Soft Stacking

In this paper, we present a continuous approach to ordering 2D images when compositing. Previous methods for stacking image layers require them to appear in a single (though possibly different) order at every point in the image. Our soft stacking approach removes this restriction – allowing layers to stack as if they were volumes of fog, appearing partially in front of and partially in back of other layers within the same pixel, and moving smoothly through other layers across the image. Our approach involves augmenting each pixel with stacking coefficients – a necessary and sufficient representation for sub-pixel stacking complexity. These stacking coefficients arise naturally when considering sub-pixel stacking complexity, much as continuous (alpha) transparency arises when considering sub-pixel coverage complexity. While the number of stacking coefficients required to represent all possible sub-pixel stacking arrangements is factorial in the number of layers in the stack, in many practical situations only a small subset of the stacking coefficients are nonzero. We use this sparsity as the basis of a prototype that allows artists to interactively paint stacking adjustments into composites. Additionally, we demonstrate how to generate optimally-stacked images under a generalized notion of stacking consistency.