Summary: Due to the fact that the segmentation accuracy of the local binary fitting energy based variational model (LBF model) is highly dependent on the kernel bandwidth, and it always leads to unsatisfactory segmentation results (e.g., unnecessary contours, rough boundaries) of inhomogeneous images because of inappropriate bandwidth, an novel edge-preserving local fitting model is proposed and well adapted to segmented images with intensity inhomogeneity. First, a geodesic time based kernel using spatial location and spectral gradient is defined, and it provides an adaptive geodesic neighborhood for every pixel. Then, an efficient multichannel gradient based extension combined with adjusted dissimilarity measure is enforced to segment color and multispectral images. Experimental results show that the proposed model can remain potential edge information while using a larger bandwidth, and desirable segmentation results of both gray and color images can be obtained.