Decomposing Images into Layers via RGB-Space Geometry

In digital image editing software, layers organize images. However, layers are often not explicitly represented in the final image, and may never have existed for a scanned physical painting or a photograph. We propose a technique to decompose an image into layers. In our decomposition, each layer represents a single-color coat of paint applied with varying opacity. Our decomposition is based on the image’s RGB-space geometry. In RGB-space, the linear nature of the standard Porter-Duff [1984] “over” pixel compositing operation implies a geometric structure. The vertices of the convex hull of image pixels in RGB-space correspond to a palette of paint colors. These colors may be “hidden” and inaccessible to algorithms based on clustering visible colors. For our layer decomposition, users choose the palette size (degree of simplification to perform on the convex hull), as well as a layer order for the paint colors (vertices). We then solve a constrained optimization problem to find translucent, spatially coherent opacity for each layer, such that the composition of the layers reproduces the original image. We demonstrate the utility of the resulting decompositions for recoloring (global and local) and object insertion. Our layers can be interpreted as generalized barycentric coordinates; we compare to these and other recoloring approaches.