Image Compositing and Editing - Computer Vision for Visual Effects - page 82

(a) (b)

Figure 3.25. (a) An original image. (b) The saliency map obtained using Itti et al.'s algorithm.

gradient magnitudes/orientations to estimate regions in the image likely to attract
visual attention; an example is illustrated in Figure 3.25 .
We partition the image into a set Q of rectangular elements, or quads , which are

defined by sets of vertices computed

as the average importance of the pixels inside it. We denote the vertices of quad q as
V q . A deformation of the quad mesh results in a new set of vertex positions

V and edges E . Each quad q is given aweight w ( q )

V with

V , we compute a

the same edges as the original mesh. For a candidate deformation

cost as:

2

v i , v j ∈ V q (

(V ) = v i − v j ) − v i − v j ) −

2

+

C w ( q ) s q ( v i − v j ) ( l ij ( v i − v j )

q ∈ Q ( v i , v j ) ∈ E

(3.35)
Here, the first term in Equation ( 3.35 ) encourages each quad q to be uniformly
scaled by a factor s q , with a higher weight on quads with higher saliency. 7 The second
term in Equation ( 3.35 ) encourages the top-to-bottomand left-to-right grid lines that
define the quads not to bend toomuch; here, l ij

v i − v j / . The basic idea is

to minimize the cost function in Equation ( 3.35 ) subject to the boundary constraints
that the output image be rectangular with the desireddimensions, resulting in a series
of linear systems in the vertex locations. Figure 3.26 illustrates an example result of
the method.

= v i − v j

3.5.2 Seam Carving

One of the most exciting approaches for image retargeting in recent years is seam
carving , a simple algorithm that can effectively resize and reshape images and that
can also be used for inpainting. The key concept is the addition and removal of

7 s q can be determined as a function of a given

V and eliminated from the equation; see

and

V

Problem 3.19 .