  Image segmentation algorithms often depend on appearance models that
characterize the distribution of pixel values in different image regions. We
describe a novel 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 algebraic expressions that relate local image
statistics to the appearance models of spatially coherent regions. We describe
two algorithms that can use the aforementioned algebraic expressions for
estimating appearance models. The first algorithm is based on solving a system
of linear and quadratic equations. 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.
