Point Pattern Synthesis via Irregular Convolution

Computer Graphics Forum (Proceedings of SGP 2019)

Peihan Tu1    Dani Lischinski   Hui Huang1*

1Shenzhen University     2Hebrew University of Jerusalem

Figure 1: Wild geese flying to the south. Our point pattern synthesis method takes a small example of a point pattern and synthesizes a larger one. The point pattern may be used to simulate object placement in virtual scenes.


Point pattern synthesis is a fundamental tool with various applications in computer graphics. To synthesize a point pattern, some techniques have taken an example-based approach, where the user provides a small exemplar of the target pattern. However, it remains challenging to synthesize patterns that faithfully capture the structures in the given exemplar. In this paper, we present a new example-based point pattern synthesis method that preserves both local and non-local structures present in the exemplar. Our method leverages recent neural texture synthesis techniques that have proven effective in synthesizing structured textures. The network that we present is end-to-end. It utilizes an irregular convolution layer, which converts a point pattern into a gridded feature map, to directly optimize point coordinates. The synthesis is then performed by matching inter- and intra-correlations of the responses produced by subsequent convolution layers. We demonstrate that our point pattern synthesis qualitatively outperforms state-of-the-art methods on challenging structured patterns, and enables various graphical applications, such as object placement in natural scenes, creative element patterns or realistic urban layouts in a 3D virtual environment.

Figure 4: Hierarchical optimization process. The point pattern used as the initial guess and the filter used in the irregular convolution layer at each of the four stages of the optimization process; the final result is shown on the right.

Figure 9: Point pattern synthesis results. We compare our method with three example-based point patter synthesis methods. From left to right, we show the exemplar, the results by [ZHWW12; MWT11; RÖM*15] and our method. From top to bottom, we use the parameters c1 = 1;1;1;1;0:5 and c2 = 4;2;3;2;2, respectively.

Figure 11: 3D object placement. Our synthesized patterns can be used to generate 3D object placement. Note that the synthesized patterns successfully preserve large structures and small local variations in the exemplars. From top to bottom, the parameters used are c1 = 1;1;2;1;2;1 and c2 = 3;4;4;4;4;4, respectively.y.

Figure 12: Natural point pattern synthesis. The input exemplars can be directly extracted from real images, leading to larger realistic 3D virtual scenes. The sunflower pattern has been extended twice while the structure is still well preserved. Parameters used: c1 = 2 and c2 = 4.

Figure 13: Application: rural layout. This input pattern has two classes of points. Red points indicate regularly distributed houses, while blue points indicate stochastically distributed trees. Parameters used: c1 = 1 and c2 = 3.

Figure 14: Application: tree grove. The input point pattern has two attributes, one is a continuous attribute representing the size of a tree, while the other is discrete class attribute indicating the tree type. Parameters used: c1 = 1 and c2 = 4.

Figure 15: Graph synthesis. Our method can also be used to synthesize graphs by adopting our soft point optimization strategy from points to edges. Graphs can be used to model man-made roads, regions or natural rivers. Parameters used: c1 = 1 and c2 = 2.

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We thank the anonymous reviewers for their valuable comments. This work was supported in parts by NSFC (61761146002), National 973 Program (2015CB352501), Guangdong Science and Technology Program (2015A030312015), Shenzhen Innovation Program (KQJSCX20170727101233642), LHTD (20170003), ISF (2366/16), and the National Engineering Laboratory for Big Data System Computing Technology.

title = {
Point Pattern Synthesis via Irregular Convolution},
author = {Peihan Tu, Dani Lischinski and Hui Huang},
journal = {Computer Graphics Forum (Proceedings of SGP 2019)},
volume = {38},
number = {5},

pages = {109--122},
year = {2019},

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