Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data

The Shape Interaction Matrix (SIM) is one of the earliest approaches to performing subspace clustering (i.e., separating points drawn from a union of subspaces). In this paper, we revisit the SIM and reveal its connections to several recent subspace clustering methods. Our analysis lets us derive a simple, yet effective algorithm to robustify the SIM and make it applicable to realistic scenarios where the data is corrupted by noise. We justify our method by intuitive examples and the matrix perturbation theory. We then show how this approach can be extended to handle missing data, thus yielding an efficient and general subspace clustering algorithm. We demonstrate the benefits of our approach over state-of-the-art subspace clustering methods on several challenging motion segmentation and face clustering problems, where the data includes corrupted and missing measurements.Comment: This is an extended version of our iccv15 pape

Comparative evaluation of instrument segmentation and tracking methods in minimally invasive surgery

Intraoperative segmentation and tracking of minimally invasive instruments is a prerequisite for computer- and robotic-assisted surgery. Since additional hardware like tracking systems or the robot encoders are cumbersome and lack accuracy, surgical vision is evolving as promising techniques to segment and track the instruments using only the endoscopic images. However, what is missing so far are common image data sets for consistent evaluation and benchmarking of algorithms against each other. The paper presents a comparative validation study of different vision-based methods for instrument segmentation and tracking in the context of robotic as well as conventional laparoscopic surgery. The contribution of the paper is twofold: we introduce a comprehensive validation data set that was provided to the study participants and present the results of the comparative validation study. Based on the results of the validation study, we arrive at the conclusion that modern deep learning approaches outperform other methods in instrument segmentation tasks, but the results are still not perfect. Furthermore, we show that merging results from different methods actually significantly increases accuracy in comparison to the best stand-alone method. On the other hand, the results of the instrument tracking task show that this is still an open challenge, especially during challenging scenarios in conventional laparoscopic surgery