Analysis of Scanline and Minimum Entropy Selection Heuristics in Model Synthesis and Wave Function Collapse

In this paper, we analyze two versions of a texture synthesis algorithm, study the cases in which they fail to produce a successful result and present modifications that could be made to lessen their rates of failure. This algorithm, Model Synthesis, and its variation Wave Function Collapse are designed to take in a small sample input image, or set of image constraints, and produce a larger pseudorandom output image in which every region of the output image is locally similar to an element of the input image. Both versions of the algorithm accomplish this task by considering their output image as a grid of cells with each cell initially in a superposition of all possibilities for itself and resolving cells one by one until all cells have been resolved from their superposition to a fixed value. One of the key differences between the two versions of the algorithm is the order in which cells are selected to be resolved, one simply selects in a scanline order, while the other resolves first those cells that have the minimum entropy, and thus which we can be most certain of their eventual state. For many inputs, the minimum entropy model reaches a state in which its output is not consistent with the input and thus fails, while the scanline model does not. This paper looks at the cases in which this occurs and concludes that this is often caused by the minimum entropy model creating regions of elevated constraints in its solution. Finally, it presents a possible alteration to the algorithm which allows a minimum entropy model to avoid this manner of failure among a subset of test cases.