Layered Solid Texture Synthesis from a Single 2D Exemplar
Kenshi Takayama∗
The University of Tokyo

1

Takeo Igarashi
The University of Tokyo,JST/ERATO

Introduction
SearchIn our previous work of lapped solid textures [Takayama et al.
2008], layered (or ‘type 1-b’) texture exemplars were used to create solid textured models such as strata and cakes. However, nomethods have been proposed so far to synthesize this kind of texture automatically. This poster proposes an extension of Kopf etal.’s method [2007] to synthesize such layered solid textures fromsingle 2D exemplars.

2Algorithm

Figure 1 illustrates the problem to be solved. The input is a 2D
exemplar image representing the cross section of layers, and theoutput is a 3D solid texture whose cross sections parallel to thedepth direction (assumed to be the z-direction) always look similar
to the 2D exemplar.

SearchFigure 3: The cause of the sweeping artifact.

We solve this problem using the following simple scheme illustrated in Figure 4. When searching neighborhoods, for each voxel,
we collect the two best matching neighborhoods in each of thex- and y-directions. If the first best matching neighborhoods inboth of the two directions point to exactly the same location in the2D exemplar, we select one of the two according to the matching
distances and assign that pixel as the best matching neighborhoodfor the selected direction. For the other direction, the second best
matching neighborhood is chosen as the matching result.

z (= depth direction)

Input:
2D exemplary,Search

Output:3D solid texture

1.2x,

1.5

Figure 1: The problem of layered solid texture synthesis.
We solve this problem by adding several extensions to Kopf et al.’smethod [2007] for synthesizing homogeneous solid textures from
2D exemplars. First, we add a depth map channel to the 2D exemplar that encodes the layer information (Fig. 2(left)). We also alter
the random initialization step of the 3D synthesis volume such thatit starts with proper depth values (Fig. 2(right)). We perform thetwo-pass synthesis process (search and optimization) only in the xand y-directions, because we have only a single 2D exemplar corresponding to those directions.

0.81.8

1.8

Select0.8

SearchFigure 4: Our solution to the sweeping problem. The numbers
shown at the neighborhoods indicate the matching distances (redand green colors correspond to the x- and y-directions, respectively).

3 Results
Figure 5 shows how this simple scheme works well for many layered textures.

Figure 2: The additional depth map channel of the 2D exemplar(left) and the altered random initialization of the 3D synthesis volume at the coarsest level (right).
Figure 5: Results of our layered solid texture synthesis algorithm.
However, the above scheme can easily lead to a severe sweeping artifact as shown in the inset. Thisis because it accepts a simple sweep of the 2D exemplar in a direction orthogonal to the z-direction
and oblique to both the x- and y-directions, as an
optimized synthesis result. In other words, for eachvoxel, the two neighborhoods of the current synthesis volume corresponding to the x- and y-directions are very likely to best matchwith exactly the same neighborhood in the 2D exemplar (Fig. 3).
∗ E-mail: kenshi@ui.is.s.u-tokyo.ac.jp

References
KOPF, J., F U , C.-W., C OHEN -O R , D., D EUSSEN , O., L ISCHIN SKI , D., AND W ONG , T.-T. 2007. Solid texture synthesis from2d exemplars. ACM Trans. Graph. 26, 3, 2.
TAKAYAMA , K., O KABE , M., I JIRI , T., AND I GARASHI , T. 2008.
Lapped solid textures: filling a model with anisotropic textures.
ACM Trans. Graph. 27, 3, 1–9.