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 |