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

Signal processing and image restoration techniques for two-dimensional eddy current nondestructive evaluation

This dissertation presents a comprehensive study on the forward modeling methods, signal processing techniques, and image restoration techniques for two-dimensional eddy current nondestructive evaluation. The basic physical forward method adopted in this study is the volume integral method. We have applied this model to the eddy current modeling problem for half space geometry and thin plate geometry. To reduce the computational complexity of the volume integral method, we have developed a wavelet expansion method which utilizes the multiresolution compression capability of the wavelet basis to greatly reduce the amount of computation with small loss in accuracy. To further improve the speed of forward modeling, we have developed a fast eddy current model based on a radial basis function neural network. This dissertation also contains investigations on signal processing techniques to enhance flaw signals in two-dimensional eddy current inspection data. The processing procedures developed in this study include a set of preprocessing techniques, a background removal technique based on principal component analysis, and grayscale morphological operations to detect flaw signals. Another important part of the dissertation concerns image restoration techniques which can remove the blurring in impedance change images due to the diffusive nature of the eddy current testing. We have developed two approximate linear image restoration methods--the Wiener filtering method and the maximum entropy method. Both linear restoration methods are based on an approximate linear forward model formulated by using the Born approximation. To improve the quality of restoration, we have also developed nonlinear image restoration methods based on simulated annealing and a genetic algorithm. Those nonlinear methods are based on the neural network forward model which is more accurate than the approximate linear forward model

SEPARATION OF SPIKY TRANSIENTS IN EEG/MEG USING MORPHOLOGICAL FILTERS IN MULTI-RESOLUTION ANALYSIS

Epileptic electroencephalographic (EEG) data often contains a large number of sharp spiky transient patterns which are diagnostically important. Background activity is the EEG activity representing the normal pattern from the brain. Transient activity manifests itself as any non-structured sharp wave with dynamically short appearance as distinguished from the background EEG. Generally speaking, the amplitude change of background activity varies slowly with time and spiky transient activity varies quickly with pointed peaks.In this thesis, a method has been developed to automatically extract transient patterns based on morphological filtering in multiresolution representation. Using a simple structuring element (SE) to match a signal's geometrical shape, mathematical morphology is applied to detect the differences of morphological characteristics of signals. If a signal contains features consistent with the geometrical feature of the structuring element, a morphological filter can recognize and extract the signal of interest. The multiresolution scheme can be based on the wavelet packet transform which decomposes a signal into scaling and wavelet coefficients of different resolutions. The morphological separation filter is applied to these coefficients to produce two subsets of coefficients for each coefficient sequence: one representing the background activity and the other representing the transients. These subsets of coefficients are processed by the inverse wavelet transform to obtain the transient component and the background component. Alternatively, a morphological lifting scheme has been proposed for separation these two components. Experimental results on both synthetic data and real EEG data have shown that the developed methods are highly effective in automatic extraction of spiky transients in the epileptic EEG data.The interictal spike trains thus extracted from multiple electrode recordings are further analyzed. Their cross-correlograms are examined according to the stochastic point process model. Our experiment result has been verified by human experts' estimation

Representations for Morphological Image Operators and Analogies with Linear Operators

1.1 Why a representation theory?...............................