
High dynamic range video and tone mapping 219
pixel (i, j) by requiring their perceptual distance (in the sense of Shen) with
L(i, j) to be equal, i.e.
L
+
(i, j) − L(i, j)
L(i, j)
=
L(i, j) − L
−
(i, j)
L(i, j)
= k
for some k > 0.
11.4.1.5 Expression of the discrete gradient
Given a constant λ ∈]0, 1[, we construct for each pixel (i, j) two images
L
+
(i, j) and L
−
(i, j) defined as follows
L
+
(i, j) : (m, n) 7−→ L(m, n)
1 + min(1/L(i, j) − 1, λ) δ((m, n) − (i, j))
L
−
(i, j) : (m, n) 7−→ L(m, n)
1 − min(1/L(i, j) − 1, λ) δ((m, n) − (i, j))
where δ is the Dirac delta function.
Remark 3. By the use of the increment k = min(1/L(i, j) −1, λ), we impose
that the values ...