The generalizability and adaptiveness of multi-modal image matching (MMIM) techniques are hampered by the nonlinear radiometric differences that vary in a highly non-uniform manner across different modal combinations. A major challenge is the extensive filter tuning required by many filter-based matching methods to mitigate the impact of radiometric aberrations. Additionally, the low correct matching rate resulting from the non-repeatability and low similarity of local or detailed features presents another significant obstacle. In this paper, we introduce a novel MMIM framework, called Adaptive Matching with enhanced Edge Sketches (AMES), for reducing manual interference in filter parameter configuration and improving the correct matching rate of extracted feature points. Specifically, AMES trains a support vector regression model to adaptively predict the optimized filtering parameters for each test image using its internal statistical factors as input. We also propose a sketch feature enhancement method, based on fusing multi-scale moment maps through principal component analysis, for cross-modal adaptive feature point extraction. We generate matching results by applying feature descriptors within the Log-Polar window and performing outlier removal following a coarse-to-fine strategy. In an evaluation involving four datasets comprising 1055 image pairs with 26 different cross-modal combinations, the assessment of 10,599 manually measured checkpoints demonstrates that AMES surpasses the state-of-the-art in terms of success rate, correct matching rate, point coverage, average matching accuracy, and spatial distribution uniformity. Our source code and multi-modal image datasets are publicly available at https://dpcv.whu.edu.cn/zm1/gksjj.htm.