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In this paper, first, we investigate the CNN templates producing periodic patterns. Next, two image processing algorithms using periodic pattern formation in cellular neural networks are proposed. By applying one to a certain image, area having spatial uniformity is removed from the original image and only parts without spatial uniformity remain. Simulation results show that when this algorithm is applied to an image containing characters (texts) or a human face image, only characters or eyes and mouth are extracted. Also, by applying the other to texture image, periodicity is enhanced in area having spatial periodicity, and texture can be segmented. Simulation results show that when this algorithm is applied to image that consists of four kinds of textures, each texture area can be segmented.