We formulate a general energy and method for segmentation that is designed to have preference for segmenting the coarse structure over the fine structure of the data, without smoothing across boundaries of regions. The energy is formulated by considering data terms at a continuum of scales from the scale space computed from the Heat Equation within regions, and integrating these terms over all time. We show that the energy may be approximately optimized without solving for the entire scale space, but rather solving time-independent linear equations at the native scale of the image, making the method computationally feasible. We provide a multi-region scheme, and apply our method to motion segmentation. Experiments on a benchmark dataset shows that our method is less sensitive to clutter or other undesirable fine-scale structure, and leads to better performance in motion segmentation.
We reexamine the role of multiscale cues in image segmentation using an architecture that constructs a globally coherent scale-space output representation. This characteristic is in contrast to many existing works on bottom-up segmentation, which prematurely compress information into a single scale. The architecture is a standard extension of Normalized Cuts from an image plane to an image pyramid, with cross-scale constraints enforcing consistency in the solution while allowing emergence of coarse-to-fine detail. We observe that multiscale processing, in addition to improving segmentation quality, offers a route by which to speed computation. We make a significant algorithmic advance in the form of a custom multigrid eigensolver for constrained Angular Embedding problems possessing coarse-to-fine structure. Multiscale Normalized Cuts is a special case. Our solver builds atop recent results on randomized matrix approximation, using a novel interpolation operation to mold its computational strategy according to cross-scale constraints in the problem definition. Applying our solver to multiscale segmentation problems demonstrates speedup by more than an order of magnitude. This speedup is at the algorithmic level and carries over to any implementation target. We propose a unified approach for bottom-up hierarchical image segmentation and object candidate generation for recognition, called Multiscale Combinatorial Grouping (MCG). For this purpose, we first develop a fast normalized cuts algorithm. We then propose a high-performance hierarchical segmenter that makes effective use of multiscale information. Finally, we propose a grouping strategy that combines our multiscale regions into highly-accurate object candidates by exploring efficiently their combinatorial space. We conduct extensive experiments on both the BSDS500 and on the PASCAL 2012 segmentation datasets, showing that MCG produces state-of-the-art contours, hierarchical regions and object candidates.