Pedro E. López-de-Teruel

Nonlinear kernel-based statistical pattern analysis

The eigenstructure of the second-order statistics of a multivariate random population can be inferred from the matrix of pairwise combinations of inner products of the samples. Therefore, it can be also efficiently obtained in the implicit, high-dimensional feature spaces defined by kernel functions. We elaborate on this property to obtain general expressions for immediate derivation of nonlinear counterparts of a number of standard pattern analysis algorithms, including principal component analysis, data compression and denoising, and Fishers discriminant. The connection between kernel methods and nonparametric density estimation is also illustrated. Using these results we introduce the kernel version of Mahalanobis distance, which originates nonparametric models with unexpected and interesting properties, and also propose a kernel version of the minimum squared error (MSE) linear discriminant function. This learning machine is particularly simple and includes a number of generalized linear models such as the potential functions method or the radial basis function (RBF) network. Our results shed some light on the relative merit of feature spaces and inductive bias in the remarkable generalization properties of the support vector machine (SVM). Although in most situations the SVM obtains the lowest error rates, exhaustive experiments with synthetic and natural data show that simple kernel machines based on pseudoinversion are competitive in problems with appreciable class overlapping.

A multisensor LBS using SIFT-based 3D models

This paper introduces an LBS multisensor system that acquires data from different sensors available in commodity smart phones to provide accurate location estimations. Our approach is based on the use of visual structure from motion techniques to run off-line 3D reconstructions of the environment from the correspondences among the SIFT descriptors of the training images. We present several solutions to reduce the deployment cost, in terms of time, and to minimize the interference degree within the environment, but also pursuing a good balance between accuracy and performance. To determine the position of the smartphones, we first obtain a coarse-grained estimation based on WiFi signals, digital compasses, and built-in accelerometers, making use of fingerprinting methods, probabilistic techniques, and motion estimators. Then, using images captured by the camera, we perform a matching process to determine correspondences between 2D pixels and model 3D points, but only analyzing a subset of the 3D model delimited by the coarse-grained estimation. We implement a resection process providing high localization accuracy when the camera has been previously calibrated, that is, we know intrinsic parameters like focal length, but it is also accurate if an auto-calibration process is required. Furthermore, our experimental tests show promising results, since we are able to provide high accuracy with an average error down to 15 cm in less than 0.5 seconds of response time, making this proposal suitable for applications combining location-services and augmented reality.

Reduced epipolar cost for accelerated incremental SfM

We propose a reduced algebraic cost based on pairwise epipolar constraints for the iterative refinement of a multiple view 3D reconstruction. The aim is to accelerate the intermediate steps required when incrementally building a reconstruction from scratch. Though the proposed error is algebraic, careful input data normalization makes it a good approximation to the true geometric epipolar distance. Its minimization is significantly faster and obtains a geometric reprojection error very close to the optimum value, requiring very few iterations of final standard BA refinement. Smart usage of a reduced measurement matrix for each pair of views allows elimination of the variables corresponding to the 3D points prior to nonlinear optimization, subsequently reducing computation, memory usage, and considerably accelerating convergence. This approach has been tested in a wide range of real and synthetic problems, consistently obtaining significant robustness and convergence improvements even when starting from rough initial solutions. Its efficiency and scalability make it thus an ideal choice for incremental SfM in real-time tracking applications or scene modelling from large image databases.

Probabilistic inference from arbitrary uncertainty using mixtures of factorized generalized gaussians

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both the joint probability density of the variables and the likelihood function of the (objective or subjective) observation are approximated by a special mixture model, in such a way that any desired conditional distribution can be directly obtained without numerical integration. We have developed an extended version of the expectation maximization (EM) algorithm to estimate the parameters of mixture models from uncertain training examples (indirect observations). As a consequence, any piece of exact or uncertain information about both input and output values is consistently handled in the inference and learning stages. This ability, extremely useful in certain situations, is not found in most alternative methods. The proposed framework is formally justified from standard probabilistic principles and illustrative examples are provided in the fields of nonparametric pattern classification, nonlinear regression and pattern completion. Finally, experiments on a real application and comparative results over standard databases provide empirical evidence of the utility of the method in a wide range of applications.

A note on principal point estimability

We provide elementary geometric arguments to show that the principal point of cameras with small to moderate field of view cannot be reliably estimated from natural, noisy images (the problem is ill-posed). We also show that in robot navigation and other noisy geometric vision applications the exact location of the principal point is irrelevant in practice. In these cases a satisfactory metric structure can be recovered from minimal information by efficient algorithms using simplified camera models.

Face Detection Using Integral Projection Models

Integral projections can be used to model the visual appearance of human faces. In this way, model based detection is done by fitting the model into an unknown pattern. Thus, the key problem is the alignment of projection patterns with respect to a given model of generic face. We provide an algorithm to align a 1-D pattern to a model consisting of the mean pattern and its variance. Projection models can also be used in facial feature location, pose estimation, expression and person recognition. Some preliminary experimental results are presented.

GEA optimization for live structureless motion estimation

In this paper we describe a highly efficient and scalable real-time camera motion estimation system. Instead of Bundle Adjustment, this system uses Global Epipolar Adjustment (GEA) [11] to correct bootstrapping and loop-closing errors during the camera tracking process. We propose a modification of the GEA algorithm to obtain a significant speed-up in the optimization, without sacrificing loop-closing error correction performance. As a result, our motion estimation system features increased performance and scalability. In addition, it can perform long-term live motion estimation without explicitly maintaining the whole 3D structure. The system stores only the 3D location for the most recently detected features, to resect the camera pose for new input frames.

Efficient Monocular 3D Reconstruction from Segments for Visual Navigation in Structured Environments

We present an algorithm for performing real time 3D reconstructions of indoor scenes from a single image. The technique has been successfully used in indoor robot visual navigation applications. To solve the depth ambiguity inherent to the process of image formation, the procedure interprets the scene in terms of a set of vertical planes in arbitrary orientations (e.g. walls and doors) lying on a common horizontal plane (the floor). Interpretation is based on a zone classification algorithm that divides the image into a set of disjoint patches, each one belonging to a different plane. In order to make the reconstruction possible in real time, we use a very fast feature extraction algorithm based on robust extraction of the most salient segments of the scene, augmented with local color information. The extracted segments help in both the construction of the zone classification machine and the posterior 3D reconstruction, which is in turn based on a powerful single image projective geometry result

Practical Planar Metric Rectification

We propose a simple method for computing a metric rectification of a plane from multiple views taken by Ki = diag( fi, fi, 1) cameras. The orthogonality properties of this camera model are exploited from an early stage to achieve a straightforward optimization process with only two degrees of freedom, even if the fi in all views are unknown. We study the optimization landscapes for several typical camera motions and varying amounts of image noise. We conclude that the problem is extremely ill conditioned and can only be realistically solved for rich camera motions and small amounts of image noise, preferably with at least one fi known in the sequence.

MPI–Delphi: an MPI implementation for visual programming environments and heterogeneous computing

The goal of a parallel program is to reduce the execution time, compared to the fastest sequential program solving the same problem. Parallel programming is growing due to the widespread use of network of workstations (NOWs) or powerful PCs in high-performance computing. Because the hardware components are all commodity devices, NOWs are much more cost-effective than custom machines with similar technology. In this environment, the typical programming model used has been message-passing and the MPI library has become the standard in the distributed-memory computing model. On the other hand, visual programming environments try to simply the task of developing applications. They provide programmers with several standard components for creating programs. Delphi constitutes one of the most popular visual programming environments nowadays in the Windows market place. In this paper, we present MPI–Delphi, an implementation of MPI for writing parallel applications using Delphi visual programming environment. We show how MPI–Delphi has been developed, and how it makes possible to manage a cluster of homogeneous/heterogeneous PCs. Two examples of use of MPI–Delphi in a heterogeneous cluster of workstations with a mixture of Windows and Linux operating systems are also included. The MPI–Delphi interface is suitable for some specific kinds of problems, such as monitoring parallel programs of long execution time, or computationally intensive graphical simulations. In addition, MPI–Delphi has proven to be a good tool for research, as the development of new algorithms can be carried out quickly and, therefore, time spent on the debugging of such algorithms is reduced. Finally, we conclude by explaining some of the tasks we think MPI–Delphi is suitable for.