Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters

This work deals with noise removal by the use of an edge preserving method whose parameters are automatically estimated, for any application, by simply providing information about the standard deviation noise level we wish to eliminate. The desired noiseless image u(x), in a Partial Differential Equation based model, can be viewed as the solution of an evolutionary differential equation u t(x) = F(u xx, u x, u, x, t) which means that the true solution will be reached when t ® ¥. In practical applications we should stop the time ''t'' at some moment during this evolutionary process. This work presents a sufficient condition, related to time t and to the standard deviation s of the noise we desire to remove, which gives a constant T such that u(x, T) is a good approximation of u(x). The approach here focused on edge preservation during the noise elimination process as its main characteristic. The balance between edge points and interior points is carried out by a function g which depends on the initial noisy image u(x, t0), the standard deviation of the noise we want to eliminate and a constant k. The k parameter estimation is also presented in this work therefore making, the proposed model automatic. The model's feasibility and the choice of the optimal time scale is evident through out the various experimental results.

A well-balanced flow equation for noise removal and edge detection

In this paper, an anisotropic nonlinear diffusion equation for image restoration is presented. The model has two terms: the diffusion and the forcing term. The balance between these terms is made in a selective way, in which boundary points and interior points of the objects that make up the image are treated differently. The optimal smoothing time concept, which allows for finding the ideal stop time for the evolution of the partial differential equation is also proposed. Numerical results show the proposed model's high performance.

Edge detection in digital images using fuzzy numbers

The purpose of this paper is to introduce a new approach for edge detection in grey shaded images. The proposed approach is based on the fuzzy number theory. The idea is to deal with the uncertainties concerning the grey shades making up the image and, thus, calculate the appropriateness of the pixels in relation to a homogeneous region around them. The pixels not belonging to the region are then classified as border pixels. The results have shown that the technique is simple, computationally efficient and with good results when compared with both the traditional border detectors and the fuzzy edge detectors. Copyright © 2009, Inderscience Publishers.

BOLD correlates of edge detection in human auditory cortex

Edges are important cues defining coherent auditory objects. As a model of auditory edges, sound on- and offset are particularly suitable to study their neural underpinnings because they contrast a specific physical input against no physical input. Change from silence to sound, that is onset, has extensively been studied and elicits transient neural responses bilaterally in auditory cortex. However, neural activity associated with sound onset is not only related to edge detection but also to novel afferent inputs. Edges at the change from sound to silence, that is offset, are not confounded by novel physical input and thus allow to examine neural activity associated with sound edges per se. In the first experiment, we used silent acquisition functional magnetic resonance imaging and found that the offset of pulsed sound activates planum temporale, superior temporal sulcus and planum polare of the right hemisphere. In the planum temporale and the superior temporal sulcus, offset response amplitudes were related to the pulse repetition rate of the preceding stimulation. In the second experiment, we found that these offset-responsive regions were also activated by single sound pulses, onset of sound pulse sequences and single sound pulse omissions within sound pulse sequences. However, they were not active during sustained sound presentation. Thus, our data show that circumscribed areas in right temporal cortex are specifically involved in identifying auditory edges. This operation is crucial for translating acoustic signal time series into coherent auditory objects.

Edge Detection by Adaptive Splitting II. The Three-Dimensional Case

In Llanas and Lantarón, J. Sci. Comput. 46, 485–518 (2011) we proposed an algorithm (EDAS-d) to approximate the jump discontinuity set of functions defined on subsets of ℝ d . This procedure is based on adaptive splitting of the domain of the function guided by the value of an average integral. The above study was limited to the 1D and 2D versions of the algorithm. In this paper we address the three-dimensional problem. We prove an integral inequality (in the case d=3) which constitutes the basis of EDAS-3. We have performed detailed computational experiments demonstrating effective edge detection in 3D function models with different interface topologies. EDAS-1 and EDAS-2 appealing properties are extensible to the 3D case

Analysis of edge detection algorithms on DIAL /

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Mach edges: a critical test of the nonlinear 3rd derivative model for edge-detection

Feature detection is a crucial stage of visual processing. In previous feature-marking experiments we found that peaks in the 3rd derivative of the luminance profile can signify edges where there are no 1st derivative peaks nor 2nd derivative zero-crossings (Wallis and George 'Mach edges' (the edges of Mach bands) were nicely predicted by a new nonlinear model based on 3rd derivative filtering. As a critical test of the model, we now use a new class of stimuli, formed by adding a linear luminance ramp to the blurred triangle waves used previously. The ramp has no effect on the second or higher derivatives, but the nonlinear model predicts a shift from seeing two edges to seeing only one edge as the added ramp gradient increases. In experiment 1, subjects judged whether one or two edges were visible on each trial. In experiment 2, subjects used a cursor to mark perceived edges and bars. The position and polarity of the marked edges were close to model predictions. Both experiments produced the predicted shift from two to one Mach edge, but the shift was less complete than predicted. We conclude that the model is a useful predictor of edge perception, but needs some modification.

Application of Fuzzy Logic on Image Edge Detection

In this paper a novel method for an application of digital image processing, Edge Detection is developed. The contemporary Fuzzy logic, a key concept of artificial intelligence helps to implement the fuzzy relative pixel value algorithms and helps to find and highlight all the edges associated with an image by checking the relative pixel values and thus provides an algorithm to abridge the concepts of digital image processing and artificial intelligence. Exhaustive scanning of an image using the windowing technique takes place which is subjected to a set of fuzzy conditions for the comparison of pixel values with adjacent pixels to check the pixel magnitude gradient in the window. After the testing of fuzzy conditions the appropriate values are allocated to the pixels in the window under testing to provide an image highlighted with all the associated edges.

Mathematical-morphology-based edge detection of retinal vessels in retinal images

Of all the important small and medium-sized blood vessels of the human body, retinal blood vessels are the only deep capillary that can be directly observed by a non-traumatic method. Retinal vascular morphology, such as vessel diameter, shape and distribution, is influenced by systemic diseases (Martinez-Perez, Hughes, Thom and Parker 2007). We can use digital fundus photography and analysis of retinal vascular morphology to find the relationship between the changes in vascular morphology and diabetes for the diagnosis of diseases. We aim at developing a retinal image processing system, that can analyze retinal images and provide helpful information for diagnosis. © 2013 Springer-Verlag.

A subpixel edge detector applied to aortic dissection detection

[EN] The aortic dissection is a disease that can cause a deadly situation, even with a correct treatment. It consists in a rupture of a layer of the aortic artery wall, causing a blood flow inside this rupture, called dissection. The aim of this paper is to contribute to its diagnosis, detecting the dissection edges inside the aorta. A subpixel accuracy edge detector based on the hypothesis of partial volume effect is used, where the intensity of an edge pixel is the sum of the contribution of each color weighted by its relative area inside the pixel. The method uses a floating window centred on the edge pixel and computes the edge features. The accuracy of our method is evaluated on synthetic images of different hickness and noise levels, obtaining an edge detection with a maximal mean error lower than 16 percent of a pixel.

Breast cancer detection from thermal images using bispectral invariant features

Highly sensitive infrared (IR) cameras provide high-resolution diagnostic images of the temperature and vascular changes of breasts. These images can be processed to emphasize hot spots that exhibit early and subtle changes owing to pathology. The resulting images show clusters that appear random in shape and spatial distribution but carry class dependent information in shape and texture. Automated pattern recognition techniques are challenged because of changes in location, size and orientation of these clusters. Higher order spectral invariant features provide robustness to such transformations and are suited for texture and shape dependent information extraction from noisy images. In this work, the effectiveness of bispectral invariant features in diagnostic classification of breast thermal images into malignant, benign and normal classes is evaluated and a phase-only variant of these features is proposed. High resolution IR images of breasts, captured with measuring accuracy of ±0.4% (full scale) and temperature resolution of 0.1 °C black body, depicting malignant, benign and normal pathologies are used in this study. Breast images are registered using their lower boundaries, automatically extracted using landmark points whose locations are learned during training. Boundaries are extracted using Canny edge detection and elimination of inner edges. Breast images are then segmented using fuzzy c-means clustering and the hottest regions are selected for feature extraction. Bispectral invariant features are extracted from Radon projections of these images. An Adaboost classifier is used to select and fuse the best features during training and then classify unseen test images into malignant, benign and normal classes. A data set comprising 9 malignant, 12 benign and 11 normal cases is used for evaluation of performance. Malignant cases are detected with 95% accuracy. A variant of the features using the normalized bispectrum, which discards all magnitude information, is shown to perform better for classification between benign and normal cases, with 83% accuracy compared to 66% for the original.

Detection of edges from projections

In a number of applications of computerized tomography, the ultimate goal is to detect and characterize objects within a cross section. Detection of edges of different contrast regions yields the required information. The problem of detecting edges from projection data is addressed. It is shown that the class of linear edge detection operators used on images can be used for detection of edges directly from projection data. This not only reduces the computational burden but also avoids the difficulties of postprocessing a reconstructed image. This is accomplished by a convolution backprojection operation. For example, with the Marr-Hildreth edge detection operator, the filtering function that is to be used on the projection data is the Radon transform of the Laplacian of the 2-D Gaussian function which is combined with the reconstruction filter. Simulation results showing the efficacy of the proposed method and a comparison with edges detected from the reconstructed image are presented

BILATERAL EDGE DETECTORS

We propose to employ bilateral filters to solve the problem of edge detection. The proposed methodology presents an efficient and noise robust method for detecting edges. Classical bilateral filters smooth images without distorting edges. In this paper, we modify the bilateral filter to perform edge detection, which is the opposite of bilateral smoothing. The Gaussian domain kernel of the bilateral filter is replaced with an edge detection mask, and Gaussian range kernel is replaced with an inverted Gaussian kernel. The modified range kernel serves to emphasize dissimilar regions. The resulting approach effectively adapts the detection mask according as the pixel intensity differences. The results of the proposed algorithm are compared with those of standard edge detection masks. Comparisons of the bilateral edge detector with Canny edge detection algorithm, both after non-maximal suppression, are also provided. The results of our technique are observed to be better and noise-robust than those offered by methods employing masks alone, and are also comparable to the results from Canny edge detector, outperforming it in certain cases.

Automated Detection of Concrete Columns from Visual Data

After earthquakes, licensed inspectors use the established codes to assess the impact of damage on structural elements. It always takes them days to weeks. However, emergency responders (e.g. firefighters) must act within hours of a disaster event to enter damaged structures to save lives, and therefore cannot wait till an official assessment completes. This is a risk that firefighters have to take. Although Search and Rescue Organizations offer training seminars to familiarize firefighters with structural damage assessment, its effectiveness is hard to guarantee when firefighters perform life rescue and damage assessment operations together. Also, the training is not available to every firefighter. The authors therefore proposed a novel framework that can provide firefighters with a quick but crude assessment of damaged buildings through evaluating the visible damage on their critical structural elements (i.e. concrete columns in the study). This paper presents the first step of the framework. It aims to automate the detection of concrete columns from visual data. To achieve this, the typical shape of columns (long vertical lines) is recognized using edge detection and the Hough transform. The bounding rectangle for each pair of long vertical lines is then formed. When the resulting rectangle resembles a column and the material contained in the region of two long vertical lines is recognized as concrete, the region is marked as a concrete column surface. Real video/image data are used to test the method. The preliminary results indicate that concrete columns can be detected when they are not distant and have at least one surface visible.