By Ken Follett

Dive into the number one manhattan *Times* bestselling author’s masterpiece of medieval drama, *The Pillars of the Earth*, and its long-awaited sequel, *World with out End*. Sweeping from twelfth to 14th century England, based round the construction of an outstanding cathedral and the households and members tormented by it, those novels “will carry you, fascinate you, encompass you” (Chicago *Tribune*) and “you will willingly lose your self for fairly a spell” (Denver *Post*).

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CfαK (x))). Random Germs and Stochastic Watershed 19 A limited number K of factorial axes is usually chosen. It is smaller than the channels number L. Therefore FCA can be seen as a projection of initial vector pixels in a factor space with a lower dimension. Moreover FCA can be used to reduce noise in the image [5,7]. Consequently, we have two spaces for the multivariate segmentation: the multispectral image space (MIS) and the factor image space (FIS). Fig. 1 gives an example of a ﬁve bands satellite simulated image PLEIADES, acquired by the CNES (Centre National d’Etudes Spatiales, the French space agency) and provided by Flouzat [4], and its corresponding FCA representation.

As for PCA, from selected factorial FCA axes the image can be partially reconstructed. The metric used in FCA is the chi-squared, which is adapted to probability laws and normalized by channels weight. FCA can be seen as a transformation going from image space to factorial space. In factorial space the coordinates of the pixels vector on each factorial axis are called pixels factors. The pixels factors can be considered as another multispectral image whose channels correspond to factorial axes: ζ : T L → T K /K < L (fλ (x) → cfα (x) = (cfα1 (x), .

The concluding section looks at some future developments in astrophysical source separation. 2 FD-CCA Model Learning Before describing our algorithm, we briefly formalize the separation problem and introduce the notation used throughout this paper. In our model, the measured data x at a generic pixel i are generated from the underlying components s through a linear, space-invariant, noisy, convolutional mixture operator described as follows [1]: x(i) = (H*As)(i) + n(i), (1) where x and s are N-dimensional and M-dimensional vectors, respectively, with N≥M, A is an unknown N×M space-invariant matrix, n is the N-dimensional, signalindependent, noise vector, the asterisk means convolution, and H is an N×N diagonal matrix whose entries are known convolutional kernels that model the telescope radiation patterns at the related measurement channels.