A method for matching stereo images using a neural network is presented. We first fit a polynomial to find a smooth continuous intensity function in a window and estimate the first order intensity derivatives. Combination of smoothing and differentiation results in a window operator which functions very similar to the human eye in detecting the intensity changes. Since natural stereo images are usually digitized for the implementation on a digital computer, we consider the effect of spatial quantization on the estimation of the derivatives from natural images. A neural network is then employed for matching the estimated first order derivatives under the epipolar, photometric and smoothness constraints. Owing to the dense intensity derivatives a dense array of disparities is generated with only a few iterations. This method does not require surface interpolation. Experimental results using natural images pairs are presented to demonstrate the efficacy of our method.