The solution of the segmentation problem requires a mechanism for partitioning the image array into low-level entities based on a model of the underlying image structure. A piecewise-smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete, noiseless image reconstruction based on the extracted functions and regions. Surface curvature sign labeling provides an initial coarse image segmentation, which is refined by an iterative region-growing method based on variable-order surface fitting. Experimental results show the algorithm's performance on six range images and three intensity images.< >