Exp Fluids (2017) 58:95
Fast volume reconstruction for 3D PIV
· Alexandra H. Techet
Received: 26 January 2017 / Revised: 18 May 2017 / Accepted: 22 May 2017
© Springer-Verlag GmbH Germany 2017
TomoPIV technique relies on images from about four or
ﬁve cameras looking at a scene from different viewpoints
to facilitate tomographic reconstruction of the investiga-
tion volume using a multiplicative algebraic reconstruction
technique (MART). Synthetic aperture (SA) PIV (SAPIV)
was introduced by Belden et al. (2010) blending light
ﬁeld imaging concepts into a 3D quantitative velocimetry
method. SAPIV uses an array of up to ten cameras and can
spatially resolve densely seeded velocity ﬁelds. Because
SA imaging facilitates focusing at any arbitrary depth in
a volume of interest, accurate intensity volumes could be
reconstructed for use in 3D cross-correlation-based PIV.
However, the original implementation of SA reconstruction
took considerable computational time.
In an entire 3D PIV process, reconstruction often
accounts for a signiﬁcant portion of the total computa-
tion time (see Fig. 1). Since TomoPIV was introduced in
2006 Elsinga et al. (2006), several improvements to tomo-
graphic reconstruction time have been made by Worth and
Nickels (2008) (MFG-MART), Atkinson and Soria (2009)
(MLOS-SMART), Discetti and Astarita (2012) (MLOS-
MR-SMART) and Lynch and Scarano (2015) (SMTE-
MART) in 2008, 2009, 2012 and 2015, respectively.
However, reconstruction time still remains a signiﬁcant
hurdle to processing large data sets, often acquired using
high-speed cameras. In addition, computation time for SA
reconstruction is in the same order of magnitude as that for
tomographic reconstruction. This drawback and the need
for processing large data sets motivates the development of
the HF method.
This paper introduces a memory-efﬁcient, faster recon-
struction technique, based on a new homography ﬁt (HF)
algorithm, for synthetic aperture (SA) refocusing. This new
algorithm is highly parallelizable and can be implemented
Abstract Presented is a memory-efﬁcient and highly par-
allelizable method for reconstructing volumes, based on a
homography ﬁt synthetic aperture refocusing method. This
technique facilitates rapid processing of very large amounts
of data, such as that recorded using high-speed cameras, for
the purpose of conducting 3D particle imaging velocimetry
and particle tracking velocimetry.
Given the unsteady, three-dimensional nature of ﬂuid ﬂows
encountered in both research and industry, there is signiﬁ-
cant demand for advanced experimental techniques that
fully resolve velocity ﬁelds in time and space. PIV has been
widely and successfully used to resolve 2D velocity ﬁelds.
However, 2D velocity ﬁelds come with certain limitations.
For example, since 2D velocity ﬁelds do not provide out-
of-plane velocity gradient information, a pressure ﬁeld cal-
culated from a 2D velocity ﬁeld contains errors. 2D ﬁelds
are often insufﬁcient for studying complex, non-symmetric
ﬂows such as highly 3D, turbulent ﬂows.
Tomographic PIV (TomoPIV), pioneered by Elsinga
et al. (2006), is a widely adopted 3D PIV technique that
has been used in a wide range of ﬂuid experiments. The
* Alexandra H. Techet
Massachusetts Institute of Technology, Cambridge, MA