches. In noisy cases, the GV-JOE implementation improves the robustness of our operators without affecting their accuracy. Moreover, compared to well-known orientation estimators, it gives the best estimates in the most difficult cases i.e. for high-frequency textures and low SNR.     

基于局部指向性的反向合成图像对齐算法

传统的反向合成图像对齐算法比较的是模板图像与输入图像之间的像素值。该方法容易受到图像中光照变化的影响，从而导致收敛性变差甚至发散。根据局部指向性对光照变化不敏感的特性，提出了一种新的反向合成图像对齐算法——反向合成梯度算法。由于局部指向性的计算在本质上是图像梯度的计算，因此采用几种不同的梯度算子来计算局部指向性。通过实验，验证了反向合成梯度算法能够有效克服图像中光照变化的影响，同时比较了不同算子在不同光照下对反向合成梯度算法的影响。     

Adaptive multi-scale AMSS operator for quality detection of silks

In order to de-noise the silk images corrupted by various noises, a new improved filter based on affine morphological scale space (AMSS) equation was proposed. In this new operator both the adaptive idea and scale space were fused into partial differential equations. Scale parameters were changed adaptively according to the presence or absence of noise in image which was detected by directional gradient operators with four templates. A new evaluating criterion was constructed to test the performance of the improved AMSS operators. Two parameters based on mean square error and minimum absolute error could be acquired to evaluate the effect of keeping edge information and the ability of smoothing noise. Experimental results illustrate that this improved operator can efficiently keep edge information, and the de-noising performance is more effective than other methods for the image with multi-noise.     

梯度算子对反向合成梯度算法的影响

反向合成梯度算法是一种基于局部指向性的反向合成图像对齐算法。与传统的反向合成图像对齐算法相比,该算法可有效地克服光照变化对匹配结果的影响[1]。由于局部指向性的计算在本质上是梯度的计算,而图像梯度的计算可以采用不同的梯度算子,因此采用4种不同的梯度算子（一阶差分算子,Roberts算子,Sobel算子和Prewitt算子）来计算局部指向性,并通过实验比较分析了4种梯度算子对反向合成梯度算法的影响。     

基于Riemann-Liouville改进的1~2阶分数阶边缘提取新模型

针对数字图像的处理中采用整数步长与0~1阶分数阶微分的掩模算子未能精确定位边缘信息、缺少图像的纹理细节的问题,在Laplacian算子的基础上提出了一种新的边缘检测掩模算子。该算法从Riemann-Liouville(R-L)定义出发,推出1~2阶分数阶微分在中频信号的增强效果优于0~1阶分数阶微分并显著提升了高频信号,最终得到精确的检测效果。仿真结果表明:提出的算子能更好地提取边缘信息,尤其对灰度变化不大的平滑区域中纹理细节丰富的图像,该算子检测到的信息优于现有0~1阶微分算子,针对主观识别有更高的准确率;客观上采用扫描法的定位误差统计,该算子的综合定位误差率为7.41%,低于整数阶微分算子(最低为10.36%)与0~1阶微分算子(最低为9.97%),有效提高了边缘定位精度。该算子尤其适用于具有较高频信息的图像边缘检测中。     

基于多尺度形态梯度的灰度图像边缘检测

研究了一种基于多尺度抗噪型形态梯度的灰度图像边缘检测算法。该算法通过构造5个不同的结构元素,结合多尺度合成对图像进行边缘检测。为验证本文算法的效果,用几种传统的微分算子对实验图像进行了边缘提取的实验,并把结果与用本文算法提取的结果进行了比较。结果表明:本文算法比较成功地完成了图像的边缘检测,且检测效果在完整性和细节的丰富性方面优于经典的Sobel算子,LOG算子和Canny算子,但在某些边缘的连接性和平滑性方面不如Canny算子,在这方面还有待改进。     

一种计算图象形态梯度的多尺度算法

分水岭变换是一种非常适用于图象分割的形态算子,然而,基于分水岭变换的图象分割方法,其性能在很大程度上依赖于用来计算待分割图象梯度的算法。为了高效地进行分水岭变换,提出了一种计算图象形态梯度的多尺度算法,从而对阶跃边缘和“模糊”边缘进行了有效的处理,此外,还提出了一种去除因噪声或量化误差造成的局部“谷底”的算法,实验结果表明,图象采用本文算法处理后,再进行分水岭变换,即使不进行区域合并,也能产生有意义的分割,因而极大地减轻了计算负担。     

双算子形态学滤波器

传统的形态学滤波算子交替性差、耗时长且抑制噪声能力弱. 基于中心互补结构元素与交替对偶算子, 提出了双算子形态学滤波器. 该滤波器继承了经典形态学滤波器的递增性、对偶性和幂等性, 但不满足扩展性和非扩展性. 双算子形态学滤波器具有离散的邻域运算特性, 采用交替小结构元素能去除较结构元素大的噪声块, 且在抑制噪声的同时有效保留了图像细节. 实验结果表明, 与基本的形态学滤波器及目前已改进的形态学滤波器相比, 双算子形态学滤波器具有更强的噪声抑制性能, 且在同等滤波效果下, 其计算量更小, 最终滤波后的图像具有较高的峰值信噪比和较小的均方根误差.     

基于梯度比率的SAR图像局部特征提取方法研究

本文研究了基于像素灰度差值计算的LBP算子和基于梯度比率的LGRP算子等局部二值模式。首先介绍了基本LBP算子和其他几种LBP算子的变形模式,并通过光学图像和实测SAR图像对LBP算子进行性能评估。针对LBP对SAR 图像乘性噪声敏感的问题,利用梯度比率计算的LGRP算子,并结合旋转不变LBP的抗旋转性,本文提出了一种改进的SAR 图像LGRP特征,获得了对SAR 图像的抗噪性和抗旋转性能。实验结果表明,由本文方法提取的SAR图像局部特征具有较好的不变性,可用于姿态角变化下的目标识别与图像纹理切片匹配。     

Use of discrete gradient operators for the automatic determination of vanishing points: Comparative analysis

Thales’ second theorem can be used for the automatic detection of the vanishing points of an image. This paper explores its reliability and accuracy according to the type of operator used for the detection of edges. An algorithm has been used which processes a photographic image according to the operator selected. The result is a point cloud which is then used to find the desired solution. The comparison between the four discrete gradient operators (Frei-Chen, Prewitt, Roberts and Sobel) has been made taking into account the resolution of the image and the number of vanishing points. The results obtained show that Frei-Chen’s operator shows good performance in determining vanishing points with respect to the spatial X axis, Sobel’s operator is the best for determining the vanishing point with respect to the spatial Y axis, Roberts’ operator gives good results for calculating vanishing points in both spatial axes, and Prewitt’s operator is not appropriate for processing this type of image.     

Improving the interest operator for face recognition

When the conventional interest operator is used as the feature extraction procedure of face recognition, it has the following two shortcomings: first, though the purpose of the conventional interest operator is to use the intensity variation between neighboring pixels to represent the image, it cannot obtain all variation information between neighboring pixels. Second, under varying lighting conditions two images of the same face usually have different feature extraction results even though the face itself does not have obvious change. In this paper, we propose two new interest operators for face recognition, which are used to calculate the pixel intensity variation information of overlapping blocks produced from the original face image. The following two factors allow the new operators to perform better than the conventional interest operator: the first factor is that by taking the relative rather than absolute variation of the pixel intensity as the feature of an image block, the new operators can obtain robust block features. The second factor is that the scheme to partition an image into overlapping rather than non-overlapping blocks allows the proposed operators to produce more representation information for the face image. Experimental results show that the proposed operators offer significant accuracy improvement over the conventional interest operator.     

Adaptive and optimal difference operators in image processing

Differential operators are essential in many image processing applications. Previous work has shown how to compute derivatives more accurately by examining the image locally, and by applying a difference operator which is optimal for each pixel neighborhood. The proposed technique avoids the explicit computation of fitting functions, and replaces the function fitting process by a function classification process using a filter bank of feature detection templates. Both the feature detectors and the optimal difference operators have a specific shape and an associated cost, defined by a rigid mathematical structure, which can be described by Gröbner bases. This paper introduces a cost criterion to select the operator of the best approximating function class and the most appropriate template size so that the difference operator can be locally adapted to the digitized function. We describe how to obtain discrete approximates for commonly used differential operators, and illustrate how image processing applications can benefit from the adaptive selection procedure for the operators by means of two example applications: tangent computation for digitized object boundaries and the Laplacian of Gaussian edge detector.     

Adaptive application of feature detection operators based on image variance

It is well known that the strength of a feature in an image may depend on the scale at which the appropriate detection operator is applied. It is also the case that many features in images exist significantly over a limited range of scales, and, of particular interest here, that the most salient scale may vary spatially over the feature. Hence, when designing feature detection operators, it is necessary to consider the requirements for both the systematic development and adaptive application of such operators over scale- and image-domains. We present an overview to the design of scalable derivative edge detectors, based on the finite element method, that addresses the issues of method and scale-adaptability. The finite element approach allows us to formulate scalable image derivative operators that can be implemented using a combination of piecewise-polynomial and Gaussian basis functions. The general adaptive technique may be applied to a range of operators. Here we evaluate the approach using image gradient operators, and we present comparative qualitative and quantitative results for both first and second order derivative methods.     

Precision edge contrast and orientation estimation

The contrast and orientation estimation accuracy of several edge operators that have been proposed in the literature is examined both for the noiseless case and in the presence of additive Gaussian noise. The test image is an ideal step edge that has been sampled with a square-aperture grid. The effects of subpixel translations and rotations of the edge on the performance of the operators are studied. It is shown that the effect of subpixel translations of an edge can generate more error than moderate noise levels. Methods with improved results are presented for Sobel angle estimates and the Nevatia-Babu operator, and theoretical noise performance evaluations are also provided. An edge operator based on two-dimensional spatial moments is presented. All methods are compared according to worst-case and RMS error in an ideal noiseless situation and RMS error under various noise levels     

采用有向梯度与RANSAC的虹膜定位算法

针对虹膜图像中有较多光斑的情况,提出一种基于有向梯度和随机抽样一致性（RANSAC）相结合的虹膜定位算法。该算法根据瞳孔内某点利用有向梯度提取内缘像素点,采用RANSAC定位虹膜内缘;下采样虹膜图像,利用圆差分算子在瞳孔左右两侧拟合出两个圆,进而合并为一个圆;根据圆的参数在虹膜图像中快速精确定位外缘。实验结果表明：该算法在正确率、定位速度和鲁棒性方面均优于传统的虹膜定位算法。     

自适应尺度的局部强度聚类图像分割模型

针对传统活动轮廓模型无法精确分割强度不均匀图像，并且对尺度参数比较敏感的问题，提出了一种基于区域信息的自适应尺度的活动轮廓模型。根据图像的局部熵构建自适应尺度算子，利用图像的局部强度聚类性质构建能量函数。使用一组平滑基函数的线性组合来表示偏移场，这样可以增加模型的稳定性。通过最小化该能量，所提模型能够同时分割图像和估计偏移场，并且估计的偏移场可以用于强度不均匀校正。实验结果表明，与其它4种模型相比，该模型拥有更高的分割精确度，且分割结果对水平集函数的初始化和噪声具有鲁棒性。     

一种新的自适应边缘提取微分算子

提出一种新的微分算子用于边缘提取,基于泰勒展开分别计算图像水平和竖直方向的灰度差分,相比传统一阶或二阶微分算子,其梯度值结果更精确,弥补了传统算子微弱边缘提取少且与原图逼近度较差的缺陷。然后基于大津法思想对图像梯度幅值直方图计算分割阈值,从而得到一种新的能自适应提取边缘的微分算子。仿真结果表明,新算子不仅能够对不同图像自适应提取边缘,并且相比传统微分算子,它能提取更多微弱边缘,尤其对灰度对比度较低的图像。同时对曲线部分具有较好的逼近效果,适用于人脸等线条细节比较丰富的图像。将新算子应用到Canny算子中能获取更精确的结果。