Notations

Spaces, sets
	space dimension
	real d-dimensional vector space
	integer d-dimensional vector space
	compact interval in
	discrete interval in or
	boolean set
	set of n first natural integers
	set of b – a integers connecting from a to b – 1

Functional notations
	set of applications X → Y
	set of tables or maps on domain X (discrete) with values in Y
f(b)	value of the function f in b
	value of the sample b of the map/table t
	integer part (the nearest inferior integer) in x
	nearest superior integer to x
	fractional part of x
[x]	the nearest integer to x: by convention, if x = k + 0.5 with

Objects
i, j, k, l, m, n	integer numbers
x, y, z	coordinates (integer or real)
t, u, v, λ, μ	real numbers
D, Δ	real lines
P, Π	real planes
v, w	vectors
A, B, C, …	points in the real affine space 2 or 3
AB	bi-point vector ranging from A to B
M, A, B	matrices
R, T	rotation and translation matrices
f, g, h	applications, functions
Φ, Ψ	operators on other sets d, d
	rotation and translation function
G, Γ	graphs
	angles
ε	threshold

Digital images
	d-dimensional signal indexation domains or spaces with a size of d
	for d = 2[3] we will use the numbers of columns, lines and planes by default
	pixel position (d = 2) or voxel position (d =3) within the indexation domain
	scalar spaces of digital values for sample components. The correspond to the number of bits used for coding real values () or integer values ( or )
	generic vectoral space for samples’ digital multi-component value
	2D or 3D signal (image or volume) table or map of values in ε indexed by
	the signal sample S in position
Neighborhoods
	d-dimensional shape, set of vectors coding the positions of each point in the shape in relation to the reference point
	neighborhood in the shape placed in : translated of in or by p
	neighborhood in the shape truncated by

Multiviews

A set of N signals (known as views within the context of this book) of the same dimensions d and sizes will both be considered as a table of N signals and as a signal with a superior dimension of

	global indexation space of a set of N views (images or volumes) with a dimension of d
	multi-signal, N views indexed by with values in ε
	digital view number d-dimensional signal
	multiview sample index: position and digital image
	different expressions shown as equivalents to reach the value in ε for the sample in position p in the view i from the last (double level indice) should be avoided