Wiberg matrix factorization breaks a matrix Y into low-rank factors U and V by solving for V in closed form given U, linearizing V(U) about U, and iteratively minimizing ||Y - UV(U)||2 with respect to U only. This approach factors the matrix while effectively removing V from the minimization. Recently Eriksson and van den Hengel extended this approach to L1 , minimizing ||Y - UV(U)||1 . We generalize their approach beyond factorization to minimize ||Y - f(U, V)||1 for more general functions f(U, V) that are nonlinear in each of two sets of variables. We demonstrate the idea with a practical Wiberg algorithm for L1 bundle adjustment. One Wiberg minimization can be nested inside another, effectively removing two of three sets of variables from a minimization. We demonstrate this idea with a nested Wiberg algorithm for L1 projective bundle adjustment, solving for camera matrices, points, and projective depths. Wiberg minimization also generalizes to handle nonlinear constraints, and we demonstrate this idea with Constrained Wiberg Minimization for Multiple Instance Learning (CWM-MIL), which removes one set of variables from the constrained optimization. Our experiments emphasize isolating the effect of Wiberg by comparing against the algorithm it modifies, successive linear programming.

Wiberg matrix factorization breaks a matrix Y into low-rank factors U and V by solving for V in closed form given U, linearizing V (U) about U, and iteratively minimizing ∥Y-UV (U)∥with respect to U only. This approach factors the matrix while effectively removing V from the minimization. Recently Eriksson and van den Hengel extended this approach to L1, minimizing ∥Y-UV (U)∥1. We generalize their approach beyond factorization to minimize an arbitrary function that is nonlinear in each of two sets of variables. We demonstrate the idea with a practical Wiberg algorithm for L1bundle adjustment. We also show that one Wiberg minimization can be nested inside another, effectively removing two of three sets of variables from a minimization. We demonstrate this idea with a nested Wiberg algorithm for L1projective bundle adjustment, solving for camera matrices, points, and projective depths. We also revisit L1factorization, giving a greatly simplified presentation of Wiberg L1factorization, and presenting a successive linear programming factorization algorithm. Successive linear programming outperforms L1Wiberg for most large inputs, establishing a new state-of-the-art for for those cases.

Rank correlation measures are known for their resilience to perturbations in numeric values and are widely used in many evaluation metrics. Such ordinal measures have rarely been applied in treatment of numeric features as a representational transformation. We emphasize the benefits of ordinal representations of input features both theoretically and empirically. We present a family of algorithms for computing ordinal embeddings based on partial order statistics. Apart from having the stability benefits of ordinal measures, these embeddings are highly nonlinear, giving rise to sparse feature spaces highly favored by several machine learning methods. These embeddings are deterministic, data independent and by virtue of being based on partial order statistics, add another degree of resilience to noise. These machine-learning-free methods when applied to the task of fast similarity search outperform state-of-the-art machine learning methods with complex optimization setups. For solving classification problems, the embeddings provide a nonlinear transformation resulting in sparse binary codes that are well-suited for a large class of machine learning algorithms. These methods show significant improvement on VOC 2010 using simple linear classifiers which can be trained quickly. Our method can be extended to the case of polynomial kernels, while permitting very efficient computation. Further, since the popular Min Hash algorithm is a special case of our method, we demonstrate an efficient scheme for computing Min Hash on conjunctions of binary features. The actual method can be implemented in about 10 lines of code in most languages (2 lines in MATLAB), and does not require any data-driven optimization.

Bag-of-words document representations are often used in text, image and video processing. While it is relatively easy to determine a suitable word dictionary for text documents, there is no simple mapping from raw images or videos to dictionary terms. The classical approach builds a dictionary using vector quantization over a large set of useful visual descriptors extracted from a training set, and uses a nearest-neighbor algorithm to count the number of occurrences of each dictionary word in documents to be encoded. More robust approaches have been proposed recently that represent each visual descriptor as a sparse weighted combination of dictionary words. While favoring a sparse representation at the level of visual descriptors, those methods however do not ensure that images have sparse representation. In this work, we use mixed-norm regularization to achieve sparsity at the image level as well as a small overall dictionary. This approach can also be used to encourage using the same dictionary words for all the images in a class, providing a discriminative signal in the construction of image representations. Experimental results on a benchmark image classification dataset show that when compact image or dictionary representations are needed for computational efficiency, the proposed approach yields better mean average precision in classification.

Position estimation for planetary rovers has been typically limited to odometry based on proprioceptive measurements such as the integration of distance traveled and measurement of heading change. Here we present and compare two methods of online visual odometry suited for planetary rovers. Both methods use omnidirectional imagery to estimate motion of the rover. One method is based on robust estimation of optical flow and subsequent integration of the flow. The second method is a full structure-from-motion solution. To make the comparison meaningful we use the same set of raw corresponding visual features for each method. The dataset is an sequence of 2000 images taken during a field experiment in the Atacama desert, for which high resolution GPS ground truth is available.

This paper presents a comparison between methods that estimate motion of a camera from a sequence of video images. We implemented two methods: a homography based method that assumes planar environments; and shape-from-motion, a general method that can deal with a fully three dimensional world. Both methods were formulated in an iterative, online form to produce estimates of camera motion. We discuss a trade-off in accuracy and run time efficiency based on experimental results for these two general methods in relation to ground truth. We show how a variation of the homography method can produce accurate results in some cases when the environment is non-planar with low computational cost.

Cameras and inertial sensors are good candidates to be deployed together for autonomous vehicle motion estimation, since each can be used to resolve the ambiguities in the estimated motion that results from using the other modality alone. We present an algorithm that computes optimal vehicle motion estimates by considering all of the measurements from a camera, rate gyro, and accelerometer simultaneously. Such optimal estimates are useful in their own right, and as a gold standard for the comparison of online algorithms. By comparing the motions estimated using visual and inertial measurements, visual measurements only, and inertial measurements only against ground truth, we show that using image and inertial data together can produce highly accurate estimates even when the results produced by each modality alone are very poor Our test datasets include both conventional and omnidirectional image sequences, and an image sequence with a high percentage of missing data.

Recent omnidirectional camera designs aim a conventional camera at a mirror that expands the camera's field of view. This wide view is ideal for three-dimensional vision tasks such as motion estimation and obstacle detection, but these applications require an accurate model of the imaging process. We present a full model of the imaging process, which includes the rotation and translation between the camera and mirror, and an algorithm that determines this relative position from observations of known points in a single image. We present tests of the model and of the calibration procedure for various amounts of misalignment between the mirror and camera. These tests show that the algorithm recovers the correct relative position, and that by using the full model, accurate shape-from-motion and stereo matching are possible even if the camera and mirror are severely misaligned.

Algorithms for shape-from-motion simultaneously estimate the camera motion and scene structure. When extended to omnidirectional cameras, shape-from-motion algorithms are likely to provide robust motion estimates, in particular, because of the camera's wide field of view. In this paper, we describe both batch and online shape-from-motion algorithms for omnidirectional cameras, and a precise calibration technique that improves the accuracy of both methods. The shape-from-motion and calibration methods are general, and they handle a wide variety of omnidirectional camera geometries. In particular, the methods do not require that the camera-mirror combination have a single center of projection. We describe a noncentral camera that we have developed, and show experimentally that combining shape-from-motion with this design produces highly accurate motion estimates.

Reconfigurable computing obtains its performance advantage over fixed processors by creating hardware configurations that are specialized for a particular application. In some cases, this advantage can be pushed even further, by creating hardware specialized to a particular instance of an application. For many problems where this approach is applicable, such as automatic target recognition, template matching and encryption, the problem parameters can change often, even within a single program execution, requiring periodic, and potentially expensive, hardware reconfigurations. To support these applications, we propose a method for on-chip configuration generation, or embedded compilation, for use with Carnegie Mellon University's PipeRench reconfigurable processor. We describe PipeRench's performance in detail for one problem, template matching, relative to the newest general-purpose processors, and show how embedded compilation can be used to support multiple problem instances for a second problem, IDEA encryption.