Geodesic Distance Function Learning via Heat Flow on Vector Fields

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if the original manifold is not Euclidean. Note that the distance function on a manifold can always be well-defined. In this paper, we propose to learn the distance function directly on the manifold without embedding. We first provide a theoretical characterization of the distance function by its gradient field. Based on our theoretical analysis, we propose to first learn the gradient field of the distance function and then learn the distance function itself. Specifically, we set the gradient field of a local distance function as an initial vector field. Then we transport it to the whole manifold via heat flow on vector fields. Finally, the geodesic distance function can be obtained by requiring its gradient field to be close to the normalized vector field. Experimental results on both synthetic and real data demonstrate the effectiveness of our proposed algorithm

Learning to open new doors

Finding and opening an unknown door autonomously is an unsolved challenge that the most advanced robots in the world have not solved yet. Door handles have diferent locations, shapes, operating mechanisms and are made of different materials. Most approaches to door opening require precise information such as its exact location and a 3D model of the door handle that must be opened. This is one of the barriers that prevents robots from being used outside of controlled environments. In this thesis, we describe an approach to solve the problem of localizing and classifying a door handle with the REEM robot with no human intervention in the process. To do so we use the data obtained from a RGB-Depth sensor to detect the position of the door handle and compute an image of it that is processed by a supervised classi er system to determine the type of door handle. The type of the handle will determine which approach and opening motion is required to open the door. In this thesis we chose to perform stacked generalization with a feed-forward neural network on the prediction of several binary classi ers. The selection of the neural network model and binary classi ers is based on the experimental results of training and evaluating several combinations of supervised classi ers such as K-NN, SVM, Adaboost and Random Tree Forests with the image feature extraction algorithms Histogram of Oriented Gradients, Covariance Matrices and edge detection. In the end we obtain a model able to classify handle images with a performance higher than any of the individual binary classifiers trained