The notion of representing a color image as a set of translucent layers, each of a single (non-primary) color, is useful in the field of digital image painting. Although the layering is not present in the source image, and may or may not reflect the production of the image, such a layered representation is useful for image editing. The authors present a method for decomposing a color image into suitable layers of single, translucent colors.

When image layers of different color and varying translucency are overlaid, the resulting image is determined by a compositing method that considers the order and translucency of each layer. The well-known Porter–Duff compositing operation determines the resulting color at each image location; note that the order of the layers is significant. This can be likened to the work of a painter applying individual pigments with varying opacity across an image. The current paper describes a process for the converse operation: from a resulting image, define a stack of translucent single-color planes that will produce the original image.

The mathematics of compositing dictates that the layer colors will form a convex hull in RGB space of the set of all colors in the original image. The authors show that the proper (tightest) convex hull contains too many colors for practical use; they relax the hull to a larger-volume polyhedron with fewer vertices, and they describe several methods for accomplishing this. Their examples have four to eight colors in the palette. Note that colors found in this fashion may be “impossible” colors, outside the RGB cube; these points are truncated to the closest point within valid RGB space.

Once the palette of colors is chosen, the translucency of each layer at each image location is computed. First, the order of the layers is determined manually. Then, an optimization method is applied to compute barycentric coordinates, expressing each pixel in the resulting image as a weighted sum of the layer colors; the weights and order determine the translucencies. The paper presents the results of applying the process to a number of images, both digitally and physically painted as well as natural scene images. Runtime is significant at several minutes for most images presented.

Tan et al. present a creative method of decomposing painted images into translucent monochrome layers to facilitate digital editing. The work is founded on well-referenced earlier research. The authors do an especially good job of describing the areas of their technique that they recommend for future work; these include better optimization of color selection, allowing multiple layers of the same color (as painters often do), and reducing the need for user input.