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where rnj and rnj are the pixel values of index j inside the original block rn and the collage block n , respectively The joining operation, called parent collage, is detailed r in the following section 10321 Collage of a source block onto a destination block The collage operation of a source block d (n) onto a destination block rn , realized by the transformation n , decomposes into two parts: a spatial transformation deforms the support of block d (n) ; a mass transformation acts on the pixel luminance of the deformed d (n) block

These two points are further detailed in this section Spatial transformation shrinks the block source d (n) of size D2 to the scale and overlaps it with the destination block rn of size B 2 The block thus transformed, noted (n) b2 , is obtained by decimating the pixels of the source block: a pixel of coordinates (n) (xi , yj ) in b2 is given by the following equation: b2 (xi , yj ) =

1 d (n) (xk , yl ) + d (n) (xk , yl+1 ) 4 + d (n) (xk+1 , yl ) + d (n) (xk+1 , yl+1 )

(1017)

.

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where (xk , yl ) are the coordinates of a pixel of intensity d (n) , and belonging to the block d (n) Mass transformation acts on block b2 to approximate the destination block rn The complexity of this transformation depends on the nature of the block rn under consideration To do so, Jacquin proposes classifying the square blocks using the method developed by Ramamurthi and Gersho [RAM 86]: all blocks of an image are grouped into three classes; homogenous blocks, textured blocks and blocks with contours (simple and divided) Depending on the class which the destination block rn belongs to, a more or less complex mass transformation is associated with it This (n) (n) depends on the decimated block b2 and/or on a constant block b1 formed of pixels (n) (n) all equal to one The block b2 will be associated with a scale coef cient denoted 2 (n) (n) and the block b1 will be associated with a shift coef cient noted 1 The choice of transformation type depends on the following procedure: if the block rn is homogenous: absorption of the gray-levels of rn No search for source blocks d (n) is carried out The transformation of rn , coded with Is bits, reads: n = 1 b1 r

1 SC Wheelwright and K Clarke (1992) Creating Project Plans to Focus Product Development, Harvard Business Review, 70 (2), pp 70 82 2 R Katz and TJ Allen (1985) Project Performance and Locus of Influence in the R&D Matrix, Academy of Management Journal, 28(1), 57 87; DH Gobeli and EW Larson (1987) Relative Effectiveness of Different Project Structures, Project Management Journal, 18(2), 81 85; and RC Ford and WA Randolph (1992) Cross-Functional Structures: A Review and Integration of Matrix Organization and Project Management, Journal of Management, 18(2), 267 294

(n) (n) (n) (n)

where the integer 1 lies between 0 and 255; if the block rn is textured: search for the source block d (n) , then perform contrast change and apply shifts The transformation of d (n) , coded with Im bits, reads: n = 2 b2 + 1 b1 r

(n) (n) (n) (n) (n)

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