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

A morphological approach to the design of complex objects

The surface-trajectory model gives a solution to some of the problems presented by the general geometric models where the design of an object is separated from its manufacture. In fact, in this model, the internal representation of objects is made up of machining trajectories. As the display systems usually need triangles to represent the objects, a process of triangulation is needed to visualize them. In other words, a secondary surface model is needed to display the objects. The following is a geometric model that, maintaining the philosophy of the surface-trajectory model, encapsulates the calculation of the machining process from the formal framework that provides the set theory and the mathematical morphology. The model addresses the process of designing objects by assimilation of a machining process by giving solutions to the design of complex objects and an arithmetic to support the generation of trajectories of manufacturing. The design process is similar to the craft work of sculptors designing their pieces by hand with their tools. It also gives a direct solution to the problems of the trajectory generation since they are already defined at the design phase. The model is generic and robust as there are no special cases or complex objects in which the model does not provide a correct solution. It also naturally incorporates the realistic display of the machined objects in a quickly and accurately way

Deterministic mathematical morphology for CAD/CAM

Purpose – The purpose of this paper is to present a new geometric model based on the mathematical morphology paradigm, specialized to provide determinism to the classic morphological operations. The determinism is needed to model dynamic processes that require an order of application, as is the case for designing and manufacturing objects in CAD/CAM environments. Design/methodology/approach – The basic trajectory-based operation is the basis of the proposed morphological specialization. This operation allows the definition of morphological operators that obtain sequentially ordered sets of points from the boundary of the target objects, inexistent determinism in the classical morphological paradigm. From this basic operation, the complete set of morphological operators is redefined, incorporating the concept of boundary and determinism: trajectory-based erosion and dilation, and other morphological filtering operations. Findings – This new morphological framework allows the definition of complex three-dimensional objects, providing arithmetical support to generating machining trajectories, one of the most complex problems currently occurring in CAD/CAM. Originality/value – The model proposes the integration of the processes of design and manufacture, so that it avoids the problems of accuracy and integrity that present other classic geometric models that divide these processes in two phases. Furthermore, the morphological operative is based on points sets, so the geometric data structures and the operations are intrinsically simple and efficient. Another important value that no excessive computational resources are needed, because only the points in the boundary are processed

Matemaattisen morfologian käyttö geometrisessa musiikinhaussa

The usual task in music information retrieval (MIR) is to find occurrences of a monophonic query pattern within a music database, which can contain both monophonic and polyphonic content. The so-called query-by-humming systems are a famous instance of content-based MIR. In such a system, the user's hummed query is converted into symbolic form to perform search operations in a similarly encoded database. The symbolic representation (e.g., textual, MIDI or vector data) is typically a quantized and simplified version of the sampled audio data, yielding to faster search algorithms and space requirements that can be met in real-life situations. In this thesis, we investigate geometric approaches to MIR. We first study some musicological properties often needed in MIR algorithms, and then give a literature review on traditional (e.g., string-matching-based) MIR algorithms and novel techniques based on geometry. We also introduce some concepts from digital image processing, namely the mathematical morphology, which we will use to develop and implement four algorithms for geometric music retrieval. The symbolic representation in the case of our algorithms is a binary 2-D image. We use various morphological pre- and post-processing operations on the query and the database images to perform template matching / pattern recognition for the images. The algorithms are basically extensions to classic image correlation and hit-or-miss transformation techniques used widely in template matching applications. They aim to be a future extension to the retrieval engine of C-BRAHMS, which is a research project of the Department of Computer Science at University of Helsinki

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

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

Orientation, sphericity and roundness evaluation of particles using alternative 3D representations

Sphericity and roundness indices have been used mainly in geology to analyze the shape of particles. In this paper, geometric methods are proposed as an alternative to evaluate the orientation, sphericity and roundness indices of 3D objects. In contrast to previous works based on digital images, which use the voxel model, we represent the particles with the Extreme Vertices Model, a very concise representation for binary volumes. We define the orientation with three mutually orthogonal unit vectors. Then, some sphericity indices based on length measurement of the three representative axes of the particle can be computed. In addition, we propose a ray-casting-like approach to evaluate a 3D roundness index. This method provides roundness measurements that are highly correlated with those provided by the Krumbein's chart and other previous approach. Finally, as an example we apply the presented methods to analyze the sphericity and roundness of a real silica nano dataset.Postprint (published version

Numerical simulation of the stress-strain state of the dental system

We present mathematical models, computational algorithms and software, which can be used for prediction of results of prosthetic treatment. More interest issue is biomechanics of the periodontal complex because any prosthesis is accompanied by a risk of overloading the supporting elements. Such risk can be avoided by the proper load distribution and prediction of stresses that occur during the use of dentures. We developed the mathematical model of the periodontal complex and its software implementation. This model is based on linear elasticity theory and allows to calculate the stress and strain fields in periodontal ligament and jawbone. The input parameters for the developed model can be divided into two groups. The first group of parameters describes the mechanical properties of periodontal ligament, teeth and jawbone (for example, elasticity of periodontal ligament etc.). The second group characterized the geometric properties of objects: the size of the teeth, their spatial coordinates, the size of periodontal ligament etc. The mechanical properties are the same for almost all, but the input of geometrical data is complicated because of their individual characteristics. In this connection, we develop algorithms and software for processing of images obtained by computed tomography (CT) scanner and for constructing individual digital model of the tooth-periodontal ligament-jawbone system of the patient. Integration of models and algorithms described allows to carry out biomechanical analysis on three-dimensional digital model and to select prosthesis design.Comment: 19 pages, 9 figure