Carlos Jacanamejoy Jamioy

La congruencia de fase es una técnica de detección de bordes de imágenes que, mediante el análisis de la fase de los componentes de frecuencia de una señal, permite encontrar la ubicación de los bordes. Según la función matemática utilizada para la cuantificación de la congruencia de fase, el resultado de la segmentación presenta variabilidad, lo cual puede resultar en una mejora potencial en la detección. Por ello, en este trabajo se realiza un estudio de la función exponencial, boxcar y cuártica utilizando dos métricas para la evaluación de técnicas de segmentación, el índice de Dice-Sorensen y la figura de mérito de Pratt. Para este estudio, se introduce una pequeña base de datos que incluye 30 imágenes originales y sus correspondientes imágenes de referencia. Además, para comparar la congruencia de fase con las técnicas basadas en el gradiente, se compararon los resultados con los obtenidos con el método de detección Canny, encontrando que la congruencia de fase permite una mejor detección de bordes en la mayoría de los casos.

Edge detection is a technique in digital image processing that detects the contours of objects based on changes in brightness. Edges can be used to determine the size, orientation, and properties of the object of interest within an image. There are different techniques employed for edge detection, one of them being phase congruency, a recently developed but still relatively unknown technique due to its mathematical and computational complexity compared to more popular methods. Additionally, it requires the adjustment of a greater number of parameters than traditional techniques. Recently, a unique formulation was proposed for the mathematical description of phase congruency, leading to a better understanding of the technique. This formulation consists of three factors, including a quantification function, which, depending on its characteristics, allows for improved edge detection. However, a detailed study of the characteristics had not been conducted. Therefore, this article proposes the development of a generalized function for quantifying phase congruency, based on the family of functions that, according to a previous study, yielded the best results in edge detection.

Phase congruency is a technique that has been used for edge, corner and symmetry detection. Its implementation through the use of monogenic filters has improved its computational cost. For this purpose, different methods of implementation have been published, but they do not use a common notation, which makes it difficult to understand. Therefore, this paper presents a unified mathematical formulation that allows a general understanding of the Monogenic phase congruency concepts and establishes criteria for its use. A new protocol for parameter tuning is also described, allowing better practical results to be obtained with this technique. Some examples are presented allowing one to observe the changes produced in the parameter tuning, evidencing the validity of the proposed criteria.

Gaussian noise estimation is an important step in some of the more recently developed noise removal methods. This is a difficult task and although several estimation techniques have been proposed recently, they generally do not produce good results. In a previous comparative study, among several noise estimation techniques, a method proposed in 2017 by Turajlić was found to give the best results. Although acceptable, they are still far from ideal. Therefore, several changes to this method are introduced in this paper to improve the estimation. Tests on monochromatic images contaminated with different levels of Gaussian noise showed that the modified method produces a significant improvement in the estimation of Gaussian noise, over 35%, at a slightly higher computational cost.

This paper introduces a method to enforce balanced power distribution between the stages of a single-phase transformer-based cascaded multilevel inverter using the new asymmetric ratio 6:7:8:9 between stages. Since the inverter is fed by a single DC source, asymmetry is enforced by means of the transformer turns ratio providing multiple redundant switching patterns to synthesize an output signal of until 35 levels. As it is developed in the paper, optimum switching patterns for the proposed ratio allow reducing typical power unbalance produced by commonly used ratios in four stage multilevel inverters (1:2:4:8 and 1:3:9:27). The proposed method consists on determining off-line the best switching patterns for minimizing deviation error, and then, storing them as lock-up tables in the digital device controlling the inverter. By permanently reproducing the selected switching patterns, balanced power distribution is achieved. A closed-loop control approach to regulate the RMS value of the output voltage compatible with the proposed method is also developed. The experimental results using a laboratory prototype are presented validating the entire approach.