# DAVIDSTUTZ

Check out our latest research on weakly-supervised 3D shape completion.
18thJANUARY2015

A. Levinshtein, A. Stere, K. N. Kutulakos, D. J. Fleet, S. J. Dickinson, K. Siddiqi. TurboPixels: Fast superpixels using geometric flows. Transactions on Pattern Analysis and Machine Intelligence, 31(12):2290–2297, 2009.

TurboPixels is one of the first superpixel algorithms (that is, the algorithm was, in contrast to Quick Shift [1] and the approach by Felzenswalb and Huttenlocher [2], originally intended to generate superpixels). Inspired by active contours, after placing superpixel centers on a reglar grid, the superpixels are grown based on an evolving contour. The contour is implemented as level set of the function

$\psi : \mathbb{R}^2 \times [0, \tau) \rightarrow \mathbb{R}^2$.

The evolution is formally defined by

$\psi_t = -v \|\ \nabla \psi\|_2$

where $\nabla\psi$ denotes the gradient of $\psi$ and $\psi_t$ is the temporal derivative. Here, the speed $v$ describes the future evolution of the contour. In practive, $\psi$ will be the signed euclidean distance and evolution is carried out using a first-order discretization. The contour in iteration $(T + 1)$ is given by

$\psi^{(T+1)} = \psi^{(T)} - v_I v_B \|\nabla \psi^{(T)}\|\Delta t$.

The speed $v$ is split up into two components: $v_I$ which depends on the image content and $v_B$ which ensures that superpixels do not overlap. Iteratively, the superpixels are grown by computing $v_I$ and $v_B$ and then applying the equation above, see the paper for details. The procedure is summarized in algorithm 1.

function turbopixels(
$I$, // Color image.
$K$, // Number of superpixels.
)
place initial superpixel centers on a regular grid
initialize $\psi^{(0)}$
repeat
compute $v_I$ and $v_B$
evolve the contour by computing $\psi^{(T+1)}$
update assigned pixels
$T := T + 1$
until all pixels are assigned
derive superpixel segmentation $S$ from $\psi$
return $S$

Algorithm 1: A brief overview over the superpixel algorithm TurboPixels.

The original MatLab implementation is available online on Alex Levinshten's homepage. Figure 1 shows superpixel segmentations generated by TurboPixels.

• [1] A. Vedaldi, S. Soatto. Quick Shift and Kernel Methods for Mode Seeking. European Conference on Computer Vision, 2008.
• [2] P. F. Felzenswalb and D. P. Huttenlocher. Efficient graph-based image segmentation. International Journal of Computer Vision, volume 59, number 2, 2004.
• [3] P. Arbeláez, M. Maire, C. Fowlkes, J. Malik. Contour detection and hierarchical image segmentation. Transactions on Pattern Analysis and Machine Intelligence, volume 33, number 5, pages 898–916, 2011.

What is your opinion on the summarized work? Or do you know related work that is of interest? Let me know your thoughts in the comments below or get in touch with me: