Computing Approximate Solutions to the Art Gallery Problem and Watchman Route Problem by Means of Photon Mapping

Wireless sensor networks (WSNs) can be partitioned component sensor nodes (SNs) who are meant to operate and sense information arriving from multiple spectra in their environment. Determining where to place a single SN or multiple SNs such that the amount of information gained is maximized while the number of SNs used to gain that information is minimized is an instance of solving the art gallery problem (AGP). In order to solve the AGP, we present the Sensor Placement Optimization via Queries (SPOQ) algorithm that uses level sets populated by queries to a photon map in order to find observation points that sense as many photons as possible. Since we are using photon mapping as our means of modeling how information is conveyed, SPOQ can then take into account static or dynamic environmental conditions and can use exploratory or precomputed sensing. Unmanned vehicles can be designated more generally as UxVs where “x” indicates the environment they are expected to operate – either in the air, on the ground, underwater or on the water’s surface. Determining how to plan an optimal route by a single UxV or multiple UxVs operating in their environment such that the amount of information gained is maximized while the cost of gaining that information is minimized is an instance of solving the watchman route problem (WRP). In order to solve the WRP, we present the Photon-mapping-Informed active-Contour Route Designator (PICRD) algorithm. PICRD heuristically solves the WRP by utilizing SPOQ’s AGP-solving vertices and connecting them with the high visibility vertices provided by a photon-mapping informed Chan-Vese segmentation mesh using a shortest-route path-finding algorithm. Since we are using photon-mapping as our foundation for determining sensor coverage by the PICRD algorithm, we can then take into account the behavior of photons as they propagate through the various environmental conditions that might be encountered by a single or multiple UxVs

Joint reconstruction-segmentation on graphs

Practical image segmentation tasks concern images which must be reconstructed from noisy, distorted, and/or incomplete observations. A recent approach for solving such tasks is to perform this reconstruction jointly with the segmentation, using each to guide the other. However, this work has so far employed relatively simple segmentation methods, such as the Chan--Vese algorithm. In this paper, we present a method for joint reconstruction-segmentation using graph-based segmentation methods, which have been seeing increasing recent interest. Complications arise due to the large size of the matrices involved, and we show how these complications can be managed. We then analyse the convergence properties of our scheme. Finally, we apply this scheme to distorted versions of ``two cows'' images familiar from previous graph-based segmentation literature, first to a highly noised version and second to a blurred version, achieving highly accurate segmentations in both cases. We compare these results to those obtained by sequential reconstruction-segmentation approaches, finding that our method competes with, or even outperforms, those approaches in terms of reconstruction and segmentation accuracy.Comment: 33 pages, 20 figure

Automated detection of extended sources in radio maps: progress from the SCORPIO survey

Automated source extraction and parameterization represents a crucial challenge for the next-generation radio interferometer surveys, such as those performed with the Square Kilometre Array (SKA) and its precursors. In this paper we present a new algorithm, dubbed CAESAR (Compact And Extended Source Automated Recognition), to detect and parametrize extended sources in radio interferometric maps. It is based on a pre-filtering stage, allowing image denoising, compact source suppression and enhancement of diffuse emission, followed by an adaptive superpixel clustering stage for final source segmentation. A parameterization stage provides source flux information and a wide range of morphology estimators for post-processing analysis. We developed CAESAR in a modular software library, including also different methods for local background estimation and image filtering, along with alternative algorithms for both compact and diffuse source extraction. The method was applied to real radio continuum data collected at the Australian Telescope Compact Array (ATCA) within the SCORPIO project, a pathfinder of the ASKAP-EMU survey. The source reconstruction capabilities were studied over different test fields in the presence of compact sources, imaging artefacts and diffuse emission from the Galactic plane and compared with existing algorithms. When compared to a human-driven analysis, the designed algorithm was found capable of detecting known target sources and regions of diffuse emission, outperforming alternative approaches over the considered fields.Comment: 15 pages, 9 figure

Formulation of hybrid 3D image segmentation algorithm based partial differential equation

Segmentation is an important tool for analysis and understanding of most images encountered in science and engineering. One of the best segmentation methods that can perform 3D segmentation is the level-set method which has its mathematical foundation in partial differential equation (PDE). Owing to its complex nature, it exhibits a level of unacceptable sluggishness on implementation hence a need to hasten up the process by hybridizing it with a faster region-based segmentation method which is inherently a logical approach to segmentation pivoted on thresholding but not as good in segmentation as the former. This work presents a mathematical hybrid of the two methods that is hoped to produce a better segmentation result

Machine Learning Methods for Breast Cancer Diagnostic

This chapter discusses radio-pathological correlation with recent imaging advances such as machine learning (ML) with the use of technical methods such as mammography and histopathology. Although criteria for diagnostic categories for radiology and pathology are well established, manual detection and grading, respectively, are tedious and subjective processes and thus suffer from inter-observer and intra-observer variations. Two most popular techniques that use ML, computer aided detection (CADe) and computer aided diagnosis (CADx), are presented. CADe is a rejection model based on SVM algorithm which is used to reduce the False Positive (FP) of the output of the Chan-Vese segmentation algorithm that was initialized by the marker controller watershed (MCWS) algorithm. CADx method applies the ensemble framework, consisting of four-base SVM (RBF) classifiers, where each base classifier is a specialist and is trained to use the selected features of a particular tissue component. In general, both proposed methods offer alternative decision-making ability and are able to assist the medical expert in giving second opinion on more precise nodule detection. Hence, it reduces FP rate that causes over segmentation and improves the performance for detection and diagnosis of the breast cancer and is able to create a platform that integrates diagnostic reporting system

Segmentation of thermographic images of hands using a genetic algorithm

This paper presents a new technique for segmenting thermographic images using a genetic algorithm (GA). The individuals of the GA also known as chromosomes consist of a sequence of parameters of a level set function. Each chromosome represents a unique segmenting contour. An initial population of segmenting contours is generated based on the learned variation of the level set parameters from training images. Each segmenting contour (an individual) is evaluated for its fitness based on the texture of the region it encloses. The fittest individuals are allowed to propagate to future generations of the GA run using selection, crossover and mutation. The dataset consists of thermographic images of hands of patients suffering from upper extremity musculo-skeletal disorders (UEMSD). Thermographic images are acquired to study the skin temperature as a surrogate for the amount of blood flow in the hands of these patients. Since entire hands are not visible on these images, segmentation of the outline of the hands on these images is typically performed by a human. In this paper several different methods have been tried for segmenting thermographic images: Gabor-wavelet-based texture segmentation method, the level set method of segmentation and our GA which we termed LSGA because it combines level sets with genetic algorithms. The results show a comparative evaluation of the segmentation performed by all the methods. We conclude that LSGA successfully segments entire hands on images in which hands are only partially visible

Image Segmentation by Energy and Related Functional Minimization Methods

Effective and efficient methods for partitioning a digital image into image segments, called ¿image segmentation,¿ have a wide range of applications that include pattern recognition, classification, editing, rendering, and compressed data for image search. In general, image segments are described by their geometry and similarity measures that identify them. For example, the well-known optimization model proposed and studied in depth by David Mumford and Jayant Shah is based on an L2 total energy functional that consists of three terms that govern the geometry of the image segments, the image fidelity (or closeness to the observed image), and the prior (or image smoothness). Recent work in the field of image restoration suggests that a more suitable choice for the fidelity measure is, perhaps, the l1 norm. This thesis explores that idea applied to the study of image segmentation along the line of the Mumford and Shah optimization model, but eliminating the need of variational calculus and regularization schemes to derive the approximating Euler-Lagrange equations. The main contribution of this thesis is a formulation of the problem that avoids the need for the calculus of variation. The energy functional represents a global property of an image. It turns out to be possible, however, to predict how localized changes to the segmentation will affect its value. This has been shown previously in the case of the l2 norm, but no similar method is available for other norms. The method described here solves the problem for the l1 norm, and suggests how it would apply to other forms of the fidelity measure. Existing methods rely on a fixed initial condition. This can lead to an algorithm finding local instead of global optimizations. The solution given here shows how to specify the initial condition based on the content of the image and avoid finding local minima