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This paper first presents a generic geometric prior for the image processing problems. The proposed term allows each individual pixel to automatically choose its own geometric prior. This behavior is fundamentally different from traditional regularizations that use only one prior for all pixels. This term, however, is difficult to be minimized by traditional optimization methods. Therefore, we further propose an iterative image filter to impose this generic geometric prior. Moreover, this proposed filter has a neural network representation, where the kernels in our filter can be learned based on the convolutional neural network. Several numerical experiments are performed to confirm the effectiveness and efficiency of this new filter and its related neural networks.