BEMDEC: An Adaptive and Robust Methodology for Digital Image Feature Extraction

The intriguing study of feature extraction, and edge detection in particular, has, as a result of the increased use of imagery, drawn even more attention not just from the field of computer science but also from a variety of scientific fields. However, various challenges surrounding the formulation of feature extraction operator, particularly of edges, which is capable of satisfying the necessary properties of low probability of error (i.e., failure of marking true edges), accuracy, and consistent response to a single edge, continue to persist. Moreover, it should be pointed out that most of the work in the area of feature extraction has been focused on improving many of the existing approaches rather than devising or adopting new ones. In the image processing subfield, where the needs constantly change, we must equally change the way we think. In this digital world where the use of images, for variety of purposes, continues to increase, researchers, if they are serious about addressing the aforementioned limitations, must be able to think outside the box and step away from the usual in order to overcome these challenges. In this dissertation, we propose an adaptive and robust, yet simple, digital image features detection methodology using bidimensional empirical mode decomposition (BEMD), a sifting process that decomposes a signal into its two-dimensional (2D) bidimensional intrinsic mode functions (BIMFs). The method is further extended to detect corners and curves, and as such, dubbed as BEMDEC, indicating its ability to detect edges, corners and curves. In addition to the application of BEMD, a unique combination of a flexible envelope estimation algorithm, stopping criteria and boundary adjustment made the realization of this multi-feature detector possible. Further application of two morphological operators of binarization and thinning adds to the quality of the operator

Multirate Frequency Transformations: Wideband AM-FM Demodulation with Applications to Signal Processing and Communications

The AM-FM (amplitude & frequency modulation) signal model finds numerous applications in image processing, communications, and speech processing. The traditional approaches towards demodulation of signals in this category are the analytic signal approach, frequency tracking, or the energy operator approach. These approaches however, assume that the amplitude and frequency components are slowly time-varying, e.g., narrowband and incur significant demodulation error in the wideband scenarios. In this thesis, we extend a two-stage approach towards wideband AM-FM demodulation that combines multirate frequency transformations (MFT) enacted through a combination of multirate systems with traditional demodulation techniques, e.g., the Teager-Kasiser energy operator demodulation (ESA) approach to large wideband to narrowband conversion factors. The MFT module comprises of multirate interpolation and heterodyning and converts the wideband AM-FM signal into a narrowband signal, while the demodulation module such as ESA demodulates the narrowband signal into constituent amplitude and frequency components that are then transformed back to yield estimates for the wideband signal. This MFT-ESA approach is then applied to the various problems of: (a) wideband image demodulation and fingerprint demodulation, where multidimensional energy separation is employed, (b) wideband first-formant demodulation in vowels, and (c) wideband CPM demodulation with partial response signaling, to demonstrate its validity in both monocomponent and multicomponent scenarios as an effective multicomponent AM-FM signal demodulation and analysis technique for image processing, speech processing, and communications based applications

Transform-based surface analysis and representation for CAD models

In most Computer-Aided Design (CAD) systems, the topological and geometrical information in a CAD model is usually represented by the edge-based data structure. With the emergence of concurrent engineering, such issues as product design, manufacturing, and process planning are considered simultaneously at the design stage. The need for the development of high-level models for completely documenting the geometry of a product and supporting manufacturing applications, such as automating the verification of a design for manufacturing (DIM) rules and generating process plans, becomes apparent;This dissertation has addressed the development of a generalized framework for high-level geometric representations of CAD models and form features to automate algorithmic search and retrieval of manufacturing information;A new wavelet-based ranking algorithm is developed to generate surface-based representations as input for the extraction of form features with non-planar surfaces in CAD models. The objective of using a wavelet-based shape analysis approach is to overcome the main limitation of the alternative feature extraction approaches, namely their restriction to planar surfaces or simple curved surfaces;A transform-invariant coding system for CAD models by multi-scale wavelet representations is also presented. The coding procedure is based on both the internal regions and external contours of topology entities---faces

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

On the Analysis and Decomposition of Intrinsically One-Dimensional Signals and their Superpositions

Computer and machine vision tasks can roughly be divided into a hierarchy of processing steps applied to input signals captured by a measuring device. In the case of image signals, the first stage in this hierarchy is also referred to as low-level vision or low-level image processing. The field of low-level image processing includes the mathematical description of signals in terms of certain local signal models. The choice of the signal model is often task dependent. A common task is the extraction of features from the signal. Since signals are subject to transformations, for example camera movements in the case of image signals, the features are supposed to fulfill the properties of invariance or equivariance with respect to these transformations. The chosen signal model should reflect these properties in terms of its parameters. This thesis contributes to the field of low-level vision. Local signal structures are represented by (sinusoidal) intrinsically one-dimensional signals and their superpositions. Each intrinsically one-dimensional signal consists of certain parameters such as orientation, amplitude, frequency and phase. If the affine group acts on these signals, the transformations induce a corresponding action in the parameter space of the signal model. Hence, it is reasonable, to estimate the model parameters in order to describe the invariant and equivariant features. The first and main contribution studies superpositions of intrinsically one-dimensional signals in the plane. The parameters of the signal are supposed to be extracted from the responses of linear shift invariant operators: the generalized Hilbert transform (Riesz transform) and its higher-order versions and the partial derivative operators. While well known signal representations, such as the monogenic signal, allow to obtain the local features amplitude, phase and orientation for a single intrinsically one-dimensional signal, there exists no general method to decompose superpositions of such signals into their corresponding features. A novel method for the decomposition of an arbitrary number of sinusoidal intrinsically one-dimensional signals in the plane is proposed. The responses of the higher-order generalized Hilbert transforms in the plane are interpreted as symmetric tensors, which allow to restate the decomposition problem as a symmetric tensor decomposition. Algorithms, examples and applications for the novel decomposition are provided. The second contribution studies curved intrinsically one-dimensional signals in the plane. This signal model introduces a new parameter, the curvature, and allows the representation of curved signal structures. Using the inverse stereographic projection to the sphere, these curved signals are locally identified with intrinsically one-dimensional signals in the three-dimensional Euclidean space and analyzed in terms of the generalized Hilbert transform and partial derivatives therein. The third contribution studies the generalized Hilbert transform in a non-Euclidean space, the two-sphere. The mathematical framework of Clifford analysis proposes a further generalization of the generalized Hilbert transform to the two-sphere in terms of the corresponding Cauchy kernel. Nonetheless, this transform lacks an intuitive interpretation in the frequency domain. A decomposition of the Cauchy kernel in terms of its spherical harmonics is provided. Its coefficients not only provide insights to the generalized Hilbert transform on the sphere, but also allow for fast implementations in terms of analogues of the convolution theorem on the sphere