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.

Hardness is one of the most important mechanical properties of materials, since it is used to estimate their quality and to determine their suitability for a particular application. One method of determining quality is the Vickers hardness test, in which the resistance to plastic deformation at the surface of the material is measured after applying force with an indenter. The hardness is measured from the sample image, which is a tedious, time-consuming, and prone to human error procedure. Therefore, in this work, a new automatic method based on image processing techniques is proposed, allowing for obtaining results quickly and more accurately even with high irregularities in the indentation mark. For the development and validation of the method, a set of microscopy images of samples indented with applied forces of $5N$ and $10N$ on AISI D2 steel with and without quenching, tempering heat treatment and samples coated with titanium niobium nitride (TiNbN) was used. The proposed method was implemented as a plugin of the ImageJ program, allowing for obtaining reproducible Vickers hardness results in an average time of $2.05$ seconds with an accuracy of $98.3\%$ and a maximum error of $4.5\%$ with respect to the values obtained manually, used as a golden standard.

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.

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.