Construction of Picture Maze along Set of Image Dot Vertices

There are three interests in this study. First is to make an analogy between graph theory and image processing. Given a number of image items (dots) on a picture, this paper shows a way to make a path (closed path) connecting and traversing all of them but each only once, imitating to construct a path (closed path) on a plane by considering a dot as a vertex and a connecting line as an edge. This looks like constructing a Hamiltonian path on a plane and drawing a plane graph connecting all vertices with no crossing among the edges. Second is to construct the maze based on the obtained path with some detouring within each of image items (dots). This path could be very long and complex. Owing to this path, the maze is constructed in an organized manner. Third is to apply this path making procedure to different pictures with different image shapes like symbols or English letters --- possibly generating a complex picture maze. Pictures or some meaningful message appear when the maze is solved. Algorithm and its proof are given with a number of successful experimental results.