The Chan-Vese method, which is based on level sets, principally employs region information for sequential evolutions of active contours of concern towards the object of interest, with the goal of minimising the fitness energy functional associated with the process. Orthodox gradient descent methods have been widely used to solve such optimization problems, but they have the flaw of becoming trapped in local minima and typically need an excessive amount of time to converge. This paper provides a Chan-Vese model with a modified gradient descent search strategy, dubbed the Delta-Bar-Delta learning algorithm, that reduces susceptibility to local minima and increases convergence rate. The suggested search method, when combined with the Chan-Vese model, outperforms classic gradient descent and previously proposed alternative adaption algorithms in this context, according to simulation findings. In this research, we present a novel and robust hierarchical GSA K-means clustering approach for segmenting fused images using the Principal Component Analysis method. Image fusion is a method of combining two or more pictures into a single image. The conventional Chan-Vese (CV) technique has been completely implemented to segment pictures using the iterative K-means clustering algorithm, which partitions an image into K number of groups. However, if the clusters' beginning points aren't chosen correctly, the approach frequently produces erroneous segmentation results. The Gravitational Search Algorithm (GSA) is used in this study to reformulate the issue and solve the new Chan-Vese picture segmentation formulation in such a way that it is invariant to the original cluster position. Extensive testing has been carried out on two-cluster and, in each case; the results of this proposed HGSA_K-means process show the improved achievement to segment the fused images.