Morphological filter mean-absolute-error representation theorems and their application to optimal morphological filter design

The present thesis derives error representations and develops design methodologies for optimal mean-absolute-error (MAE) morphological-based filters. Four related morphological-based filter-types are treated. Three are translation-invariant, monotonically increasing operators, and our analysis is based on the Matheron (1975) representation. In this class we analyze conventional binary, conventional gray-scale, and computational morphological filters. The fourth filter class examined is that of binary translation invariant operators. Our analysis is based on the Banon and Barrera (1991) representation and hit-or-miss operator of Serra (1982). A starting point will be the optimal morphological filter paradigm of Dougherty (1992a,b) whose analysis de scribes the optimal filter by a system of nonlinear inequalities with no known method of solution, and thus reduces filter design to minimal search strategies. Although the search analysis is definitive, practical filter design remained elu sive because the search space can be prohibitively large if it not mitigated in some way. The present thesis extends from Dougherty\u27s starting point in several ways. Central to the thesis is the MAE analysis for the various filter settings, where in each case, a theorem is derived that expresses overall filter MAE as a sum of MAE values of individual structuring-element filters and MAE of combinations of unions (maxima) of those elements. Recursive forms of the theorems can be employed in a computer algorithm to rapidly evaluate combinations of structuring elements and search for an optimal filter basis. Although the MAE theorems provide a rapid means for examining the filter design space, the combinatoric nature of this space is, in general, too large for a exhaustive search. Another key contribution of this thesis concerns mitigation of the computational burden via design constraints. The resulting constrained filter will be suboptimal, but, if the constraints are imposed in a suitable man ner, there is little loss of filter performance in return for design tractability. Three constraint approaches developed here are (1) limiting the number of terms in the filter expansion, (2) constraining the observation window, and (3) employing structuring element libraries from which to search for an optimal basis. Another contribution of this thesis concerns the application of optimal morphological filters to image restoration. Statistical and deterministic image and degradation models for binary and low-level gray images were developed here that relate to actual problems in the optical character recognition and electronic printing fields. In the filter design process, these models are employed to generate realizations, from which we extract single-erosion and single-hit-or-miss MAE statistics. These realization-based statistics are utilized in the search for the optimal combination of structuring elements

Iterative morphological filters and application in document restoration

The binary nature of document degradation decides the suitability of morphological methods for restoration. Although the computational burden in morphological filter design can be mitigated by imposing constraints on the filter and employing the morphological filter MAE theorem in an efficient search strategy, the design constraints on the filter limit the performance of single-pass filter. It has been shown that iterative morphological filters can outperform single-pass filters. The investigation of iterative morphological filter design for image restoration is the main contribution of the present thesis. The study of iterative morphological filter design provides the understanding in depth of how filters achieve a better restoration in an iterative way. Various image-noise processes have been used to examine the effect of iteration on window constraint. Through iteration we have increased the class of filters from which an increasing estimator may be designed, so that the window constraint can be compensated by employing iterative morphological filter. Practically, we arrive at the conclusion that smaller size observation windows can achieve very similar restoration result in a MAE sense as large size windows by employing iterative design. It provides us a better practical design of increasing operators for document restoration compared to the single-pass filter using large size window. Theoretically, we arrive at the conclusion that it is not important if two operators are quite different in logical structure, and they can achieve very similar restoration effect as long as they are statistically similar

Robotic navigation algorithm with machine vision

In the field of robotics, it is essential to know the work area in which the agent is going to develop, for that reason, different methods of mapping and spatial location have been developed for different applications. In this article, a machine vision algorithm is proposed, which is responsible for identifying objects of interest within a work area and determining the polar coordinates to which they are related to the observer, applicable either with a fixed camera or in a mobile agent such as the one presented in this document. The developed algorithm was evaluated in two situations, determining the position of six objects in total around the mobile agent. These results were compared with the real position of each of the objects, reaching a high level of accuracy with an average error of 1.3271% in the distance and 2.8998% in the angle

SoFiA: a flexible source finder for 3D spectral line data

We introduce SoFiA, a flexible software application for the detection and parameterization of sources in 3D spectral-line datasets. SoFiA combines for the first time in a single piece of software a set of new source-finding and parameterization algorithms developed on the way to future HI surveys with ASKAP (WALLABY, DINGO) and APERTIF. It is designed to enable the general use of these new algorithms by the community on a broad range of datasets. The key advantages of SoFiA are the ability to: search for line emission on multiple scales to detect 3D sources in a complete and reliable way, taking into account noise level variations and the presence of artefacts in a data cube; estimate the reliability of individual detections; look for signal in arbitrarily large data cubes using a catalogue of 3D coordinates as a prior; provide a wide range of source parameters and output products which facilitate further analysis by the user. We highlight the modularity of SoFiA, which makes it a flexible package allowing users to select and apply only the algorithms useful for their data and science questions. This modularity makes it also possible to easily expand SoFiA in order to include additional methods as they become available. The full SoFiA distribution, including a dedicated graphical user interface, is publicly available for download.Comment: MNRAS, accepted. SoFiA is registered at the Astrophysics Source Code Library with ID ascl:1412.001. Download SoFiA at https://github.com/SoFiA-Admin/SoFi

Brain extraction using the watershed transform from markers

Isolation of the brain from other tissue types in magnetic resonance (MR) images is an important step in many types of neuro-imaging research using both humans and animal subjects. The importance of brain extraction is well appreciated—numerous approaches have been published and the benefits of good extraction methods to subsequent processing are well known. We describe a tool—the marker based watershed scalper (MBWSS)—for isolating the brain in T1-weighted MR images built using filtering and segmentation components from the Insight Toolkit (ITK) framework. The key elements of MBWSS—the watershed transform from markers and aggressive filtering with large kernels—are techniques that have rarely been used in neuroimaging segmentation applications. MBWSS is able to reliably isolate the brain without expensive preprocessing steps, such as registration to an atlas, and is therefore useful as the first stage of processing pipelines. It is an informative example of the level of accuracy achievable without using priors in the form of atlases, shape models or libraries of examples. We validate the MBWSS using a publicly available dataset, a paediatric cohort, an adolescent cohort, intra-surgical scans and demonstrate flexibility of the approach by modifying the method to extract macaque brains

Convergence of adaptive morphological filters in the context of Markov chains

A typical parameterized r-opening *r is a filter defined as a union of openings by a collection of compact, convex structuring elements, each of which is governed by a parameter vector r. It reduces to a single parameter r-opening filter by a set of structuring elements when r is a scalar sizing parameter. The parameter vector is adjusted by a set of adaptation rules according to whether the re construction Ar derived from r correctly or incorrectly passes the signal and noise grains sampled from the image. Applied to the signal-union-noise model, the optimization problem is to find the vector of r that minimizes the Mean-Absolute-Error between the filtered and ideal image processes. The adaptive r-opening filter fits into the framework of Markov processes, the adaptive parameter being the state of the process. For a single parameter r-opening filter, we proved that there exists a stationary distribution governing the parameter in the steady state and convergence is characterized in terms of the steady-state distribution. Key filter properties such as parameter mean, parameter variance, and expected error in the steady state are characterized via the stationary distribution. Steady-state behavior is compared to the optimal solution for the uniform model, for which it is possible to derive a closed-form solution for the optimal filter. We also developed the Markov adaptation system for multiparameter opening filters and provided numerical solutions to some special cases. For multiparameter r-opening filters, various adaptive models derived from various assumptions on the form of the filter have been studied. Although the state-probability increment equations can be derived from the appropriate Chapman-Kolmogorov equations, the closed-form representation of steady-state distributions is mathematically problematic due to the support geometry of the boundary states and their transitions. Therefore, numerical methods are employed to approximate for steady state probability distributions. The technique developed for conventional opening filters is also applied to bandpass opening filters. In present thesis study, the concept of signal and noise pass sets plays a central role throughout the adaptive filter analysis. The pass set reduces to the granulometric measure (or {&r}-measure) of the signal and noise grain. Optimization and adaptation are characterized in terms of the distribution of the granulometric measures for single parameter filters, or in terms of the multivariate distribution of the signal and noise pass sets. By introducing these concepts, this thesis study also provides some optimal opening filter error equations. It has been shown in the case of the uniform distribution of single sizing parameter that there is a strong agreement between the adaptive filter and optimal filter based on analytic error minimization. This agreement has been also demonstrated in various r-opening filters. Furthermore, the probabilistic interpretation has a close connection to traditional linear adaptive filter theory. The method has been applied to the classical grain separation (clutter removal) problem. *See content for correct numerical representation

Study of Target Enhancement Algorithms to Counter the Hostile Nuclear Environment

A necessary requirement of strategic defense is the detection of incoming nuclear warheads in an environment that may include nuclear detonations of undetected or missed target warheads. A computer model is described which simulates incoming warheads as distant endoatmospheric targets. A model of the expected electromagnetic noise present in a nuclear environment is developed using estimates of the probability distributions. Predicted atmospheric effects are also included. Various image enhancement algorithms, both linear and nonlinear, are discussed concerning their anticipated ability to suppress the noise and atmospheric effects of the nuclear environment. These algorithms are then tested, using the combined target and noise models, and evaluated in terms of the stated figures of merit

Genetic programming applied to morphological image processing

This thesis presents three approaches to the automatic design of algorithms for the processing of binary images based on the Genetic Programming (GP) paradigm. In the first approach the algorithms are designed using the basic Mathematical Morphology (MM) operators, i.e. erosion and dilation, with a variety of Structuring Elements (SEs). GP is used to design algorithms to convert a binary image into another containing just a particular characteristic of interest. In the study we have tested two similarity fitness functions, training sets with different numbers of elements and different sizes of the training images over three different objectives. The results of the first approach showed some success in the evolution of MM algorithms but also identifed problems with the amount of computational resources the method required. The second approach uses Sub-Machine-Code GP (SMCGP) and bitwise operators as an attempt to speed-up the evolution of the algorithms and to make them both feasible and effective. The SMCGP approach was successful in the speeding up of the computation but it was not successful in improving the quality of the obtained algorithms. The third approach presents the combination of logical and morphological operators in an attempt to improve the quality of the automatically designed algorithms. The results obtained provide empirical evidence showing that the evolution of high quality MM algorithms using GP is possible and that this technique has a broad potential that should be explored further. This thesis includes an analysis of the potential of GP and other Machine Learning techniques for solving the general problem of Signal Understanding by means of exploring Mathematical Morphology

FPGA implementation and performance comparison of a Bayesian face detection system

Face detection has primarily been a software-based effort. A hardware-based approach can provide significant speed-up over its software counterpart. Advances in transistor technology have made it possible to produce larger and faster FPGAs at more affordable prices. Through VHDL and synthesis tools it is possible to rapidly develop a hardware-based solution to face detection on an FPGA. This work analyzes and compares the performance of a feature-invariant face detection method implemented in software and an FPGA. The primary components of the face detector were a Bayesian classifier used to segment the image into skin and nonskin pixels, and a direct least square elliptical fitting technique to determine if the skin region\u27s shape has elliptical characteristics similar to a face. The C++ implementation was benchmarked on several high performance workstations, while the VHDL implementation was synthesized for FPGAs from several Xilinx product lines. The face detector used to compare software and hardware performance had a modest correct detection rate of 48.6% and a false alarm rate of 29.7%. The elliptical-shape of the region was determined to be an inaccurate approach for filtering out non-face skin regions. The software-based face detector was capable of detecting faces within images of approximately 378x567 pixels or less at 20 frames per second on Pentium 4 and Pentium D systems. The FPGA-based implementation was capable of faster detection speeds; a speedup of 3.33 was seen on a Spartan 3 and 4.52 on a Virtex 4. The comparison shows that an FPGA-based face detector could provide a significant increase in computational speed