Fast multiscale image segmentation

Abstract

We introduce a fast, multiscale algorithm for image segmentation. Our algorithm uses modern numeric techniques to nd an approximate solution to normalized cut measures in time that is linear in the size of the image with only a few dozen operations per pixel. In just one pass the algorithm provides a complete hierarchical decomposition of the image into segments. The algorithm detects the segments by applying a process of recursive coarsening in which the same minimization problem is represented with fewer and fewer variables producing an irregular pyramid. During this coarsening process we may compute additional internal statistics of the emerging segments and use these statistics to facilitate the segmentation process. Once the pyramid is completed it is scanned from the top down to associate pixels close to the boundaries of segments with the appropriate segment. The algorithm is inspired by algebraic multigrid (AMG) solvers of minimization problems of heat or electric networks. We demonstrate the algorithm by applying it to real images.

TurboPixels: Fast Superpixels Using Geometric Flows

“…Space and runtime complexity also depend on the number of segments, and become prohibitive with large numbers of segments. In [20], a further reduction in complexity by a factor of ffiffiffiffi ffi N p is achieved, based on a recursive coarsening of the segmentation problem. However, the number of superpixels is no longer directly controlled nor is the algorithm designed to ensure the quasi uniformity of segment size and shape.…”

Annealing and the normalized N-cut

“…As β decreases, the elements of Y aggregate to form classes. Similar ideas have been used in [23] for fast multiscale image segmentation.…”

“…Since at the bifurcation off of q(η|y) = 1/N a new branch emanates from an existing branch, we need only investigate when the eigenvalues of the smaller Hessian ΔF are zero. We solve the system (22) for any nontrivial vector w. We rewrite (22) as an eigenvalue problem (23) Since this matrix ΔF is block diagonal with blocks B i , i = 1, …, N and by symmetry [25] at q (η|y) all the blocks B i are identical, we will from now on only compute with one diagonal block B ≔ B i .…”

Multilevel Spectral Partitioning for Efficient Image Segmentation and Tracking

“…This can interpreted as a very simple multilevel technique with uncertain convergence. Sharon et al [10] proposed an approximation of the normalized cut, solved using Algebraic Multigrid (AMG). While both of these methods provide great computational gains neither method is solving the exact normalized cut or a complete bounded relaxation.…”

“…The solutions obtained are shown to be superior to approximation techniques in [13,5] that sample the graph representation to reduce computational cost of the eigenstructure computation. Unlike approximation techniques, including the algebraic multigrid approach of Sharon et al [10], our multilevel method maintains the quality bound given for spectral relaxations. We present image segmentation and tracking results.…”