Dimension reduction for linear separation with curvilinear distances

Any high dimensional data in its original raw form may contain obviously classifiable clusters which are difficult to identify given the high-dimension representation. In reducing the dimensions it may be possible to perform a simple classification technique to extract this cluster information whilst retaining the overall topology of the data set. The supervised method presented here takes a high dimension data set consisting of multiple clusters and employs curvilinear distance as a relation between points, projecting in a lower dimension according to this relationship. This representation allows for linear separation of the non-separable high dimensional cluster data and the classification to a cluster of any successive unseen data point extracted from the same higher dimension

Multi-stage Suture Detection for Robot Assisted Anastomosis based on Deep Learning

In robotic surgery, task automation and learning from demonstration combined with human supervision is an emerging trend for many new surgical robot platforms. One such task is automated anastomosis, which requires bimanual needle handling and suture detection. Due to the complexity of the surgical environment and varying patient anatomies, reliable suture detection is difficult, which is further complicated by occlusion and thread topologies. In this paper, we propose a multi-stage framework for suture thread detection based on deep learning. Fully convolutional neural networks are used to obtain the initial detection and the overlapping status of suture thread, which are later fused with the original image to learn a gradient road map of the thread. Based on the gradient road map, multiple segments of the thread are extracted and linked to form the whole thread using a curvilinear structure detector. Experiments on two different types of sutures demonstrate the accuracy of the proposed framework.Comment: Submitted to ICRA 201

The Riemannian Geometry of Deep Generative Models

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate the Riemannian geometry of these generated manifolds. First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold. Second, we develop an algorithm for parallel translation of a tangent vector along a path on the manifold. We show how parallel translation can be used to generate analogies, i.e., to transport a change in one data point into a semantically similar change of another data point. Our experiments on real image data show that the manifolds learned by deep generative models, while nonlinear, are surprisingly close to zero curvature. The practical implication is that linear paths in the latent space closely approximate geodesics on the generated manifold. However, further investigation into this phenomenon is warranted, to identify if there are other architectures or datasets where curvature plays a more prominent role. We believe that exploring the Riemannian geometry of deep generative models, using the tools developed in this paper, will be an important step in understanding the high-dimensional, nonlinear spaces these models learn.Comment: 9 page