Edges In Noisy Images Research Articles

Efficient Bayesian Detection of Faint Curved Edges in Noisy Images

Efficient Bayesian Detection of Faint Curved Edges in Noisy Images

Edge detection in noisy images with different edge types

Edge Detection in an image is a process that produces edges of image objects, the purpose of which is to mark the parts that become detailed images to improve the details of blurry images, which occur due to the effects of the image acquisition process. Edge is defined as a change in the intensity of a large distance. Based on changes in intensity, there are three types of edges in digital images, namely, step edges, ramps edge, and noisy edge. On step edges where the intensity or gray value changes very fast The Gradient Method is able to detect better. On the ramp edge where the gray value slowly changes the Laplace method is able to detect better than the Gradient Method. On a noisy edge, the existence of noise in the image can bring up the other edges around the actual edge and can also shift the actual edge position. In this study, the authors conducted edge detection in the image by means of determining the right edge detection method to detect edges in noisy images. Noise is obtained by generating a Gaussian Noise in the image. The results showed that, without filtering the image, in noisy edge, the LoG operator was able to detect edges and reduce noise better than Canny. However, by selecting the right threshold that matches the σ (standard deviation), Canny also capable to provide good edge detection results.

On Detection of Faint Edges in Noisy Images.

A fundamental question for edge detection in noisy images is how faint can an edge be and still be detected. In this paper we offer a formalism to study this question and subsequently introduce computationally efficient multiscale edge detection algorithms designed to detect faint edges in noisy images. In our formalism we view edge detection as a search in a discrete, though potentially large, set of feasible curves. First, we derive approximate expressions for the detection threshold as a function of curve length and the complexity of the search space. We then present two edge detection algorithms, one for straight edges, and the second for curved ones. Both algorithms efficiently search for edges in a large set of candidates by hierarchically constructing difference filters that match the curves traced by the sought edges. We demonstrate the utility of our algorithms in both simulations and applications involving challenging real images. Finally, based on these principles, we develop an algorithm for fiber detection and enhancement. We exemplify its utility to reveal and enhance nerve axons in light microscopy images.

Detecting Curved Edges in Noisy Images in Sublinear Time

Detecting edges in noisy images is a fundamental task in image processing. Motivated, in part, by various real-time applications that involve large and noisy images, in this paper we consider the problem of detecting long curved edges under extreme computational constraints, that allow processing of only a fraction of all image pixels. We present a sublinear algorithm for this task, which runs in two stages: (1) a multiscale scheme to detect curved edges inside a few image strips; and (2) a tracking procedure to estimate their extent beyond these strips. We theoretically analyze the runtime and detection performance of our algorithm and empirically illustrate its competitive results on both simulated and real images.

Detection of Long Edges on a Computational Budget: A Sublinear Approach

Edge detection is a challenging, important task in image analysis. Various applications require real-time detection of long edges in large and noisy images, possibly under limited computational resources. While standard edge detection methods are computationally fast, they perform well only at low levels of noise. Modern sophisticated methods, in contrast, are robust to noise, but may be too slow for real-time processing of large images. This raises the following question, which is the focus of our paper: How well can one detect long edges in noisy images under severe computational constraints that allow only a fraction of all image pixels to be processed? We make several theoretical and practical contributions regarding this problem. We develop possibly the first sublinear algorithm to detect long straight edges in noisy images. In addition, we theoretically analyze the inevitable tradeoff between its detection performance and the allowed computational budget. Finally, we demonstrate its competitive perf...

A novel particle swarm optimisation approach to detecting continuous, thin and smooth edges in noisy images

Detection of continuous edges is a hard problem and most edge detection algorithms produce jagged and thick edges particularly in noisy images. This paper firstly presents a novel constrained optimisation model for detecting continuous, thin and smooth edges in such images. Then two particle swarm optimisation-based algorithms are applied to search for good solutions. These two algorithms utilise two different constraint handling methods: penalising and preservation. The algorithms are examined and compared with a modified version of the Canny algorithm as a Gaussian filter-based edge detector and the robust rank order (RRO)-based algorithm as a statistical-based edge detector on two sets of images with different types and levels of noise. Pratt’s figure of merit as a measure of localisation accuracy is used for the comparison of these algorithms. Experimental results show that the proposed edge detectors are more robust under noisy conditions and their performances are better than the Canny and RRO algorithms for the images corrupted by impulsive and Gaussian noise. The proposed algorithm based on the penalising method is faster than the algorithm using the preservation method to handle the constraints.

Ambrosio-Tortorelli Segmentation of Stochastic Images: Model Extensions, Theoretical Investigations and Numerical Methods

We discuss an extension of the Ambrosio-Tortorelli approximation of the Mumford-Shah functional for the segmentation of images with uncertain gray values resulting from measurement errors and noise. Our approach yields a reliable precision estimate for the segmentation result, and it allows us to quantify the robustness of edges in noisy images and under gray value uncertainty. We develop an ansatz space for such images by identifying gray values with random variables. The use of these stochastic images in the minimization of energies of Ambrosio-Tortorelli type leads to stochastic partial differential equations for a stochastic smoothed version of the original image and a stochastic phase field for the edge set. For the discretization of these equations we utilize the generalized polynomial chaos expansion and the generalized spectral decomposition (GSD) method. In contrast to the simple classical sampling technique, this approach allows for an efficient determination of the stochastic properties of the output image and edge set by computations on an optimally small set of random variables. Also, we use an adaptive grid approach for the spatial dimensions to further improve the performance, and we extend an edge linking method for the classical Ambrosio-Tortorelli model for use with our stochastic model. The performance of the method is demonstrated on artificial data and a data set from a digital camera as well as real medical ultrasound data. A comparison of the intrusive GSD discretization with a stochastic collocation and a Monte Carlo sampling is shown.

Segmentation of Stochastic Images using Stochastic Extensions of the Ambrosio‐Tortorelli and the Random Walker Model

AbstractWe discuss methods based on stochastic PDEs for the segmentation of images with uncertain gray values resulting from measurement errors and noise. Our approach yields a reliable precision estimate for the segmentation result, and it allows us to quantify the robustness of edges in noisy images and under gray value uncertainty. The ansatz space for such images identifies gray values with random variables. For their discretization we utilize generalized polynomial chaos expansions and the generalized spectral decomposition method. This leads to the stochastic generalization of the Ambrosio‐Tortorelli approximation of the Mumford‐Shah functional. Moreover, we present the extension of the random walker segmentation for our stochastic images, which is based on an identification of the graph weights with random variables. We demonstrate the performance of the methods on a data set obtained from a digital camera as well as real medical ultrasound data. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

New method for edge detection and de noising via fuzzy cellular automata

In this article, a new method is presented for eliminating noise and for detecting image edges through the use of fuzzy cellular automata. The algorithm based on the proposed method is used for edge detection in Gray level images and for noise elimination in images containing salt and pepper noise. In this method, eight specific contiguity states are considered for each pixel and sixteen numbers are derived from these states. These numbers are used as input for the fuzzy member ship function. The fuzzy rule base is constructed in such a way as to correctly recognize the state of each pixel. The ability to detect edges in different directions and to determine suitable edges in noisy images are among the advantages of the proposed method. In comparison to common methods of edge detection, like the Sobel and the Robert methods of edge detection and the mean-filter and the median-filter methods of noise elimination, our proposed method shows a higher efficiency. Key words: Fuzzy cellular automata, image processing, noise elimination, edge detecting.

Image edge detection with the use of the Tikhonov regularization method

The study considers application of the Tikhonov regularization method for smoothing of 1D signals, noise suppression, and determination of objects’ edges in images. An analytic solution to the Euler equation is obtained in the 1D case for certain stabilizers. Application of the considered method for determination of objects’ edges in noisy images is analyzed.

THE CONSTRUCTION OF 2D ROTATIONALLY INVARIANT WAVELETS AND THEIR APPLICATION IN IMAGE EDGE DETECTION

Construction of rotationally invariant 2D wavelets is important in image processing, but is difficult. In this paper, the discrete form of a 2D rotationally invariant wavelet is constructed by back-projection from a 1D symmetrical wavelet. Such rotationally invariant 2D wavelets allow effective edge detection in any direction. These wavelets are combined with the 2D directional wavelets for the use in non-maximum suppression edge detection. The resulting binary edges are characterized by finer contours, differential detection characteristics and noise robustness compared to other edge detectors in various test images. In particular, where fine binary edges in noisy images are required, this novel approach compares favorably to the classical methods of Canny and Mallat with detection of more edges thanks to the implicit denoising properties and the full rotational invariance of the method.

Robust rank-order test for edge detection in noisy images

We describe a new edge detector based on the robust rank-order (RRO) test, which is a useful alternative to the Wilcoxon test, for detecting edges in noisy images. Our method is based on detecting local changes in gray level intensity between adjacent pixel neighborhoods using an edge-height model to extract exact edges from images corrupted with noises. Some experiments of statistical edge detectors based on the Wilcoxon test and T test, and the well-known Canny detector and Sobel detector with our RRO detector are carried out on synthetic and real images corrupted by both Gaussian and impulsive noises. The results show that the performance of the proposed edge detector appears to be the most robust to variations in noise, performing well in all noise distributions tested.

Simple consistent cluster methods based on redescending M-estimators with an application to edge identification in images

We use the local maxima of a redescending M-estimator to identify cluster, a method proposed already by Morgenthaler (in: H.D. Lawrence, S. Arthur (Eds.), Robust Regression, Dekker, New York, 1990, pp. 105–128) for finding regression clusters. We work out the method not only for classical regression but also for orthogonal regression and multivariate location and show that all three approaches are special cases of a general approach which includes also other cluster problems. For the general case we show consistency for an asymptotic objective function which generalizes the density in the multivariate case. The approach of orthogonal regression is applied to the identification of edges in noisy images.

Comparison of two-sample tests for edge detection in noisy images

We describe three statistical two-sample tests such as the Wilcoxon test, T-test and Kolmogorov-Smirnov test for detecting edges in noisy images. Each of the edge detectors is based on the computation of a test statistic obtained on the modified grey level values by using an edge height parameter which is compared with the threshold given in existing null distribution tables. Some experimental results for these edge detectors with a Sobel operator on sample images both with and without additive noise are given and the performances of these detectors are compared in terms of the quantitative measures.

Multiresolution gradient-based edge detection in noisy images using wavelet domain filters

We detected edges in noisy images using multiresolution analysis with the wavelet transform. products of wavelet coefficients at several scales were used to identify and locate edges. We found that it was important to consider the changes in edge position at different scales to detect edges in noisy imagery. We analyzed one-dimensional edges and compared the results of our approach with the first derivative of the signal. In addition, we compared the results of noisy images with another wavelet-based edge detection method. Our results led to improved edge detection in noisy images.

Dual stack filters and the modified difference of estimates approach to edge detection

The theory of optimal stack filtering has been used in the difference of estimates (DoE) approach to the detection of intensity edges in noisy images. The DoE approach is modified by imposing a symmetry condition on the data used to train the two stack filters. Under this condition, the stack filters obtained are duals of each other. Only one filter must therefore be trained; the other is simply its dual. This new technique is called the symmetric difference of estimates (SDoE) approach. The dual stack filters obtained under the SDoE approach are shown to be comparable. This allows the difference of these two filters to be represented by a single equivalent edge operator. This latter result suggests that an edge operator can be found by directly training a (possibly nonpositive) Boolean function to be used on each level of the threshold decomposition architecture. This approach, which is called the threshold Boolean filter (TBF) approach, requires less training time but produces operators that are less robust than those produced by the SDoE approach. This is demonstrated and interpreted via comparisons of results for natural images.

Edge detection using a neural network

Artificial neural networks have been shown to perform well in many image processing applications such as coding, pattern recognition and texture segmentation. In a typical multi-layer model of this class, neurons in each layer are linked by synaptic weights to a receptive field region in the layer below it. The input image itself is linked to the lowest layer. We propose here a two stage encoder-detector network for edge detection. The single layer encoder stage, trained in a competitive mode, compresses data from an input receptive field and drives a back-propagation-trained detector network whose two outputs represent components of an edge vector. Experimental results show that for the case of step edges in noisy images, the performance of the neural edge detector is comparable to that of the Canny detector.

The Nonlinear Prefiltering and Difference of Estimates Approaches to Edge Detection: Applications of Stack Filters

The theory of stack filtering, which is a generalization of median filtering, is used in two different approaches to the detection of intensity edges in noisy images. The first approach is a generalization of median prefiltering: a stack filter or another median-type filter is used to smooth an image before a standard gradient estimator is applied. These prefiltering schemes retain the robustness of the median prefilter, but allow resolution of finer detail. The second approach, called the Difference of Estimates (DoE) approach, is a new formulation of a morphological scheme [Lee et al., IEEE Trans. Robotics Automat. RA-3, Apr. 1987, 142-156, Maragos and Ziff, IEEE Trans. Pattern Anal. Mach. Intell. 12(5), May 1990.] which has proven to be very sensitive to impulsive noise. In this approach, stack filters are applied to a noisy image to obtain local estimates of the dilated and eroded versions of the noise-free image. Thresholding the difference between these two estimates yields the edge map. We find, for example, that this approach yields results comparable to those obtained with the Canny operator for images with additive Gaussian noise, but works much better when the noise is impulsive. In both approaches, the stack filters employed are trained to be optimal on images and noise that are "typical" examples of the target image. The robustness of stack filters leads to good performance for the target image, even when the statistics of the noise and/or image vary from those used in training. This is verified with extensive simulations.

The Nonlinear Prefiltering and Difference of Estimates Approaches to Edge Detection: Applications of Stack Filters

The theory of stack filtering, which is a generalization of median filtering, is used in two different approaches to the detection of intensity edges in noisy images. The first approach is a generalization of median prefiltering: a stack filter or another median-type filter is used to smooth an image before a standard gradient estimator is applied. These prefiltering schemes retain the robustness of the median prefilter, but allow resolution of finer detail. The second approach, called the Difference of Estimates (DoE) approach, is a new formulation of a morphological scheme [Lee et al., IEEE Trans. Robotics Automat. RA-3, Apr. 1987, 142-156, Maragos and Ziff, IEEE Trans. Pattern Anal. Mach. Intell. 12(5), May 1990.] which has proven to be very sensitive to impulsive noise. In this approach, stack filters are applied to a noisy image to obtain local estimates of the dilated and eroded versions of the noise-free image. Thresholding the difference between these two estimates yields the edge map. We find, for example, that this approach yields results comparable to those obtained with the Canny operator for images with additive Gaussian noise, but works much better when the noise is impulsive. In both approaches, the stack filters employed are trained to be optimal on images and noise that are "typical" examples of the target image. The robustness of stack filters leads to good performance for the target image, even when the statistics of the noise and/or image vary from those used in training. This is verified with extensive simulations.

Optimal frequency domain textural edge detection filter

An optimal frequency domain textural edge detection filter is developed and its performance evaluated. For the given model and filter bandwidth, the filter maximizes the amount of output image energy placed within a specified resolution interval centered on the textural edge. Filter derivation is based on relating textural edge detection to tonal edge detection via the complex low-pass equivalent representation of narrowband bandpass signals and systems. The filter is specified in terms of the prolate spheroidal wave functions translated in frequency. Performance is evaluated using the asymptotic approximation version of the filter. This evaluation demonstrates satisfactory filter performance for ideal and nonideal textures. In addition, the filter can be adjusted to detect textural edges in noisy images at the expense of edge resolution.