Point pattern synthesis requires capturing both local and non-local correlations from a given exemplar. Recent works employ deep hierarchical representations from VGG-19 convolutional network to capture the features for both point-pattern and texture synthesis. In this work, we develop a simplified optimization pipeline that uses more traditional Gabor transform-based features. These features when convolved with simple random filters gives highly expressive feature maps. The resulting framework requires significantly less feature maps compared to VGG-19-based methods, better captures both the local and non-local structures, does not require any specific data set training and can easily extend to handle multi-class and multi-attribute point patterns, e.g., disk and other element distributions. To validate our pipeline, we perform qualitative and quantitative analysis on a large variety of point patterns to demonstrate the effectiveness of our approach. Finally, to better understand the impact of random filters, we include a spectral analysis using filters with different frequency bandwidths.
Overview of our pipeline. We propose to use continuous Gabor transform combined with a multi-resolution convolutional filtering step to compute Correlation and Gram statistics. Since all components are differentiable, we perform end-to-end optimization to update output pattern by minimizing the Correlation and Gram losses.
Single-class point-pattern expansion comparison between ours and previous methods. Our approach preserves the local and non-local structures better than previous methods.
Multi-class point-pattern expansion. Our method performs better in terms of global structure and local distances between point samples. PPS [TLH19] does not handle well point patterns with multiple classes. We enhance PPS with our sequential multi- class synthesis approach but it still shows artifacts. The bottom row shows rendered results with object placement at point locations.
Discrete element-pattern expansion. Our method naturally supports point-based element patterns. We treat each color as a separate class. Each column here is a 4-class pattern with two attributes (scale and depth) per element.
Comparison of our method with PPS [TLH19], PPS++ (our enhanced variant of PPS) and Ecormier et al. [EMGC19a] on disk and multi-class disk distributions. Our method better preserves the overall structure for both regular and irregular structures. Meanwhile, we achieve comparable results with Ecormier et al. [EMGC19a] on the second row, in terms of preserving non-overlapping disks.
We perform user study and compute an average score across 28 users. We show different point patterns and ask users to score between 1 (worst) and 5 (best). Ours (in blue) gets better score for all but one pattern. All patterns and their comparisons can be found in the supplemental document.
Analysis on using different filters in our filtering pipeline. Using Low-pass (Gaussian), band-pass filters (Sobel) and high-pass filters (derivative) fail to preserve complicated structures on the output pattern. While a simple combination of low-, band- and high-pass filters start giving correct orientation and overall structures.
@article {huang22point,
journal = {Computer Graphics Forum},
title = {{Point-Pattern Synthesis using Gabor and Random Filters}},
author = {Huang, Xingchang and Memari, Pooran and Seidel, Hans-Peter and Singh, Gurprit},
year = {2022},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.14596}
}