Pixel-accurate tracking of objects is a key element in many computer vision applications, often solved by iterated individual object tracking or instance segmentation followed by object matching. Here we introduce cross-classification clustering (3C), a technique that simultaneously tracks complex, interrelated objects in an image stack. The key idea in cross-classification is to efficiently turn a clustering problem into a classification problem by running a logarithmic number of independent classifications per image, letting the cross-labeling of these classifications uniquely classify each pixel to the object labels. We apply the 3C mechanism to achieve state-of-the-art accuracy in connectomics - the nanoscale mapping of neural tissue from electron microscopy volumes. Our reconstruction system increases scalability by an order of magnitude over existing single-object tracking methods (such as flood-filling networks). This scalability is important for the deployment of connectomics pipelines, since currently the best performing techniques require computing infrastructures that are beyond the reach of most laboratories. Our algorithm may offer benefits in other domains that require pixel-accurate tracking of multiple objects, such as segmentation of videos and medical imagery.

The current design trend in large scale machine learning is to use distributed clusters of CPUs and GPUs with MapReduce-style programming. Some have been led to believe that this type of horizontal scaling can reduce or even eliminate the need for traditional algorithm development, careful parallelization, and performance engineering. This paper is a case study showing the contrary: that the benefits of algorithms, parallelization, and performance engineering, can sometimes be so vast that it is possible to solve "cluster-scale" problems on a single commodity multicore machine.

In human motor control studies, end-effector (e.g., hand) trajectories have been successfully modeled using optimization principles. Yet, it remains unclear how such trajectories are updated when the end-effector or task goals are perturbed. Here, we present an approach to human and robotic task-level trajectory planning and modification using geometrical invariance and optimization, allowing to adapt learned movements to a priori unknown boundary conditions. The optimization criterion represents a tradeoff between smoothness (minimum jerk) and accuracy (jerk-accuracy model). We show that planning maximally smooth movements allows recovery from perturbations by superimposing specific affine orbits on maximally smooth preplanned trajectories. The generated trajectories are compared with those resulting from other recent approaches used in robotics. Finally, we discuss conditions for affine invariance of maximally smooth task-space trajectories. Possible applications of this study to both human motor control and robotics research studies are discussed.