Enhancing the detection accuracy of the edges of the geological features within the subsurface remains a significant objective in geophysical data interpretation. Despite numerous advancements, approaches stemming from the directional gradients of gravity and magnetic fields still grapple with challenges such as low-resolution outcomes and susceptibility to noise contamination. In this study, we introduce a novel filtering framework based on the total horizontal gradient and its derivatives, designed to yield more precise and coherent edges free from false boundaries or disruptive artifacts. Validation using synthetic Bishop complex magnetic and gravity datasets, alongside Tuangiao aeromagnetic data from Vietnam, substantiates the robustness and applicability of our modified approach. Furthermore, recognizing the inherent susceptibility of edge detection filters to noise contamination resulting from directional derivatives, we employ the recently developed modified non-local means (MNLM) algorithm to alleviate noise effects prior to the analysis of noisy synthetic and real datasets. Our findings confirm the efficacy of the proposed method in reducing false artifacts and identifying edges with heightened precision, positioning MHGA as a valuable alternative for processing potential field data.