The Visual Computer (2018) 34:863–873
Incremental Voronoi sets for instant stippling
· Yanyun Chen
· Yinling Qian
· Hanqiu Sun
Published online: 14 May 2018
© Springer-Verlag GmbH Germany, part of Springer Nature 2018
This paper presents a fast digital stippling algorithm, which makes a fair balance on result quality and computational efﬁciency.
The algorithm is based on precomputed blue noise point sets constructed by incremental Voronoi sets (IVS) and a real-time
parallelized rejection strategy. The proposed technique is readily extended to generate multi-tone-level or multi-nib-size
stippling results of increased pleasure visual impressions with smooth tone transition. The IVS can also be regressed to
generate blue noise masks for digital halftoning.
Keywords Real-time · Stippling · Multi-tones · Voronoi
Stippling, which is commonly used for illustrations in printed
books for archeology and biology , is the art of placing
dots [24,26,44]. In general, it replaces tiny dots of ink with
large, clearly visible stipples. The stipples are usually placed
evenly yet randomly such that human vision does not per-
ceive spurious patterns that are inconsistent with the intended
Manual stippling by artists is an extremely tedious process
that often takes hours. In computer graphics research, differ-
ent digital stippling methods have been proposed over recent
Special thanks to Wenjuan Shen.
Electronic supplementary material The online version of this article
(https://doi.org/10.1007/s00371-018-1541-7) contains supplementary
material, which is available to authorized users.
University of Chinese Academy of Sciences, Beijing, China
State Key Laboratory of Computer Science, Institue of
Software Chinese Academy of Sciences, Beijing, China
Chinese University of Hong Kong, Hong Kong, China
years [5,15,23,30,42,55]. Real-time methods that produce
competitive quality solutions are important and favorable
because they allow users to acquire desired results instantly.
Numerous methods have been proposed for real-time stip-
pling for different purposes in various areas, such as printing
and artistic work. In terms of quality, a point distribution with
blue noise properties is generally regarded a good one.
In this paper, we propose a novel, efﬁcient, and instant
stippling method based on a precomputed sample set. This
sample set, called the incremental Voronoi set (IVS), is pre-
computed with the greedy farthest strategy and then used to
efﬁciently generate stipples with a rejection strategy at run-
time. Compared with prior arts, our algorithm can be easily
parallelized and achieve better performance. Furthermore, it
can be extended to generate multi-tone-level or multi-nib-
size stipples, which are much further perceptually enjoyable
with minimal extra runtime cost.
Blue noise mask (BNM) techniques, which are widely
used in digital halftoning, can also be used for stippling.
Samples of a BNM are distributed on a lattice space of a given
resolution. Stippling and dithering based on BNM are highly
parallelizable. In this perspective, an IVS can be considered
a resolution-independent BNM, so it is highly ﬂexible for
stipple generation. We demonstrate that IVS can be regressed
to ordinary BNMs of any given resolution.
In brief, this paper presents the following contributions:
– a fast stippling method that uses IVS;
– extension of the proposed method to a multi-level one to
achieve further perceptual satisfaction;
– resolution-adaptive BNM based on IVS.