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To address the issues that the traditional Chan-Vese (C-V) model tends to lose weak boundaries and fails to correctly segment inhomogeneous regions when processing images with intensity inhomogeneity, this paper proposes an improved locally adaptive C-V model. Based on the traditional global binary fitting energy term, the proposed model introduces a local neighborhood gray-level mean computed via a Gaussian window, thereby constructing a segmentation energy functional that incorporates both global and local information. By deriving the level set evolution equation through the calculus of variations, the contour driving force is simultaneously constrained by the global region uniformity assumption and the local gray-level variation characteristics. This allows the model to accurately capture large-scale structures while finely delineating gray-level variations in the neighborhood of each point, thus preserving weak contrast edges. The theoretical derivation, computational complexity analysis, and complete numerical implementation procedure are presented in detail. Comparative experiments are conducted on a synthetic liver image with intensity inhomogeneity, using Dice similarity coefficient, Jaccard index, sensitivity, specificity, and Hausdorff distance for quantitative evaluation. The results demonstrate that the proposed improved algorithm achieves significantly higher segmentation accuracy than the traditional C-V model and the purely local model, with a Dice coefficient of 1.000 and a specificity of 1.000. It effectively segments inhomogeneous targets without background false positives, exhibiting good robustness.