Anisometric Results - IMPLEMENTATION AND RESULTS

CHAPTER 5 IMPLEMENTATION AND RESULTS

5.2 Anisometric Results

We show anisometric results with different vector field controls : circular pattern on XY plane, oval pattern on XY plane, slant pattern on XY plane, zigzag pattern on XY plane, and slant control on 3D space. In order to emphasize the control effect, we show the results about structural textures, as brickwalls and woods et. al.

The vector field about circular control is in Fig. 5.8. The results with circular pattern control on the XY plane are shown in Fig. 5.9 and Fig. 5.10. Fig. 5.9 shows the result for case_5. The result is good because of its small and compact pattern. The input data in Fig. 5.10(b) (case_8) is wood texture, it is continuous on the two directions and broken on the other direction. We can see the patterns changed with circular control on XY plane.

(a) (b) Figure 5.8 5×5×5 3D vector field about circular control

(a) XY plane (b) three orthogonal axes at every point

(a) (b)

(a) cross section at X=126, Y=126, and Z=126 for result data (b) cross section at X=80, Y=80, and Z=80 for result data (c) cross section at X=64, Y=64, and Z=64 for result data (d) anisometric result with circular control for case_5

(a) (b)

(e) (f)

Figure 5.10 Input data and anisometric result with circular control for case_8 (a) cross sections at X=32, Y=32, and Z=32 for input data

(b) input volume data for case_8

(c) cross section at X=126, Y=126, and Z=126 for result data (d) cross section at X=80, Y=80, and Z=80 for result data (e) cross section at X=64, Y=64, and Z=64 for result data (f) anisometric result with circular control for case_8

The vector field about oval control is in Fig. 5.11. The results with oval pattern control on the XY plane are shown in Fig. 5.12 and Fig. 5.13. Fig. 5.12 shows the result for case_5, it is good at this kind of control. Fig. 5.13 is the result for case_8, it is continuous with the oval control.

(a) (b) Figure 5.11 5×5×5 3D vector field about oval control

(a) XY plane (b) three orthogonal axes at every point

(a) (b)

The vector field about slant control is in Fig. 5.14. The results with slant control on the XY plane are shown in Fig. 5.15 and Fig. 5.16. As we can see, there are slant control on XY direction, and no change from isometric results on XZ and YZ direction. The input data in Fig. 5.15(b) (case_9) is about brickwalls, a kind of structural texture. The result in Fig. 5.15(c)~(f) is continuous with the slant control at the whole volume. It is good at the cross sections of different planes. Fig 5.16 shows the result for case_5, there is a little discontinuity on XY plane and no change on the other planes.

(a) (b)

(a) one axes on XY plane (b) one axes at every point

(a) (b)

(e) (f)

Figure 5.15 Input data and anisometric result with slant control for case_9 (a) cross sections at X=32, Y=32, and Z=32 for input data (b) input volume data for case_9

(a) (b)

The vector field about zigzag control is in Fig. 5.17, and we make it changed by two different directions for slant. We make the texture results changed on the XY plane with zigzag control, as shown in Fig. 5.18~ Fig. 5.20. As Fig. 5.15(b) shown, there is almost no information on XZ plane in the input data for case_9.

We reconstruct the texture and there are some information shown in the result volume data (Fig. 5.18). The zigzag control is the same as we expect for case_9.

Fig. 5.19 shows the result for case_5 with zigzag control on XY plane, and it is better than slant control (Fig. 5.16). Fig. 5.20 shows the result for case_8, the patterns on XY plane are changed by zigzag control. It keeps the continuity between different planes (XY planes with XZ planes, and XY planes with YZ planes).

(a) (b)

(a) one axes on XY plane (b) one axes at every point

(a) (b)

The vector field about 3D slant control is in Fig. 5.21. We make the results changed in the 3D space with slant control, as shown in Fig. 5.22~ Fig. 5.24.

There are slant patterns on all planes and inside the volume results. Besides, they are continuous between different planes. Fig. 5.22 shows the anisometric result for case_9. There are on information on XZ plane of the input data for case_9, but it is continuous on all planes and inside the result in Fig. 5.22. The result is good in Fig. 5.23 because of the compact information in the input data. The anisometric result for case_8 is in Fig. 5.24. After 3D slant control, the information ion XZ plane shows up, even the result is not very continuous.

(a) (b)

(a) one axes on XY plane (b) one axes at every point

(a) (b)

Chapter 6 Conclusions and Future Works

We have presented an exemplar-based system for solid texture synthesis with anisometric control. We apply 2D texture synthesis algorithm to 3D space.

In the preprocessing, we construct the feature vectors and a similarity set for an input volume data. We use the feature vectors not traditional RGB values to construct neighbor vectors for more accurate neighborhood matching. The similarity set which records 3 candidates for each voxel helps more effective neighborhood matching. In the synthesis process, we use the pyramid synthesis method to synthesize textures from coarse level to fine level, from one voxel to m×m×m result data. We can only use 8 locations of each voxel for neighborhood matching in synthesis process. In the anisometric synthesis process, we generate vector fields and make the result textures changed by the vector fields.

Comparing to other methods for solid synthesis, they only considered the information on three orthogonal 2D slices. They could not capture the information in the 3D space, and they can only control the textures on the slices not in the 3D space. We present a system for more accurate, effective and various solid texture synthesis.

In the future, we may control the anisometric textures with flow fields that make the results changed with time. Kwatra et. al. [9] presented a method for 3D surface texture synthesis with flow field. We may apply their method to synthesize anisometric textures changing with time in the 3D space. Besides, we may reduce the cost time for similarity set construction. The most time are spent on constructing similarity set in our system now, we may try another algorithm for similarity set construction to make the system more effective.

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