# DAVIDSTUTZ

JANUARY2015

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.