We can represent these 2-D regions by their low-order statistics.
Clusters of 2-D points have 2-D spatial means and covariance matrices,
which we shall denote and . The blob spatial statistics
are described in terms of their second-order properties; for computational
convenience we will interpret this as a Gaussian model:
The Gaussian interpretation is not terribly significant, because we also keep a pixel-by-pixel support map showing the actual occupancy. We define , the support map for blob k, to be
The aggregate support map s(x,y) over all the blob models represents the segmentation of the image into spatio-color classes.
Like other representations used in computer vision and signal analysis, including superquadrics, modal analysis, and eigenvector representations, blobs represent the global aspects of the shape and can be augmented with higher-order statistics to attain more detail if the data supports it. The reduction of degrees of freedom from individual pixels to blob parameters is a form of regularization which allows the ill-conditioned problem to be solved in a principled and stable way.
Each blob has a spatial (x,y) and color (Y,U,V) component. Color is expressed in the YUV color space. We could additionally use motion and texture measurements as part of the blob descriptions, but current hardware has restricted us to use position and color only. Because of their different semantics, the spatial and color distributions are assumed to be independent. That is, is block-diagonal, with uncoupled spatial and spectral components. Each blob can also have a detailed representation of its shape and appearance, modeled as differences from the underlying blob statistics. The ability to efficiently compute compact representations of people's appearance is useful for low-bandwidth applications.
The statistics of each blob are recursively updated to combine information contained in the most recent image with knowledge contained in the current class statistics and the priors.