Gray-scale Mathematical Morphology Research Articles

Generalized morphological components based on interval descriptors and n-ary aggregation functions

Morphological perceptrons (MPs) can be characterized as feedforward morphological neural networks (MNNs) with applications in classification and regression. The neuronal aggregation functions of current MP versions are drawn from gray-scale mathematical morphology (MM) that can be described in terms of matrix products in a lattice algebra called minimax algebra. Specifically, MPs have components each of which computes a pair-wise infimum of an erosion and an anti-dilation that can be expressed in terms of products of matrices with entries in a complete l-group extension.In this paper, we use the novel concept of an interval descriptor and an n-ary aggregation function on a bounded poset in order to generalize existing gray-scale and fuzzy morphological components (MCs) of morphological and hybrid morphological/linear perceptrons (HMLPs). In addition, we present several other examples of generalized morphological components (GMCs) that can and will be incorporated as computational units into shallow and deep artificial neural networks.

Automatic Reference Color Selection for Adaptive Mathematical Morphology and Application in Image Segmentation.

This paper proposes a novel automatic reference color selection (ARCS) scheme for the adaptive mathematical morphology (MM) method, and is specifically designed for color image segmentation applications. Because of the main advantages of being intuitive and simple, in the past decade, it has contributed to the growing popularity of binary and gray-scale MM processing. However, the MM process typically neglects the details of reference color determination. Applying other ordering methods, which select only black as the reference color for sorting pixels, result in the problem in which the scope of the distance measurement is not optimal. The proposed ARCS scheme is used for determining the ideal reference color for MM and for color image segmentation application. In addition, we use both 1D histogram-based modeling scheme binning from 3D color spaces, such as red-green-blue and hue-saturation-intensity, and 2D color models, such as (H, S), (Cb, Cr), and (I, By). According to the results of the quartile analysis, the threshold determination reacts with less sensitivity to the context variations of the images tested. The experiments focused on color-based image segmentation using the proposed ARCS scheme for color MM processing through a bottom-up scenario. To evaluate the system, four quantitative indices were utilized for an ARCS comparison using advanced segmentation methods in the experiments. The cross validation with different system parameters and a comparison of the morphological gradient operation with different color models are also presented.

Study on inspection method of glass defect based on phase image processing

To solve the problem in projecting grating method, the paper presents an inspection method based on phase image processing for glass defects. In the proposed method, the wrapped phase difference is achieved according to the images of defect-free and defect-containing. The unwrapping phase algorithm, based on jump corrected is used to eliminate jump error. The segmentation of defect region is implemented by integrating grayscale mathematical morphology with high-low threshold segmentation, and the boundary coordinate of connected region is used to calculate the size and location of defect. The results demonstrate that the proposed method provides reliable identification of defects.

RATS: Rapid Automatic Tissue Segmentation in rodent brain MRI

BackgroundHigh-field MRI is a popular technique for the study of rodent brains. These datasets, while similar to human brain MRI in many aspects, present unique image processing challenges. We address a very common preprocessing step, skull-stripping, which refers to the segmentation of the brain tissue from the image for further processing. While several methods exist for addressing this problem, they are computationally expensive and often require interactive post-processing by an expert to clean up poorly segmented areas. This further increases total processing time per subject. New methodWe propose a novel algorithm, based on grayscale mathematical morphology and LOGISMOS-based graph segmentation, which is rapid, robust and highly accurate. ResultsComparative results obtained on two challenging in vivo datasets, consisting of 22 T1-weighted rat brain images and 10 T2-weighted mouse brain images illustrate the robustness and excellent performance of the proposed algorithm, in a fraction of the computational time needed by existing algorithms. Comparison with existing methodsIn comparison to current state-of-the-art methods, our approach achieved average Dice similarity coefficient of 0.92±0.02 and average Hausdorff distance of 13.6±5.2 voxels (vs. 0.85±0.20, p<0.05 and 42.6±22.9, p≪0.001) for the rat dataset, and 0.96±0.01 and average Hausdorff distance of 21.6±12.7 voxels (vs. 0.93±0.01, p≪0.001 and 33.7±3.5, p≪0.001) for the mouse dataset. The proposed algorithm took approximately 90s per subject, compared to 10–20min for the neural-network based method and 30–90min for the atlas-based method. ConclusionsRATS is a robust and computationally efficient method for accurate rodent brain skull-stripping even in challenging data.

Observation of wheat flour doughs under mechanical treatment using confocal microscopy and classification of their microstructures

RheOptiCAD® is a cell allowing observation of microstructures under thermo-mechanical treatments. Using the device fitted on a confocal microscope, wheat flour doughs containing 3 levels of water were studied. Dough were placed between 2 parallel plates and submitted to motion of the bottom one. Temperature was controlled and fixed at 20 °C. Methodology and experimental parameters, but also balance between optical and mechanical ones are described and justified to set a dynamic observation in real time. Rhodamine B labeled gluten network was observed under dynamic mechanical treatment, i.e. a 0.4 mm-0.3 Hz oscillation applied during 30 s. The evolution of the gluten network microstructure along time of deformation and depending on the recipe was studied. Image sequences are presented to visualize the qualitative differences in the network. Differences in microstructures were observed. A grey scale mathematical morphology is proposed to qualify and quantify these differences. Images can be separated according to the level of orientation of the network and to the local protein concentration in the gluten fibers.

Nondestructive Testing of Blockboard Using Combination of Wavelet Transform and Gray-Scale Mathematical Morphology

This paper presents a scheme for blockboard nondestructive detection. X-ray nondestructive testing system has been used to obtain blockboard x-ray images. In order to recognize defects of blockboard effectively through x-ray images, an image processing method based on wavelet transform and gray-scale mathematical morphology is proposed. Firstly, image noises are reduced by wavelet soft threshold de-noising, and then a new modified mathematical morphology edge detection operator is used to detect edges of the de-noised image. The experiment results show that the method performs well in noise-suppression and edge detection. The proposed nondestructive testing method of blockboard is practical and easy to implement.

On the Decomposition of Interval-Valued Fuzzy Morphological Operators

Interval-valued fuzzy mathematical morphology is an extension of classical fuzzy mathematical morphology, which is in turn one of the extensions of binary morphology to greyscale morphology. The uncertainty that may exist concerning the grey value of a pixel due to technical limitations or bad recording circumstances, is taken into account by mapping the pixels in the image domain onto an interval to which the pixel's grey value is expected to belong instead of one specific value. Such image representation corresponds to the representation of an interval-valued fuzzy set and thus techniques from interval-valued fuzzy set theory can be applied to extend greyscale mathematical morphology. In this paper, we study the decomposition of the interval-valued fuzzy morphological operators. We investigate in which cases the [? 1,? 2]-cuts of these operators can be written or approximated in terms of the corresponding binary operators. Such conversion into binary operators results in a reduction of the computation time and is further also theoretically interesting since it provides us a link between interval-valued fuzzy and binary morphology.

An 8$\times$8 Cell Analog Order-Statistic-Filter Array With Asynchronous Grayscale Morphology in 0.13-$\mu{\hbox{m}}$ CMOS

This paper presents an integrated 8 times 8 cell image processor array demonstrating the parallel implementation of analog order-statistic filtering and grayscale mathematical morphology. Each cell, connected locally to four nearest neighbors and sized 30 times 28 mum2, includes a digitally programmable five-input analog current-mode ranked-order filter. The array also demonstrates an implementation of asynchronously propagating morphological grayscale reconstruction, which is robust against device mismatch. The measurement results of all programmable order-statistic operations are shown, verifying the correct operation of the array. The chip was manufactured in a 0.13- mum 1-poly 6-metal CMOS technology and operates from a single 1.3-V power supply.

Classification of Fuzzy Mathematical Morphologies Based on Concepts of Inclusion Measure and Duality

Mathematical morphology was originally conceived as a set theoretic approach for the processing of binary images. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory. This paper discusses and compares several well-known and new approaches towards gray-scale and fuzzy mathematical morphology. We show in particular that a certain approach to fuzzy mathematical morphology ultimately depends on the choice of a fuzzy inclusion measure and on a notion of duality. This fact gives rise to a clearly defined scheme for classifying fuzzy mathematical morphologies. The umbra and the level set approach, an extension of the threshold approach to gray-scale mathematical morphology, can also be embedded in this scheme since they can be identified with certain fuzzy approaches.

Technical Note: Confocal Scanning Laser Microscopy and Quantitative Image Analysis: Application to Cream Cheese Microstructure Investigation

The naked eye observation of cream cheese confocal scanning laser microscopy images only provides qualitative information about its microstructure. Because those products are dense dairy gels, confocal scanning laser microscopy images of 2 different cream cheeses may appear close. Quantitative image analysis is then necessary to compensate for human eye deficiency (e.g., lack of precision, subjectivity). Two kinds of quantitative image analysis were performed in this study: high-order statistical methods and grayscale mathematical morphology. They were applied to study the microstructure of 3 different cream cheeses (same manufacturing process, same dry matter content, but different fat and protein contents). Advantages and drawbacks of both methods are reviewed. The way they may be used to describe cream cheese microstructure is also presented.

The recognition of road network from high‐resolution satellite remotely sensed data using image morphological characteristics

With the development of remote sensors and satellite technologies, high‐resolution satellite data such as IKONOS images have been available recently. By these new high‐resolution satellite data, remote sensing technologies can be successfully applied to more application areas such as extracting road network from high‐resolution satellite images. This paper proposes a newly developed approach to extract a road network from high‐resolution satellite images. The approach is based on the binary and greyscale mathematical morphology and a line segment match method. First, the outline of road network is detected based on the grey morphological characteristics. Then, the basic road network is detected by the line segment match method. Next, the detected basic road network is processed based on the knowledge about the roads and binary mathematical morphological methods. Finally, visual analysis and three indicators are used to evaluate the accuracy of the extracted road networks. The results of the accuracy evaluation demonstrate that the developed road network extraction approach can provide both good visual effect and high positional accuracy.

How to reduce 3-D gray-scale mathematical morphology to 2-D

A planar encoding of three-dimensional (3-D) images, which is commutative with respect to set and gray-scale morphological operations, is proposed. Such an encoding indicates a way to reduce 3-D set and mathematical morphology operations to two-dimensional (2-D) ones.

モルフォロジー演算による線図形画像から特定の長さを持つ線図形の抽出

モルフォロジー演算による線図形画像から特定の長さを持つ線図形の抽出

Implementation of binary and gray-scale mathematical morphology on the CNN universal machine

A cellular neural network(CNN)-based morphological engine is proposed. An effective implementation method of binary and gray-scale erosion, dilation, and reconstruction is introduced. The binary morphological operators are successfully implemented on an actual CNN universal chip. Experimental results are shown.

APPLICATION OF FUZZY CELLULAR NEURAL NETWORK TO MORPHOLOGICAL GREY-SCALE RECONSTRUCTION

The fuzzy cellular neural network (FCNN) is a brand new branch of cellular neural network (CNN). In this paper, an additive structure of FCNN is proposed for the purpose of implementation of grey-scale mathematical morphology operators. Then this additive FCNN is used to implement morphological grey-scale reconstruction. Some applications of the FCNN to image processing are proposed based on morphological grey-scale reconstruction. Computer simulation results are given. © 1997 by John-Wiley & Sons, Ltd.

Threshold Decomposition of Gray-Scale Soft Morphology into Binary Soft Morphology

Gray-scale soft mathematical morphology is the natural extension of binary soft mathematical morphology which has been shown to be less sensitive to additive noise and to small variations. But gray-scale soft morphological operations are difficult to implement in real time. In this Note, a superposition property called threshold decomposition and another property called stacking are applied successfully on gray-scale soft morphological operations. These properties allow gray-scale signals and structuring elements to be decomposed into their binary sets respectively and operated by only logic gates in new VLSI architectures, and then these binary results are combined to produce the desired output as of the time-consuming gray-scale processing.

Computational Gray-scale Mathematical Morphology on Lattices (A Comparator-based Image Algebra) Part 1: Architecture

Computational mathematical-morphology has been developed to provide a directly computable alternative to classical gray-scale morphology that is range preserving and compatible with the design of statistically optimal filters based on morphological representation. It serves as an image algebra because of the expressive capability of its image-operator representations. Because representations are based on binary comparators used in conjunction with AND and OR operations, it provides a low-level, efficient computational environment that is a direct extension of the finite Boolean operational environment. The paper focuses on development of the comparator-based representation, providing the relevant representation theory for lattice operators and lattice-vector operators. Computational lattice-operator theory represents a comparator-based alternative to the classical morphological lattice theory, one that is directly implementable in logic. For totally ordered valuation spaces, the lattice theory reduces to a simplified form appropriate to straightforward optimization. The present paper treats architectural considerations and a second part considers the implications for latticevalued image operators.

An alternative to computing grey-scale mathematical morphological operations and its optical implementation

An alternative to the umbra definition on grey-scale mathematical morphology is proposed in this paper, which uses the top-surface set instead of the umbra to represent grey-scale structuring element. This algorithm greatly decreases the neighborhood connections for the binary morphological operation transformed from a grey-scale morphological operation. An optical incoherent correlator architecture with threshold device is developed to carry out the suggested algorithm, while a spatial digital coding method is used to represent input 3D binary data in a 2D arrangement. Experimental results are demonstrated too.

An image processing system for locating craniofacial landmarks

A new automatic target recognition algorithm has been developed to extract craniofacial landmarks from lateral skull X-rays (cephalograms). The locations of these landmarks are used by orthodontists in what is referred to as a cephalometric evaluation. The evaluation assists in the diagnosis of anomalies and in the monitoring of treatments. The algorithm is based on gray-scale mathematical morphology. A statistical approach to training was used to overcome subtle differences in skeletal topographies. Decomposition was used to desensitize the algorithm to size differences. A system was trained to locate 20 landmarks. Tests on 40 X-rays showed an 85% recognition rate on average.

Texture Classification and Segmentation Based on Iterative Morphological Decomposition

This paper presents a new method for texture classification and textured image segmentation based on grayscale mathematical morphology. It defines a recursive morphological decomposition algorithm by using a group of structuring elements with different sizes which decomposes a texture image into a series of component images according to texture primitive sizes and gray levels. Each component image contains only the texture primitives of a certain size, and the original texture image can be exactly reconstructed by the sum of all of its component images. Many texture features can be extracted from these component images for texture classification and textured image segmentation. This paper, then, proposes an adaptive textured image segmentation technique. The size of the window from which texture features are extracted is selected according to expectation of misclassification from the textures to be segmented. The window position for each pixel is determined by its neighborhood. This technique can improve segmentation results, especially along texture boundaries. The experimental results show that the method presented is fast in computation and efficient for classification and segmentation of both structural and random textures. Fairly good experimental results have been obtained, even though few features have been used.