The output distribution of important LULU-operators

Two procedures to compute the output distribution phi_S of certain stack filters S (so called erosion-dilation cascades) are given. One rests on the disjunctive normal form of S and also yields the rank selection probabilities. The other is based on inclusion-exclusion and e.g. yields phi_S for some important LULU-operators S. Properties of phi_S can be used to characterize smoothing properties of S. One of the methods discussed also allows for the calculation of the reliability polynomial of any positive Boolean function (e.g. one derived from a connected graph).Comment: 20 pages, up to trivial differences this is the final version to be published in Quaestiones Mathematicae 201

Calculating the output distribution of stack filters that are erosion-dilation cascades, in particular LULU-filters

Original article available at http://arxiv.org/ENGLISH ABSTRACT: Two procedures to compute the output distribution 0S of certain stack filters S (so called erosion-dilation cascades) are given. One rests on the disjunctive normal form of S and also yields the rank selection probabilities. The other is based on inclusion-exclusion and e.g. yields 0S for some important LULU-operators S. Properties of 0S can be used to characterize smoothing properties.Preprin

Trajectory-Based Morphological Operators: A Model for Efficient Image Processing

Mathematical morphology has been an area of intensive research over the last few years. Although many remarkable advances have been achieved throughout these years, there is still a great interest in accelerating morphological operations in order for them to be implemented in real-time systems. In this work, we present a new model for computing mathematical morphology operations, the so-called morphological trajectory model (MTM), in which a morphological filter will be divided into a sequence of basic operations. Then, a trajectory-based morphological operation (such as dilation, and erosion) is defined as the set of points resulting from the ordered application of the instant basic operations. The MTM approach allows working with different structuring elements, such as disks, and from the experiments, it can be extracted that our method is independent of the structuring element size and can be easily applied to industrial systems and high-resolution images

Computing the output distribution and selection probabilities of a stack filter from the DNF of its positive Boolean function

Many nonlinear filters used in practise are stack filters. An algorithm is presented which calculates the output distribution of an arbitrary stack filter S from the disjunctive normal form (DNF) of its underlying positive Boolean function. The so called selection probabilities can be computed along the way.Comment: This is the version published in Journal of Mathematical Imaging and Vision, online first, 1 august 201

Morphological erosions and openings: fast algorithms based on anchors

Several efficient algorithms for computing erosions and openings have been proposed recently. They improve on VAN HERK's algorithm in terms of number of comparisons for large structuring elements. In this paper we introduce a theoretical framework of anchors that aims at a better understanding of the process involved in the computation of erosions and openings. It is shown that the knowledge of opening anchors of a signal f is sufficient to perform both the erosion and the opening of f. Then we propose an algorithm for one-dimensional erosions and openings which exploits opening anchors. This algorithm improves on the fastest algorithms available in literature by approximately 30% in terms of computation speed, for a range of structuring element sizes and image content

Calculating the output distribution of stack filters that are erosion-dilation cascades, in particular Lulu-filters

Two procedures to compute the output distribution ϕS of certain stack lters S (so called erosion-dilation cascades) are given. One rests on the disjunctive normal form of S and also yields the rank selection probabilities. The other is based on inclusion-exclusion and e.g. yields ϕS for some important LULU-operators S. Properties of ϕS can be used to characterize smoothing properties of S. Also, in the same way as our polynomials ϕS are computed one could compute the reliability polynomial of a connected graph, or more generally the reliability polynomial w.r.t. any positive Boolean function.http://www.tandfonline.com/loi/tqma202016-12-31hb201

Medical Image Segmentation Using Multifractal Analysis

Image segmentation plays a key role in image analysis processes. The operations performed on a segmented image tend to affect it differently than if they were performed on the original image; therefore, segmenting an image can show radically different results from the original image and successfully doing so can yield features and other important information about the image. Proper image analysis is of high importance to the medical community as accurately classifying different conditions and diseases can be facilitated with excellent patient imaging. Multifractal analysis can be leveraged for performing texture classification and image segmentation. In this paper, we propose fusion-based algorithms utilizing multifractal analysis for medical image segmentation. We use two specific multifractal masks: square and quincunx. Our techniques show new insights by using methods such as histogram decomposition in conjunction with new techniques, such as fusion. By fusing different slope images, we can extract more features thus making our proposed algorithms more robust and accurate than traditional multifractal analysis techniques. These methods are further capable of reliably segmenting medical images by implementing multifractal analysis techniques in coordination with methods such as gaussian blurring and morphological operations. The resulting image can then be easily analyzed by medical professionals for diagnosing medical conditions. The outcomes show that the proposed algorithms extract dominant features that are more encompassing and powerful than classical techniques

Designing a face detection CAPTCHA

Completely Automated Tests for Telling Computers and Humans Apart (CAPTCHAs) are quickly becoming a standard for security in every online interface that could be the subject to spam or other exploitation. The majority of today\u27s CAPTCHA technologies rely on text-based images, which present the user with a string of distorted characters and asks the user to type out the characters. The problem with CAPTCHAs is that they are often difficult to solve and can generally be successfully defeated using techniques such as segmentation and optical character recognition. We introduce an image face recognition based CAPTCHA which presents the user with a series of distorted images and the question of deciding which of these images contain a human face. The user is required to click on all presented face images in order to successfully pass the CAPTCHA. The concept relies on the strength of the human ability to detect a face even amongst heavy distortion as well as the inaccuracies and short-comings of face recognition software. The CAPTCHA application was designed with a web interface and deployed on West Virginia University\u27s Computer Science 101 attendance website. To test the success of the CAPTCHA, data for human success rates was compared alongside facial recognition software which attempted to solve the CAPTCHA. The results of the data gathered during testing not only prove the feasibility of face recognition based CAPTCHAs in general, but also provide valuable data regarding human versus computer recognition rates under varying types of image distortion