Optimum non linear binary image restoration through linear grey-scale operations

Non-linear image processing operators give excellent results in a number of image processing tasks such as restoration and object recognition. However they are frequently excluded from use in solutions because the system designer does not wish to introduce additional hardware or algorithms and because their design can appear to be ad hoc. In practice the median filter is often used though it is rarely optimal. This paper explains how various non-linear image processing operators may be implemented on a basic linear image processing system using only convolution and thresholding operations. The paper is aimed at image processing system developers wishing to include some non-linear processing operators without introducing additional system capabilities such as extra hardware components or software toolboxes. It may also be of benefit to the interested reader wishing to learn more about non-linear operators and alternative methods of design and implementation. The non-linear tools include various components of mathematical morphology, median and weighted median operators and various order statistic filters. As well as describing novel algorithms for implementation within a linear system the paper also explains how the optimum filter parameters may be estimated for a given image processing task. This novel approach is based on the weight monotonic property and is a direct rather than iterated method

Phase behavior and morphology of multicomponent liquid mixtures

Multicomponent systems are ubiquitous in nature and industry. While the physics of few-component liquid mixtures (i.e., binary and ternary ones) is well-understood and routinely taught in undergraduate courses, the thermodynamic and kinetic properties of $N$-component mixtures with $N>3$ have remained relatively unexplored. An example of such a mixture is provided by the intracellular fluid, in which protein-rich droplets phase separate into distinct membraneless organelles. In this work, we investigate equilibrium phase behavior and morphology of $N$-component liquid mixtures within the Flory-Huggins theory of regular solutions. In order to determine the number of coexisting phases and their compositions, we developed a new algorithm for constructing complete phase diagrams, based on numerical convexification of the discretized free energy landscape. Together with a Cahn-Hilliard approach for kinetics, we employ this method to study mixtures with $N=4$ and $5$ components. We report on both the coarsening behavior of such systems, as well as the resulting morphologies in three spatial dimensions. We discuss how the number of coexisting phases and their compositions can be extracted with Principal Component Analysis (PCA) and K-Means clustering algorithms. Finally, we discuss how one can reverse engineer the interaction parameters and volume fractions of components in order to achieve a range of desired packing structures, such as nested `Russian dolls' and encapsulated Janus droplets.Comment: 16 pages, 11 figures + hyperlinks to 7 video

Morphological operations in image processing and analysis

Morphological operations applied in image processing and analysis are becoming increasingly important in today\u27s technology. Morphological operations which are based on set theory, can extract object features by suitable shape (structuring elements). Morphological filters are combinations of morphological operations that transform an image into a quantitative description of its geometrical structure which based on structuring elements. Important applications of morphological operations are shape description, shape recognition, nonlinear filtering, industrial parts inspection, and medical image processing. In this dissertation, basic morphological operations are reviewed, algorithms and theorems are presented for solving problems in distance transformation, skeletonization, recognition, and nonlinear filtering. A skeletonization algorithm using the maxima-tracking method is introduced to generate a connected skeleton. A modified algorithm is proposed to eliminate non-significant short branches. The back propagation morphology is introduced to reach the roots of morphological filters in only two-scan. The definitions and properties of back propagation morphology are discussed. The two-scan distance transformation is proposed to illustrate the advantage of this new definition. G-spectrum (geometric spectrum) which based upon the cardinality of a set of non-overlapping segments in an image using morphological operations is presented to be a useful tool not only for shape description but also for shape recognition. The G-spectrum is proven to be translation-, rotation-, and scaling-invariant. The shape likeliness based on G-spectrum is defined as a measurement in shape recognition. Experimental results are also illustrated. Soft morphological operations which are found to be less sensitive to additive noise and to small variations are the combinations of order statistic and morphological operations. Soft morphological operations commute with thresholding and obey threshold superposition. This threshold decomposition property allows gray-scale signals to be decomposed into binary signals which can be processed by only logic gates in parallel and then binary results can be combined to produce the equivalent output. Thus the implementation and analysis of function-processing soft morphological operations can be done by focusing only on the case of sets which not only are much easier to deal with because their definitions involve only counting the points instead of sorting numbers, but also allow logic gates implementation and parallel pipelined architecture leading to real-time implementation. In general, soft opening and closing are not idempotent operations, but under some constraints the soft opening and closing can be idempotent and the proof is given. The idempotence property gives us the idea of how to choose the structuring element sets and the value of index such that the soft morphological filters will reach the root signals without iterations. Finally, summary and future research of this dissertation are provided

Understanding Genomic Evolution of Olfactory Receptors through Fractal and Mathematical Morphology

Fractals and Mathematical Morphology are immensely used to study many problems in different branches of science and technology including the domain of Biology. There are many more unrevealed facts and figures of genes and genome in Computational Biology. In this paper, our objective is to explore how the evolutionary network is associated among Human, Chimpanzee and Mouse with regards to their genomic information. We are about to explore their genomic evolution through the quantitative measures of fractals and morphology. We have considered olfactory receptors for our case study. These olfactory receptors do function in different species with subtle differences in the structures of DNA sequences. Those subtle differences can be exposed through intricate details of Fractals and Mathematical Morphology

Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version

Optical implementation of visible gray-image morphology with the visual-area-coding technique

This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/AO.35.001234 Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law

Image morphological processing

Mathematical Morphology with applications in image processing and analysis has been becoming increasingly important in today\u27s technology. Mathematical Morphological operations, which are based on set theory, can extract object features by suitably shaped structuring elements. Mathematical Morphological filters are combinations of morphological operations that transform an image into a quantitative description of its geometrical structure based on structuring elements. Important applications of morphological operations are shape description, shape recognition, nonlinear filtering, industrial parts inspection, and medical image processing. In this dissertation, basic morphological operations, properties and fuzzy morphology are reviewed. Existing techniques for solving corner and edge detection are presented. A new approach to solve corner detection using regulated mathematical morphology is presented and is shown that it is more efficient in binary images than the existing mathematical morphology based asymmetric closing for corner detection. A new class of morphological operations called sweep mathematical morphological operations is developed. The theoretical framework for representation, computation and analysis of sweep morphology is presented. The basic sweep morphological operations, sweep dilation and sweep erosion, are defined and their properties are studied. It is shown that considering only the boundaries and performing operations on the boundaries can substantially reduce the computation. Various applications of this new class of morphological operations are discussed, including the blending of swept surfaces with deformations, image enhancement, edge linking and shortest path planning for rotating objects. Sweep mathematical morphology is an efficient tool for geometric modeling and representation. The sweep dilation/erosion provides a natural representation of sweep motion in the manufacturing processes. A set of grammatical rules that govern the generation of objects belonging to the same group are defined. Earley\u27s parser serves in the screening process to determine whether a pattern is a part of the language. Finally, summary and future research of this dissertation are provided

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing