Improving the Otsu Thresholding Method of Global Binarization Using Ring Theory for Ultrasonographies of Congestive Heart Failure

Ring Theory states that a ring is an algebraic structure where two binary operations can be performed among the elements addition and multiplication. Binarization is a method of image processing where values within pixels are reduced to a scale from zero to one, with zero representing the most absence of light and one representing the most presence of light. Currently, sonograms are implemented in scanning for congestive heart failure. However, the renowned Playboy Bunny symbol representing the ailment becomes increasingly difficult to isolate due to surrounding organs and lower quality image productions. This paper examines the Otsu thresholding method and incorporates new elements to account for different image features meant to better isolate congestive heart failure indicators in ultrasound images.

Application of the Ring Theory in the Segmentation of Digital Images

Ring theory is one of the branches of the abstract algebra that has been broadly used in images. However, ring theory has not been very related with image segmentation. In this paper, we propose a new index of similarity among images using Zn rings and the entropy function. This new index was applied as a new stopping criterion to the Mean Shift Iterative Algorithm with the goal to reach a better segmentation. An analysis on the performance of the algorithm with this new stopping criterion is carried out. The obtained results proved that the new index is a suitable tool to compare images.

New similarity index based on entropy and group theory

In this work, we propose a new similarity index for images considering the entropy function and group theory. This index considers an algebraic group of images, it is defined by an inner law that provides a novel approach for the subtraction of images. Through an equivalence relationship in the field of images, we prove the existence of the quotient group, on which the new similarity index is defined. We also present the main properties of the new index, and the immediate application thereof as a stopping criterion of the "Mean Shift Iterative Algorithm".

A new stopping criterion for the mean shift iterative algorithm

The mean shift iterative algorithm was proposed in 2006, for using the entropy as a stopping criterion. From then on, a theoretical base has been developed and a group of applications has been carried out using this algorithm. This paper proposes a new stopping criterion for the mean shift iterative algorithm, where stopping threshold via entropy is used now, but in another way. Many segmentation experiments were carried out by utilizing standard images and it was verified that a better segmentation was reached, and that the algorithm had better stability. An analysis on the convergence, through a theorem, with the new stopping criterion was carried out. The goal of this paper is to compare the new stopping criterion with the old criterion. For this reason, the obtained results were not compared with other segmentation approaches, since with the old stopping criterion were previously carried out.

Stopping Criterion for the Mean Shift Iterative Algorithm

Image segmentation is a critical step in computer vision tasks constituting an essential issue for pattern recognition and visual interpretation. In this paper, we propose a new stopping criterion for the mean shift iterative algorithm by using images defined in Zn ring, with the goal of reaching a better segmentation. We carried out also a study on the weak and strong of equivalence classes between two images. An analysis on the convergence with this new stopping criterion is carried out too.