Yubin Kuang

A complete characterization and solution to the microphone position self-calibration problem

This paper presents a complete characterization and solution to microphone position self-calibration problem for time-of-arrival (TOA) measurements. This is the problem of determining the positions of receivers and transmitters given all receiver-transmitter distances. Such calibration problems arise in application such as calibration of radio antenna networks, audio or ultra-sound arrays and WiFi transmitter arrays. We show for what cases such calibration problems are well-defined and derive efficient and numerically stable algorithms for the minimal TOA based self-calibration problems. The proposed algorithms are non-iterative and require no assumptions on the sensor positions. Experiments on synthetic data show that the minimal solvers are numerically stable and perform well on noisy data. The solvers are also tested on two real datasets with good results.

Time delay estimation for TDOA self-calibration using truncated nuclear norm regularization

Measurements with unknown time delays are common in different applications such as microphone array, radio antenna array calibration, where the sources (e.g. sounds) are transmitted in unknown time instants. In this paper, we present a method for estimating unknown time delays from Time-Difference-of-Arrival (TDOA) measurements. We propose a novel rank constraint on a matrix depending on the measurements and the unknown time delays. The time delays are recovered by solving a truncated nuclear norm minimization problem using alternating direction method of multipliers (ADMM). We show in synthetic experiments that the proposed method recovers the time delays with good accuracy for noisy and missing data.

Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion

In this paper, we study the problems of estimating relative pose between two cameras in the presence of radial distortion. Specifically, we consider minimal problems where one of the cameras has no or known radial distortion. There are three useful cases for this setup with a single unknown distortion: (i) fundamental matrix estimation where the two cameras are uncalibrated, (ii) essential matrix estimation for a partially calibrated camera pair, (iii) essential matrix estimation for one calibrated camera and one camera with unknown focal length. We study the parameterization of these three problems and derive fast polynomial solvers based on Gröbner basis methods. We demonstrate the numerical stability of the solvers on synthetic data. The minimal solvers have also been applied to real imagery with convincing results.

Pose Estimation with Unknown Focal Length Using Points, Directions and Lines

In this paper, we study the geometry problems of estimating camera pose with unknown focal length using combination of geometric primitives. We consider points, lines and also rich features such as quivers, i.e.\ points with one or more directions. We formulate the problems as polynomial systems where the constraints for different primitives are handled in a unified way. We develop efficient polynomial solvers for each of the derived cases with different combinations of primitives. The availability of these solvers enables robust pose estimation with unknown focal length for wider classes of features. Such rich features allow for fewer feature correspondences and generate larger inlier sets with higher probability. We demonstrate in synthetic experiments that our solvers are fast and numerically stable. For real images, we show that our solvers can be used in RANSAC loops to provide good initial solutions.

Single antenna anchor-free UWB positioning based on multipath propagation

Radio based localization and tracking usually require multiple receivers/transmitters or a known floor plan. This paper presents a method for anchor free indoor positioning based on single antenna ultra wideband (UWB) measurements. By using time of arrival information from multipath propagation components stemming from scatterers with different, but unknown, positions we estimate the movement of the receiver as well as the angle of arrival of the considered multipath components. Experiments are shown for real indoor data measured in a lecture room with promising results. Simultaneous estimation of both receiver motion, transmitter and scatterer positions is performed using an factorization based approach followed by non-linear least squares optimization. A RANSAC approach to automatic matching of data has also been implemented and tested. The resulting reconstruction is compared to ground truth motion as given by the antenna positioner. The resulting accuracy is in the order of one cm.

TOA sensor network self-calibration for receiver and transmitter spaces with difference in dimension

We study and solve the previously unstudied problem of finding both sender and receiver positions from time of arrival (TOA) measurements when there is a difference in dimensionality between the affine subspaces spanned by receivers and senders. Anchor-free TOA network calibration has uses both in sound, radio and radio strength applications. Using linear techniques and requiring only a minimal number of receivers and senders, an algorithm is constructed for general dimension p for the lower dimensional subspace. Degenerate cases are determined and partially characterized as when receivers or senders inhabits a lower dimensional affine subspace than was given as input. The algorithm is further extended to the overdetermined case in a straightforward manner. Simulated experiments show good accuracy for the minimal solver and good performance under noisy measurements. An indoor environment experiment using microphones and speakers gives a RMSE of 2.35cm on receiver and sender positions compared to computer vision reconstruction.

Supervised feature quantization with entropy optimization

Feature quantization is a crucial component for efficient large scale image retrieval and object recognition. By quantizing local features into visual words, one hopes that features that match each other obtain the same word ID. Then, similarities between images can be measured with respect to the corresponding histograms of visual words. Given the appearance variations of local features, traditional quantization methods do not take into account the distribution of matched features. In this paper, we investigate how to encode additional prior information on the feature distribution via entropy optimization by leveraging ground truth correspondence data. We propose a computationally efficient optimization scheme for large scale vocabulary training. The results from our experiments suggest that entropy-optimized vocabulary performs better than unsupervised quantization methods in terms of recall and precision for feature matching. We also demonstrate the advantage of the optimized vocabulary for image retrieval.

Partial Symmetry in Polynomial Systems and Its Applications in Computer Vision

Algorithms for solving systems of polynomial equations are key components for solving geometry problems in computer vision. Fast and stable polynomial solvers are essential for numerous applications e.g. minimal problems or finding for all stationary points of certain algebraic errors. Recently, full symmetry in the polynomial systems has been utilized to simplify and speed up state-of-the-art polynomial solvers based on Gröbner basis method. In this paper, we further explore partial symmetry (i.e. where the symmetry lies in a subset of the variables) in the polynomial systems. We develop novel numerical schemes to utilize such partial symmetry. We then demonstrate the advantage of our schemes in several computer vision problems. In both synthetic and real experiments, we show that utilizing partial symmetry allow us to obtain faster and more accurate polynomial solvers than the general solvers.

Optimizing visual vocabularies using soft assignment entropies

The state of the art for large database object retrieval in images is based on quantizing descriptors of interest points into visual words. High similarity between matching image representations (as bags of words) is based upon the assumption that matched points in the two images end up in similar words in hard assignment or in similar representations in soft assignment techniques. In this paper we study how ground truth correspondences can be used to generate better visual vocabularies. Matching of image patches can be done e.g. using deformable models or from estimating 3D geometry. For optimization of the vocabulary, we propose minimizing the entropies of soft assignment of points. We base our clustering on hierarchical k-splits. The results from our entropy based clustering are compared with hierarchical k-means. The vocabularies have been tested on real data with decreased entropy and increased true positive rate, as well as better retrieval performance.

Tracking and positioning using phase information from estimated multi-path components

High resolution radio based positioning and tracking is a key enabler for new or improved cellular services. In this work, we are aiming to track user movements with accuracy down to centimeters using standard cellular bandwidths of 20-40 MHz. The goal is achieved by using phase information from the multi-path components (MPCs) of the radio channels. First, an extended Kalman filter (EKF) is used to estimate and track the phase information of the MPCs. Each of the tracked MPCs can be seen as originating from a virtual transmitter at an unknown position. By using a time difference of arrival (TDOA) positioning algorithm based on a structure-of-motion approach and translating the tracked phase information into propagation distances, the user movements can be estimated with a standard deviation of the error of 4.0 cm. The paper should be viewed as a proof-of-principle and it is shown by measurements that phase based positioning can be a promising solution for movement tracking in cellular systems with extraordinary accuracy.