  Image segmentation algorithms often depend on appearance models that
characterize the distribution of pixel values in different image regions. We
describe a new approach for estimating appearance models directly from an
image, without explicit consideration of the pixels that make up each region.
Our approach is based on novel algebraic expressions that relate local image
statistics to the appearance of spatially coherent regions. We describe two
algorithms that can use the aforementioned algebraic expressions to estimate
appearance models directly from an image. The first algorithm solves a system
of linear and quadratic equations using a least squares formulation. The second
algorithm is a spectral method based on an eigenvector computation. We present
experimental results that demonstrate the proposed methods work well in
practice and lead to effective image segmentation algorithms.
