Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing

Hybrid mamdani fuzzy rules and convolutional neural networks for analysis and identification of animal images

Accurate, fast, and automatic detection and classification of animal images is challenging, but it is much needed for many real-life applications. This paper presents a hybrid model of Mamdani Type-2 fuzzy rules and convolutional neural networks (CNNs) applied to identify and distinguish various animals using different datasets consisting of about 27,307 images. The proposed system utilizes fuzzy rules to detect the image and then apply the CNN model for the object’s predicate category. The CNN model was trained and tested based on more than 21,846 pictures of animals. The experiments’ results of the proposed method offered high speed and efficiency, which could be a prominent aspect in designing image-processing systems based on Type 2 fuzzy rules characterization for identifying fixed and moving images. The proposed fuzzy method obtained an accuracy rate for identifying and recognizing moving objects of 98% and a mean square error of 0.1183464 less than other studies. It also achieved a very high rate of correctly predicting malicious objects equal to recall = 0.98121 and a precision rate of 1. The test’s accuracy was evaluated using the F1 Score, which obtained a high percentage of 0.99052

An Optical Machine Vision System for Applications in Cytopathology

This paper discusses a new approach to the processes of object detection, recognition and classification in a digital image focusing on problem in Cytopathology. A unique self learning procedure is presented in order to incorporate expert knowledge. The classification method is based on the application of a set of features which includes fractal parameters such as the Lacunarity and Fourier dimension. Thus, the approach includes the characterisation of an object in terms of its fractal properties and texture characteristics. The principal issues associated with object recognition are presented which include the basic model and segmentation algorithms. The self-learning procedure for designing a decision making engine using fuzzy logic and membership function theory is also presented and a novel technique for the creation and extraction of information from a membership function considered. The methods discussed and the algorithms developed have a range of applications and in this work, we focus the engineering of a system for automating a Papanicolaou screening test

Fuzzy-based Propagation of Prior Knowledge to Improve Large-Scale Image Analysis Pipelines

Many automatically analyzable scientific questions are well-posed and offer a variety of information about the expected outcome a priori. Although often being neglected, this prior knowledge can be systematically exploited to make automated analysis operations sensitive to a desired phenomenon or to evaluate extracted content with respect to this prior knowledge. For instance, the performance of processing operators can be greatly enhanced by a more focused detection strategy and the direct information about the ambiguity inherent in the extracted data. We present a new concept for the estimation and propagation of uncertainty involved in image analysis operators. This allows using simple processing operators that are suitable for analyzing large-scale 3D+t microscopy images without compromising the result quality. On the foundation of fuzzy set theory, we transform available prior knowledge into a mathematical representation and extensively use it enhance the result quality of various processing operators. All presented concepts are illustrated on a typical bioimage analysis pipeline comprised of seed point detection, segmentation, multiview fusion and tracking. Furthermore, the functionality of the proposed approach is validated on a comprehensive simulated 3D+t benchmark data set that mimics embryonic development and on large-scale light-sheet microscopy data of a zebrafish embryo. The general concept introduced in this contribution represents a new approach to efficiently exploit prior knowledge to improve the result quality of image analysis pipelines. Especially, the automated analysis of terabyte-scale microscopy data will benefit from sophisticated and efficient algorithms that enable a quantitative and fast readout. The generality of the concept, however, makes it also applicable to practically any other field with processing strategies that are arranged as linear pipelines.Comment: 39 pages, 12 figure