2-D generating function of the zernike polynomials and their application for image classification

This work proposes a new approach to find the generating function (GF) of the Zernike polynomials in two dimensional form. Combining the methods of GFs and discrete-time systems, we can develop two dimensional digital systems for systematic generation of entire orders of Zernike polynomials. We establish two different formulas for the GF of the radial Zernike polynomials based on both the degree and the azimuthal order of the radial polynomials. In this paper, we use four terms recurrence relation instead of the ordinary three terms recursion to calculate the radial Zernike polynomials and their GFs using unilateral 2D Z-transform. A spatio-temporal implementation scheme is developed for generation of the radial Zernike polynomials. Since Zernike moments (ZMs) are invariant with respect to rotation, translation and scaling, the experimental schemes show the image classification applications by using the proposed algorithm

Zernike velocity moments for sequence-based description of moving features

The increasing interest in processing sequences of images motivates development of techniques for sequence-based object analysis and description. Accordingly, new velocity moments have been developed to allow a statistical description of both shape and associated motion through an image sequence. Through a generic framework motion information is determined using the established centralised moments, enabling statistical moments to be applied to motion based time series analysis. The translation invariant Cartesian velocity moments suffer from highly correlated descriptions due to their non-orthogonality. The new Zernike velocity moments overcome this by using orthogonal spatial descriptions through the proven orthogonal Zernike basis. Further, they are translation and scale invariant. To illustrate their benefits and application the Zernike velocity moments have been applied to gait recognition—an emergent biometric. Good recognition results have been achieved on multiple datasets using relatively few spatial and/or motion features and basic feature selection and classification techniques. The prime aim of this new technique is to allow the generation of statistical features which encode shape and motion information, with generic application capability. Applied performance analyses illustrate the properties of the Zernike velocity moments which exploit temporal correlation to improve a shape's description. It is demonstrated how the temporal correlation improves the performance of the descriptor under more generalised application scenarios, including reduced resolution imagery and occlusion

Filter-generating system of Zernike polynomials

This work proposes a new approach to find the generating function (GF) of the Zernike polynomials in two dimensional form. Combining the methods of GFs and discrete-time systems, we can develop two dimensional digital systems for systematic generation of entire orders of Zernike polynomials. We establish two different formulas for the GF of the radial Zernike polynomials based on both the degree and the azimuthal order of the radial polynomials. In this paper, we use four terms recurrence relation instead of the ordinary three terms recursion to calculate the radial Zernike polynomials and their GFs using unilateral 2D Z-transform. A spatio-temporal implementation scheme is developed for generation of the radial Zernike polynomials. The case study shows a reliable way to evaluate Zernike polynomials with arbitrary degrees and azimuthal orders

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

A very simple framework for 3D human poses estimation using a single 2D image: Comparison of geometric moments descriptors.

In this paper, we propose a framework in order to automatically extract the 3D pose of an individual from a single silhouette image obtained with a classical low-cost camera without any depth information. By pose, we mean the configuration of human bones in order to reconstruct a 3D skeleton representing the 3D posture of the detected human. Our approach combines prior learned correspondences between silhouettes and skeletons extracted from simulated 3D human models publicly available on the internet. The main advantages of such approach are that silhouettes can be very easily extracted from video, and 3D human models can be animated using motion capture data in order to quickly build any movement training data. In order to match detected silhouettes with simulated silhouettes, we compared geometrics invariants moments. According to our results, we show that the proposed method provides very promising results with a very low time processing