Measuring the circularity of congressional districts

Shape analysis has special importance in the detection of manipulated redistricting, which is called gerrymandering. In most of the US states, this process is made by non-independent actors and often causes debates about partisan manipulation. The somewhat ambiguous concept of compactness is a standard criterion for legislative districts. In the literature, circularity is widely used as a measure of compactness, since it is a natural requirement for a district to be as circular as possible. In this paper, we introduce a novel and parameter-free circularity measure that is based on Hu moment invariants. This new measure provides a powerful tool to detect districts with abnormal shapes. We examined some districts of Arkansas, Iowa, Kansas, and Utah over several consecutive periods and redistricting plans, and also compared the results with classical circularity indexes. We found that the fall of the average circularity value of the new measure indicates potential gerrymandering

Ellipticity and circularity measuring via Kullback-Leibler divergence

Using the Kullback-Leibler divergence we provide a simple statistical measure which uses only the covariance matrix of a given set to verify whether the set is an ellipsoid. Similar measure is provided for verification of circles and balls. The new measure is easily computable, intuitive, and can be applied to higher dimensional data. Experiments have been performed to illustrate that the new measure behaves in natural way

Nanoparticle shapes: Quantification by elongation, convexity and circularity measures

The goal of the nanoparticle synthesis is, first of all, the production of nanoparticles that will be more similar in size and shape. This is very important for the possibility of studying and applying nanomaterials because of their characteristics that are very sensitive to size and shape such as, for example, magnetic properties. In this paper, we propose the shape analysis of the nanoparticles using three shape descriptors – elongation, convexity and circularity. Experimental results were obtained by using TEM images of hematite nanoparticles that were, first of all, subjected to segmentation in order to obtain isolated nanoparticles, and then the values of elongation, convexity and circularity were measured. Convexity C x ( S ) is regarded as the ratio between shape’s area and area of the its convex hull. The convexity measure defines the degree to which a shape differs from a convex shape while the circularity measure defines the degree to which a shape differs from an ideal circle. The range of convexity and circularity values is (0, 1], while the range of elongation values is [1, ∞). The circle has lowest elongation (ε = 1), while it has biggest convexity and circularity values ( C x = 1; C = 1). The measures ε( S ), C x ( S ), C ( S ) proposed and used in the experiment have the few desirable properties and give intuitively expected results. None of the measures is good enough to describe all the shapes, and therefore it is suggested to use a variety of measures so that the shapes can be described better and then classify and control during the synthesis process

Medición sobre MRI para diagnóstico de cáncer de próstata

The male reproductive system has a gland located below the bladder and in front of the rectum: the prostate. It surrounds the urethra and has the function of producing a fluid component in the seminal fluid. Over time, this gland tends to enlarge and block the urethra, making it difficult to urinate or sexual function. This alteration is known as harmless prostatic hyperplasia, which is corrected with surgery. Sometimes it is confused with prostate cancer due to the similarity of the symptoms, which is frequent in men. Diagnosis of this disease is generally made using a manual technique called a digital rectal examination and a laboratory test that measures PSA levels in the blood. It is a substance found in the blood of someone who usually has prostate cancer. Additionally, the diagnosis is supported by a transrectal ultrasound through a catheter. This comprehensive process helps to determine the extension of prostate cancer and designate the correct treatment. The status of prostate injury is assessed by practicing a Magnetic Resonance Imaging (MRI). It is a procedure performed by radio waves and a computer that creates detailed prostate areas' images. It analyzes the prostate condition and determines the procedure or treatment according to the injury's status, for example, surgery, radiation therapy, or monitored observation. To define what kind of treatment, it is essential to analyze the different disease stages and the Gleason Score, a measurement of the histological grade, ranging from 2 to 10, that indicates the probability of spreading or extending the tumor. This research focuses on the analysis and the extraction of measurements to classify forms of prostate lesions to support its diagnosis. It considers the PI-RADS categorization, which currently determines the probability of suffering from clinically significant prostate cancer. For this purpose, an analysis was made using a geometric interpretation from different categorizations of cancer (4-5). A digital processing of Python images on T2, ADC, and DWI was made applicating the concept of the curve, Zernike moments, fractal dimension, Caliper dimension, the total absolute curvature, the energy bending, direction, convexity, circularity, compactness, Hu moments, dimension, eccentricity, extent, solidity, orientation, largest axis length, smallest axis length, radius, center, centroid, length, area.El aparato reproductor masculino tiene una glándula ubicada debajo de la vejiga y frente al recto: la próstata. Rodea la uretra y tiene la función de producir un componente líquido en el líquido seminal. Con el tiempo, esta glándula tiende a agrandarse y bloquear la uretra, lo que dificulta la micción o la función sexual. Esta alteración se conoce como hiperplasia prostática, que se corrige con cirugía. En ocasiones se confunde con el cáncer de próstata por la similitud de los síntomas, que es frecuente en los hombres. El diagnóstico de esta enfermedad generalmente se realiza mediante una técnica manual llamada tacto rectal y una prueba de laboratorio que mide los niveles de PSA en la sangre. Es una sustancia que se encuentra en la sangre de una persona que suele tener cáncer de próstata. Además, el diagnóstico se apoya en una ecografía transrectal a través de un catéter. Este proceso integral ayuda a determinar la extensión del cáncer de próstata y a designar el tratamiento correcto. El estado de la lesión de próstata se evalúa mediante la práctica de una resonancia magnética (MRI). Es un procedimiento realizado por ondas de radio y una computadora que crea imágenes detalladas de áreas de la próstata. Analiza la condición de la próstata y determina el procedimiento o tratamiento de acuerdo con el estado de la lesión, por ejemplo, cirugía, radioterapia u observación monitoreada. Para definir qué tipo de tratamiento es fundamental analizar los diferentes estadios de la enfermedad y el Gleason Score, una medida del grado histológico, que va de 2 a 10, que indica la probabilidad de diseminación o extensión del tumor. Esta investigación se centra en el análisis y la extracción de medidas para clasificar formas de lesiones prostáticas que apoyen su diagnóstico. Considera la categorización PI-RADS, que actualmente determina la probabilidad de padecer cáncer de próstata clínicamente significativo. Para ello, se realizó un análisis utilizando una interpretación geométrica de diferentes categorizaciones de cáncer (4-5). Se realizó un procesamiento digital de imágenes de Python en T2, ADC y DWI aplicando el concepto de curva, momentos Zernike, dimensión fractal, dimensión Caliper, la curvatura absoluta total, la flexión de energía, dirección, convexidad, circularidad, compacidad, momentos Hu, dimensión, excentricidad, extensión, solidez, orientación, longitud del eje más grande, longitud del eje más pequeño, radio, centro, centroide, longitud y área

Effects of discrete wavelet compression on automated mammographic shape recognition

At present early detection is critical for the cure of breast cancer. Mammography is a breast screening technique which can detect breast cancer at the earliest possible stage. Mammographic lesions are typically classified into three shape classes, namely round, nodular and stellate. Presently this classification is done by experienced radiologists. In order to increase the speed and decrease the cost of diagnosis, automated recognition systems are being developed. This study analyses an automated classification procedure and its sensitivity to wavelet based image compression; In this study, the mammographic shape images are compressed using discrete wavelet compression and then classified using statistical classification methods. First, one dimensional compression is done on the radial distance measure and the shape features are extracted. Second, linear discriminant analysis is used to compute the weightings of the features. Third, a minimum distance Euclidean classifier and the leave-one-out test method is used for classification. Lastly, a two dimensional compression is performed on the images, and the above process of feature extraction and classification is repeated. The results are compared with those obtained with uncompressed mammographic images

Connected image processing with multivariate attributes: an unsupervised Markovian classification approach

International audienceThis article presents a new approach for constructing connected operators for image processing and analysis. It relies on a hierarchical Markovian unsupervised algorithm in order to classify the nodes of the traditional Max-Tree. This approach enables to naturally handle multivariate attributes in a robust non-local way. The technique is demonstrated on several image analysis tasks: filtering, segmentation, and source detection, on astronomical and biomedical images. The obtained results show that the method is competitive despite its general formulation. This article provides also a new insight in the field of hierarchical Markovian image processing showing that morphological trees can advantageously replace traditional quadtrees

A Sensitivity Study of L-Band Synthetic Aperture Radar Measurements to the Internal Variations and Evolving Nature of Oil Slicks

This thesis focuses on the use of multi-polarization synthetic aperture radar (SAR) for characterization of marine oil spills. In particular, the potential of detecting internal zones within oil slicks in SAR scenes are investigated by a direct within-slick segmentation scheme, along with a sensitivity study of SAR measurements to the evolving nature of oil slicks. A simple, k-means clustering algorithm, along with a Gaussian Mixture Model are separately applied, giving rise to a comparative study of the internal class structures obtained by both strategies. As no optical imagery is available for verification, the within-slick segmentations are evaluated with respect to the behavior of a set of selected polarimetric features, the prevailing wind conditions and weathering processes. In addition, a fake zone detection scheme is established to help determine if the class structures obtained potentially reflect actual internal variations within the slicks. Further, the evolving nature of oil slicks is studied based on the temporal development of a set of selected geometric region descriptors. Two data sets are available for the investigation presented in this thesis, both captured by a full-polarization L-band airborne SAR system with high spatial- and temporal resolution. The results obtained with respect to the zone detection scheme developed supports the hypothesis of the existence of detectable zones within oil spills in SAR scenes. Additionally, the method established for studying the evolving nature of oil slicks is found convenient for accessing the general behavior of the slicks, and simplifies interpretation