We study informative path planning for active regression in Gaussian Processes (GP). Here, a resource constrained robot team collects measurements of an unknown function, assumed to be a sample from a GP, with the goal of minimizing the trace of the$M$-weighted expected squared estimation error covariance (where$M$is a positive semidefinite matrix) resulting from the GP posterior mean. While greedy heuristics are a popular solution in the case of length constrained paths, it remains a challenge to computeoptimalsolutions in the discrete setting subject to routing constraints. We show that this challenge is surprisingly easy to circumvent. Using the optimality of the posterior mean for a class of functions of the squared loss yields an exact formulation as a mixed integer program. We demonstrate that this approach finds optimal solutions in a variety of settings in seconds and when terminated early, it finds sub-optimal solutions of higher quality than existing heuristics.

We study the sample placement and shortest tour problem for robots tasked with mapping environmental phenomena modeled as stationary random fields. The objective is to minimize the resources used (samples or tour length) while guaranteeing estimation accuracy. We give approximation algorithms for both problems in convex environments. These improve previously known results, both in terms of theoretical guarantees and in simulations. In addition, we disprove an existing claim in the literature on a lower bound for a solution to the sample placement problem.

Using content-based binary codes to tag digital images has emerged as a promising retrieval technology. Recently, Radon barcodes (RBCs) have been introduced as a new binary descriptor for image search. RBCs are generated by binarization of Radon projections and by assembling them into a vector, namely the barcode. A simple local thresholding has been suggested for binarization. In this paper, we put forward the idea of “autoencoded Radon barcodes”. Using images in a training dataset, we autoencode Radon projections to perform binarization on outputs of hidden layers. We employed the mini-batch stochastic gradient descent approach for the training. Each hidden layer of the autoencoder can produce a barcode using a threshold determined based on the range of the logistic function used. The compressing capability of autoencoders apparently reduces the redundancies inherent in Radon projections leading to more accurate retrieval results. The IRMA dataset with 14,410 x-ray images is used to validate the performance of the proposed method. The experimental results, containing comparison with RBCs, SURF and BRISK, show that autoencoded Radon barcode (ARBC) has the capacity to capture important information and to learn richer representations resulting in lower retrieval errors for image retrieval measured with the accuracy of the first hit only.