Game Development Reference

In-Depth Information

Structure

Tensor

Calculation

Structure

Tensor

Calculation

Structure

Tensor

Smoothing

Structure

Te n s o r

Smoothing

Merge

Merge

Relax

Local Orientation Estimation

Local Orientation Estimation

Flow-

Guided

Smoothing

Shock

Filter

Edge

Smoothing

Input

Output

Figure 5.3.
Schematic overview of the presented algorithm.

controlling the strength of the abstraction. For each iteration, adaptive flow-

guided smoothing (
Figure 5.1(a)
) and sharpening (
Figure 5.1(b))
are performed.

Both techniques require information about the local structure, which is obtained

by an eigenvalue analysis of the smoothed structure tensor and computed twice

for every iteration, once before the smoothing and again before the sharpening.

With every iteration, the result becomes closer to a piecewise-constant image,

with large smooth or even flat image regions where no distinguished orientation is

defined. Since having valid orientations defined for these regions is important for

the stability of the algorithm, the structure tensor from the previous calculation

is used in this case. For the first calculation, where no result from a previous

computation is available, a relaxation of the structure tensor is performed. As a

final step, edges are smoothed by flow-guided smoothing with a small filter kernel

(
Figure 5.1(c)
)
. In the following sections, the different stages of the algorithm

are examined in detail.

5.2

Local Orientation Estimation

To guide the smoothing and shock-filtering operations, the dominant local ori-

entation at each pixel must be estimated. For smooth grayscale images with

nonvanishing derivative, a reasonable choice are the local orientations given by

tangent spaces of the isophote curves (i.e., curves with constant gray value). Since

for smooth images the gradient is perpendicular to the isophote curves, the local

orientations can easily be derived from the gradient vectors by rotating them 90

degrees (
Figure 5.4
)
. Unfortunately, real images are seldom smooth, and com-

putation of the gradient is highly sensitive to noise and other image artifacts.

This is illustrated in
Figure 5.5(a)
,
where an image with single dominant orien-

tation is shown. Since it is suciently smooth, all gradient vectors induce the

same orientation. Adding a small amount of Gaussian noise, however, results

in noisy gradients and a poor orientation estimation, as shown in
Figure 5.4(b)
.

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