A robust hit-or-miss transform for template matching applied to very noisy astronomical images

The morphological hit-or-miss transform (HMT) is a powerful tool for digital image analysis. Its recent extensions to grey level images have proven its ability to solve various template matching problems. In this paper we explore the capacity of various existing approaches to work in very noisy environments and discuss the generic methods used to improve their robustness to noise. We also propose a new formulation for a fuzzy morphological HMT which has been especially designed to deal with very noisy images. Our approach is validated through a pattern matching problem in astronomical images that consists of detecting very faint objects: low surface brightness galaxies. Despite their influence on the galactic evolution model, these objects remain mostly misunderstood by the astronomers. Due to their low signal to noise ratio, there is no automatic and reliable detection method yet. In this paper we introduce such a method based on the proposed hit-or-miss operator. The complete process is described starting from the building of a set of patterns until the reconstruction of a suitable map of detected objects. Implementation, running cost and optimisations are discussed. Outcomes have been examined by astronomers and compared to previous works. We have observed promising results in this difficult context for which mathematical morphology provides an original solution.     

基于形态学的快速拐点检测统一模型

拐点检测一直是计算机的视觉和图像处理中的关键问题，传统方法是通过计算曲率来实现拐点的检测，其要求准确定位拐点所在局部区域的位置，并易受到噪声干扰，为此提出了一种的新的基于形态骨架的快速拐眯检测方法，该方法基于物体条件骨架原理，采用改进的非对称开运算算子，并利用内外骨架分别实现对物体凸点和凹点的检测，以保证对拐点检测的完整性；对于有噪声图象，则采用多刻度形态滤波进行去噪预处理；对拐点给出了统一的检测和实现模型。实验结果表明，该统一算法检测准确度高、具有旋转不变性、计算量小、硬件实现简单，对有噪声干扰图象也能很好地进行检验。     

A probabilistic hit-and-miss transform for face localization

Face localization is needed for any face processing procedure whose applications range from biometric identification to content-based image retrieval. It consists in giving the image coordinates of the face. In this paper we propose a probabilistic pattern matching procedure for face localization in greyscale images similar to the morphological hit-and-miss-transform (HMT), which we call probabilistic HMT (PHMT). This procedure is defined on the morphological multiscale fingerprints (MMF), which are image features extracted from the morphological erosion/dilation scale spaces. The face location is estimated as the maximum likelihood image window matching both erosive and dilative MMF models of the object. The MMF models are computed at a discrete set of scales. The MMF models may be built up from a small set of training face images and do not involve numerically sophisticated training algorithms. Training does not use non-face sample images. Therefore resampling is not needed for the construction of the MMF models. The experimental results on the NIST Mugshot Identification Database endorse our claims about the accuracy and robustness of the proposed procedure.     

Virtual double-sided image probing: A unifying framework for non-linear grayscale pattern matching

This paper focuses on non-linear pattern matching transforms based on mathematical morphology for gray level image processing. Our contribution is on two fronts. First, we unify the existing and a priori unconnected approaches to this problem by establishing their theoretical links with topology. Setting them within the same context allows to highlight their differences and similarities, and to derive new variants. Second, we develop the concept of virtual double-sided image probing (VDIP), a broad framework for non-linear pattern matching in grayscale images. VDIP extends our work on the multiple object matching using probing (MOMP) transform we previously defined to locate multiple grayscale patterns simultaneously. We show that available methods as well as the topological approach can be generalized within the VDIP framework. They can be formulated as particular variants of a general transform designed for virtual probing. Furthermore, a morphological metric, called SVDIP (single VDIP), is deduced from the VDIP concept. Some results are presented and compared with those obtained with classical methods.     

Indistinguishability operators in measurement theory,Part I: Conversions of indistinguishability operators with respect to scales

For two given ordinal scales in a measurement process, the present paper investigates how an indistinguishability operator evaluated according to one of these ordinal scales can be converted to another indistinguishability operator w.r.t. the other ordinal scale, and establishes the mathematical base of these conversions under the framework of measurement theory [Krantz, D.H., Luce, R.D., Suppes, P., Tversky, A. (1971) Foundations of Measurement, Vol. 1 (Academic Press, San Diego)]. Additionally, this work exposes the rudimentary facts behind the studies in [“Fuzzy Numbers and Equality Relations”, Proc. FUZZ'IEEE 93 (1993) 1298–1301; “Fuzzy Sets and Vague Environments”, Fuzzy Sets and Systems 66 (1994) 207–221; “Fuzzy Control on the Basis of Equality Relations-with an Example from Idle Speed Control”, IEEE Transactions on Fuzzy Systems 3 (1995) 336–350; and “T-partitions of the Real Line Generated by Idempotent Shapes”, Fuzzy Sets and Systems 91 (1997) 177–184], and points out the measurement theoretic derivations of the results in these studies.     

Mathematical Morphology Based on Linear Combined Metric Spaces on Z2 (Part I): Fast Distance Transforms

Mathematical Morphology (MM) is a general method for image processing based on set theory. The two basic morphological operators are dilation and erosion. From these, several non linear filters have been developed usually with polynomial complexity, and this because the two basic operators depend strongly on the definition of the structural element. Most efforts to improve the algorithm's speed for each operator are based on structural element decomposition and/or efficient codification.A new framework and a theoretical basis toward the construction of fast morphological operators (of zero complexity) for an infinite (countable) family of regular metric spaces are presented in work. The framework is completely defined by the three axioms of metric. The theoretical basis here developed points out properties of some metric spaces and relationships between metric spaces in the same family, just in terms of the properties of the four basic metrics stated in this work. Concepts such as bounds, neighborhoods and contours are also related by the same framework.The presented results, are general in the sense that they cover the most commonly used metrics such as the chamfer, the city block and the chess board metrics. Generalizations and new results related with distances and distance transforms, which in turn are used to develop the morphologic operations in constant time, in contrast with the polynomial time algorithms are also given.     

Morphological perceptrons with competitive learning: Lattice-theoretical framework and constructive learning algorithm

A morphological neural network is generally defined as a type of artificial neural network that performs an elementary operation of mathematical morphology at every node, possibly followed by the application of an activation function. The underlying framework of mathematical morphology can be found in lattice theory.With the advent of granular computing, lattice-based neurocomputing models such as morphological neural networks and fuzzy lattice neurocomputing models are becoming increasingly important since many information granules such as fuzzy sets and their extensions, intervals, and rough sets are lattice ordered. In this paper, we present the lattice-theoretical background and the learning algorithms for morphological perceptrons with competitive learning which arise by incorporating a winner-take-all output layer into the original morphological perceptron model. Several well-known classification problems that are available on the internet are used to compare our new model with a range of classifiers such as conventional multi-layer perceptrons, fuzzy lattice neurocomputing models, k-nearest neighbors, and decision trees.     

Liver segmentation in MRI: A fully automatic method based on stochastic partitions

There are few fully automated methods for liver segmentation in magnetic resonance images (MRI) despite the benefits of this type of acquisition in comparison to other radiology techniques such as computed tomography (CT). Motivated by medical requirements, liver segmentation in MRI has been carried out. For this purpose, we present a new method for liver segmentation based on the watershed transform and stochastic partitions. The classical watershed over-segmentation is reduced using a marker-controlled algorithm. To improve accuracy of selected contours, the gradient of the original image is successfully enhanced by applying a new variant of stochastic watershed. Moreover, a final classifier is performed in order to obtain the final liver mask. Optimal parameters of the method are tuned using a training dataset and then they are applied to the rest of studies (17 datasets). The obtained results (a Jaccard coefficient of 0.91 ± 0.02) in comparison to other methods demonstrate that the new variant of stochastic watershed is a robust tool for automatic segmentation of the liver in MRI.     

Box-Jenkins identification revisited—Part I: Theory

In classical time domain Box-Jenkins identification discrete-time plant and noise models are estimated using sampled input/output signals. The frequency content of the input/output samples covers uniformly the whole unit circle in a natural way, even in case of prefiltering. Recently, the classical time domain Box-Jenkins framework has been extended to frequency domain data captured in open loop. The proposed frequency domain maximum likelihood (ML) solution can handle (i) discrete-time models using data that only covers a part of the unit circle, and (ii) continuous-time models. Part I of this series of two papers (i) generalizes the frequency domain ML solution to the closed loop case, and (ii) proves the properties of the ML estimator under non-standard conditions. Contrary to the classical time domain case it is shown that the controller should be either known or estimated. The proposed ML estimators are applicable to frequency domain data as well as time domain data.     

Indistinguishability operators in measurement theory,Part II: Construction of indistinguishability operators based on probability distributions

As a continuation of the work initiated by Demirci, the main subject of this paper is the problem of constructing indistinguishability operators in terms of probability distribution functions and the probability density functions, addressed in Demirci [“Indistinguishability operators in measurement theory, Part I: Conversions of indistinguishability operators with respect to scales”, Int. J. General Systems (2003f) To appear]. In detail, two different approaches have been developed for the solution of this construction problem.     

An annotated bibliography of GRASP – Part I: Algorithms

A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. It is a multi-start or iterative process, in which each GRASP iteration consists of two phases, a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Since 1989, numerous papers on the basic aspects of GRASP, as well as enhancements to the basic metaheuristic have appeared in the literature. GRASP has been applied to a wide range of combinatorial optimization problems, ranging from scheduling and routing to drawing and turbine balancing. This is the first of two papers with an annotated bibliography of the GRASP literature from 1989 to 2008. This paper covers algorithmic aspects of GRASP.     

Mathematical Morphology Based on Linear Combined Metric Spaces on Z2 (Part II): Constant Time Morphological Operations

Mathematical Morphology (MM) is a general method for image processing based on set theory. The two basic morphological operators are dilation and erosion. From these, several non linear filters have been developed, usually with polynomial complexity and this because the two basic operators depend strongly on the definition of the structural element. Most efforts to improve the algorithm's speed for each operator are based on structural element decomposition and/or efficient codification.In this second part, the concepts developed in part I (see Díaz de León and Sossa Azuela, Mathematical morphology based on linear combined metric spaces on Z¹ (part I): Fast distance transforms, Journal of Mathematical Imaging and Vision, Vol. 12, No. 2, pp. 137–154, 2000) are used to prove that it is possible to reduce the complexity of the morphological operators to zero complexity (constant time algorithms) for any regular discrete metric space and to eliminate the use of the structural element. In particular, this is done for an infinite family of metric spaces further defined. The use of the distance transformation is proposed for it comprises the information concerning all the discs included in a region to obtain fast morphological operators: erosions, dilations, openings and closings (of zero complexity) for an infinite (countable) family of regular metric spaces. New constant time, in contrast with the polynomial time algorithms, for the computation of these basics operators for any structural element are next derived by using this background. Practical examples showing the efficiency of the proposed algorithms, final comments and present research are also given here.     

Logic, probability theory, and artificial intelligence - Part I: the probabilistic foundations of logic

Many AI researchers have come to be dissatisfied with approaches to their discipline based on formal logic. Various alternatives are often suggested, including probability theory. This paper investigates the intimate connection between probability theory and various logics. We show that probability theory, broadly conceived, may be used as a formal semantics for virtually any monotonic logic. Thus, rather than being seen as competing, it is more appropriate to view formal logics as very special cases of probability theory, usually special cases that are computationally more tractable than the more general theory. Thus, probability theory and logic should be seen as complementary. Viewing probability theory in this abstract way may help to shed light on various recalcitrant problems in AI. De nombreux chercheurs dans le domaine de l'intelligence artificielle manifestent une certaine insatisfaction vis-à-vis certaines approches basées sur la logique formelle. Diverses solutions sont souvent proposées, y compris la théorie des probabilityés. Cet article analyse la relation intime entre la théorie des probabilités et diverses logiques. Il est démontré que la théorie des probabilityés, conçue de manière générale, peut ětre utilisée comme une sémantique formelle pour presque toute logique monotonique. Au lieu de percevoir les logiques formelles comme étant en opposition, il est plus approprié de les considérer comme des cas trés spéciaux de la théorie des probabilityés, habituellement plus traitables au niveau calcul que la théorie plus générate. Par conséquent, la théorie des probabilityés et la logique doivent ětre percues comme des éléments complémentaires. Le fait de considérer la théorie des probabilityés d'une manière abstraite peut contribuer à la compréhension de divers problèmes ardus dans le domaine de l'intelligence artificielle.     

The AB‐C Doherty power amplifier. Part I: Theory

In this article, the complete theoretical analysis of a Doherty amplifier employing a Class AB bias condition for the Main and a Class C one for the Auxiliary devices, respectively, is presented. Starting from the simplified model of an active device, the analysis of the AB‐C Doherty behavior is carried out as a function of the input signal. In particular, the proposed approach is based on the analysis of the output drain current waveforms generated by the two active devices, while assuming a Tuned Load configuration (i.e., short circuit condition) for higher harmonic terminations. A closed form formulation is derived in order to directly design an AB‐C Doherty amplifier, while fully understanding the basis of its physical behavior. Finally, which Doherty parameters can be chosen by the designer or have to be implicitly fixed are discussed and clarified. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.     

An alternative structure for next generation regulatory controllers: Part I: Basic theory for design, development and implementation

Even though employed widely in industrial practice, the popular PID controller has weaknesses that limit its achievable performance, and an intrinsic structure that makes tuning not only more complex than necessary, but also less transparent with respect to the key attributes of the overall controller performance, namely: robustness, set-point tracking, and disturbance rejection. In this paper, we propose an alternative control scheme that combines the simplicity of the PID controller with the versatility of model predictive control (MPC) while avoiding the tuning problems associated with both. The tuning parameters of the proposed control scheme are related directly to the controller performance attributes; they are normalized to lie between 0 and 1; and they arise naturally from the formulation in a manner that makes it possible to tune the controller directly for each performance attribute independently. The result is a controller that can be designed and implemented much more directly and transparently, and one that outperforms the classical PID controller both in set-point tracking and disturbance rejection while using precisely the same process reaction curve information required to tune PID controllers. The design, implementation and performance of the controller are demonstrated via simulation on a nonlinear polymerization process.     

Feedback stabilization of bifurcations in multivariable nonlinear systems—Part I: equilibrium bifurcations

Under certain non‐degeneracy conditions, necessary and sufficient conditions for stabilizability are obtained for multi‐input nonlinear systems possessing a simple equilibrium bifurcation with the critical mode being linearly uncontrollable. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the bifurcation of the closed‐loop system is a supercritical pitchfork bifurcation, which is equivalent to local asymptotic stability of the system at the bifurcation point. Stabilizability is reduced to the existence of solutions to a third order algebraic inequality, coupled with a quadratic algebraic equation, with the unknowns being the feedback gains. Explicit conditions for the existence of solutions to the algebraic equation and the inequality are derived. Part of the sufficient conditions are equivalent to the rank conditions of augmented matrices. Conditions under which there exists a stabilizing linear feedback law are also derived. The theoretical results are applied to active control of rotating stall in axial compressors using bleed valve as actuator. Copyright © 2006 John Wiley & Sons, Ltd.     

Passive and Conservative Continuous-Time Impedance and Scattering Systems. Part I: Well-Posed Systems

 Let U be a Hilbert space. By an ℒ (U)-valued positive analytic function on the open right half-plane we mean an analytic function which satisfies the condition . This function need not be proper, i.e., it need not be bounded on any right half-plane. We study the question under what conditions such a function can be realized as the transfer function of an impedance passive system. By this we mean a continuous-time state space system whose control and observation operators are not more unbounded than the (main) semigroup generator of the system, and, in addition, there is a certain energy inequality relating the absorbed energy and the internal energy. The system is (impedance) energy preserving if this energy inequality is an equality, and it is conservative if both the system and its dual are energy preserving. A typical example of an impedance conservative system is a system of hyperbolic type with collocated sensors and actuators. We give several equivalent sets of conditions which characterize when a system is impedance passive, energy preserving, or conservative. We prove that a impedance passive system is well-posed if and only if it is proper. We furthermore show that the so-called diagonal transform (which may be regarded as a slightly modified feedback transform) maps a proper impedance passive (or energy preserving or conservative) system into a (well-posed) scattering passive (or energy preserving or conservative) system. This implies that, just as in the finite-dimensional case, if we apply negative output feedback to a proper impedance passive system, then the resulting system is (energy) stable. Finally, we show that every proper positive analytic function on the right half-plane has a (essentially unique) well-posed impedance conservative realization, and it also has a minimal impedance passive realization. Date received: October 22, 2001. Date revised: May 13, 2002.