Segmentation and Estimation of Spatially Varying Illumination

In this paper, we present an unsupervised method for segmenting the illuminant regions and estimating the illumination power spectrum from a single image of a scene lit by multiple light sources. Here, illuminant region segmentation is cast as a probabilistic clustering problem in the image spectral radiance space. We formulate the problem in an optimization setting, which aims to maximize the likelihood of the image radiance with respect to a mixture model while enforcing a spatial smoothness constraint on the illuminant spectrum. We initialize the sample pixel set under each illuminant via a projection of the image radiance spectra onto a low-dimensional subspace spanned by a randomly chosen subset of spectra. Subsequently, we optimize the objective function in a coordinate-ascent manner by updating the weights of the mixture components, sample pixel set under each illuminant, and illuminant posterior probabilities. We then estimate the illuminant power spectrum per pixel making use of these posterior probabilities. We compare our method with a number of alternatives for the tasks of illumination region segmentation, illumination color estimation, and color correction. Our experiments show the effectiveness of our method as applied to one hyperspectral and three trichromatic image data sets.