Equivalent (k0,k1)(k0,k1)-covering and generalized digital lifting

This paper studies various properties of (k0,k1)(k0,k1)-continuity in relation to uniform (k0,k1)(k0,k1)-continuity and a pasting theorem, which can be used in image synthesis, image segmentation, and image weaving. Furthermore, we establish an equivalent (k0,k1)(k0,k1)-covering and provide some condition to construct the generalized digital lifting of an equivalent (k0,k1)(k0,k1)-covering map which is used to calculate the digital fundamental group of a digital image and to classify digital images by a discrete Deck’s transformation group. To be specific, let p:(E,e0)→(B,b0)p:(E,e0)→(B,b0) be a pointed (k0,k1)(k0,k1)-covering map and let f:(X,x0)→(B,b0)f:(X,x0)→(B,b0) be a pointed (k2,k1)(k2,k1)-continuous map. Then, we can provide a condition to have a concerning pointed (k2,k0)(k2,k0)-continuous map f˜:(X,x0)→(E,e0) such that p∘f˜=f.