Multi-edge detection by isotropical 2-D ISEF cascade

Most research in edge detection has been based on the classical mono-edge model. In the present paper, we propose an optimal edge detector for complicated noisy multi-edge images and the isotropical 2-D realization of the optimal filter. We introduce at first the complicated multi-edge model and show that the optimal filter as a preparation for multi edge detection, is a cascade of Infinite size Symmetrical Exponential Filters (ISEF). We then propose a fast realization of the isotropical 2-D optimal filter. Experimental results are also presented.     

伪球滤波和边缘检测

提出了一种图像滤波器——伪球滤波器.在伪球滤波器中,除了尺度参数外,还引入了边缘保持参数,因而它能较好地解决传统滤波器的平滑性能与边缘定位精度之间的矛盾.以伪球滤波器取代经典Canny边缘检测算子中的高斯滤波器,得到一种基于伪球的边缘检测算子.模拟图像和真实图像的实验结果表明,与经典的Canny边缘检测算子相比,在具有相当平滑性的条件下,基于伪球的边缘检测算子对边缘定位具有更高的精度.     

The Max Roberts Operator is a Hueckel-Type Edge Detector

Hueckel's edge detector finds the best-fitting ideal step edge to a given picture neighborhood by expanding the neighborhood and step edge in terms of a set of nine basis functions. A very simple case of this approach uses a 2 × 2 neighborhood and three basis functions. This case is solved explicitly using elementary methods. The magnitude of the best-fitting step edge for the neighborhood AB CD turns out to be the Roberts operator max (|A - D|, |B - C|).     

Gabor filter-based edge detection

It is common practice to utilize evidence from biological and psychological vision experiments to develop computational models for low-level feature extraction. The receptive profiles of simple cells in mammalian visual systems have been found to closely resemble Gabor filters. Daugman proved that Gabor filters achieve joint minimal joint uncertainty. These results led researchers to develop computational models based on Gabor filters for several low-level vision applications such as edge detection, texture classification, optical flow estimation and data compression. In this paper, the performance of a Gabor odd filter-based edge detector is investigated using the measures proposed by Canny. Based on this performance analysis a design criterion for one-dimensional (1D) Gabor filter-based edge detector is derived. It is shown that this design criterion also holds good for a two-dimensional (2D) Gabor filter-based edge detector. Experimental results are presented to demonstrate the performance of the Gabor filter-based edge detector.     

Regularized Laplacian Zero Crossings as Optimal Edge Integrators

We view the fundamental edge integration problem for object segmentation in a geometric variational framework. First we show that the classical zero-crossings of the image Laplacian edge detector as suggested by Marr and Hildreth, inherently provides optimal edge-integration with regard to a very natural geometric functional. This functional accumulates the inner product between the normal to the edge and the gray level image-gradient along the edge. We use this observation to derive new and highly accurate active contours based on this functional and regularized by previously proposed geodesic active contour geometric variational models. We also incorporate a 2D geometric variational explanation to the Haralick edge detector into the geometric active contour framework.     

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。     

基于多结构元的形态图像边缘检测算法

基于修正的边缘检测算子和形态滤波思想,提出一种新的多结构元素形态学灰度图像边缘检测算法。在该算法中,自适应确定权重,并将各个结构元素下的检测信息进行加权求和,得到噪声存在条件下较为理想的图像边缘。仿真结果表明所给算法效果优于经典的边缘检测方法。     

Edge detection and speckle adaptive filtering for SAR images based on a second-order textural measure

An edge detector based on a second-order texture measure is presented. It is demonstrated that the operator is well adapted for SAR image analysis: it possesses good sensitivity to edges and its response does not depend on the image brightness. In the second part of the paper, an adaptive speckle filter based on the presented edge detector is introduced. The potential of the filter is illustrated using an airborne SAR image. It is shown that the filter preserves edges better than filters based on the coefficient of variation and still provides good sensitivity to textural patterns other than speckle. Considering the recognized importance of texture in the interpretation of radar imagery, these filters may be useful for pre-interpretation image enhancement.     

Edge location to subpixel values in digital imagery

A new method for locating edges in digital data to subpixel values and which is invariant to additive and multiplicative changes in the data is presented. For one-dimensional edge patterns an ideal edge is fit to the data by matching moments. It is shown that the edge location is related to the so-called ``Christoffel numbers.' Also presented is the study of the effect of additive noise on edge location. The method is extended to include two-dimensional edge patterns where a line equation is derived to locate an edge. This in turn is compared with the standard Hueckel edge operator. An application of the new edge operator as an edge detector is also provided and is compared with Sobel and Hueckel edge detectors in presence and absence of noise.     

Using Canny's criteria to derive a recursively implemented optimal edge detector

A highly efficient recursive algorithm for edge detection is presented. Using Canny's design [1], we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension, which can be efficiently implemented by two recursive filters moving in opposite directions. In addition to the noise truncature immunity which results, the recursive nature of the filtering operations leads, with sequential machines, to a substantial saving in computational effort (five multiplications and five additions for one pixel, independent of the size of the neighborhood). The extension to the two-dimensional case is considered and the resulting filtering structures are implemented as two-dimensional recursive filters. Hence, the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm. Performance measures of this new edge detector are given and compared to Canny's filters. Various experimental results are shown.