Scalable Object Recognition Using Hierarchical Quantization with a Vocabulary Tree

An image retrieval technique employing a novel hierarchical feature/descriptor vector quantizer tool—‘vocabulary tree’, of sorts comprising hierarchically organized sets of feature vectors—that effectively partitions feature space in a hierarchical manner, creating a quantized space that is mapped to integer encoding. The computerized implementation of the new technique(s) employs subroutine components, such as: A trainer component of the tool generates a hierarchical quantizer, Q, for application/use in novel image-insertion and image-query stages. The hierarchical quantizer, Q, tool is generated by running k-means on the feature (a/k/a descriptor) space, recursively, on each of a plurality of nodes of a resulting quantization level to ‘split’ each node of each resulting quantization level. Preferably, training of the hierarchical quantizer, Q, is performed in an ‘offline’ fashion

Self-Calibration of Cameras with Euclidean Image Plane in Case of Two Views and Known Relative Rotation Angle

The internal calibration of a pinhole camera is given by five parameters that are combined into an upper-triangular $3\times 3$ calibration matrix. If the skew parameter is zero and the aspect ratio is equal to one, then the camera is said to have Euclidean image plane. In this paper, we propose a non-iterative self-calibration algorithm for a camera with Euclidean image plane in case the remaining three internal parameters --- the focal length and the principal point coordinates --- are fixed but unknown. The algorithm requires a set of $N \geq 7$ point correspondences in two views and also the measured relative rotation angle between the views. We show that the problem generically has six solutions (including complex ones). The algorithm has been implemented and tested both on synthetic data and on publicly available real dataset. The experiments demonstrate that the method is correct, numerically stable and robust.Comment: 13 pages, 7 eps-figure

1 Preemptive RANSAC for Live Structure and Motion Estimation

A system capable of performing robust live ego-motion estimation for perspective cameras is presented. The system is powered by random sample consensus with preemptive scoring of the motion hypotheses. A general statement of the problem of efficient preemptive scoring is given. Then a theoretical investigation of preemptive scoring under a simple inlier-outlier model is performed. A practical preemption scheme is proposed and it is shown that the preemption is powerful enough to enable robust live structure and motion estimation

Projective reconstruction Untwisting a Projective Reconstruction

Quasi-affine transformation

Structure from motion with missing data is NP -hard

This paper shows that structure from motion is NP-hard for most sensible cost functions when missing data is allowed. The result provides a fundamental limitation of what is possible to achieve with any structure from motion algorithm. Even though there are recent, promising attempts to compute globally optimal solutions, there is no hope of obtaining a polynomial time algorithm unless P=NP. The proof proceeds by encoding an arbitrary Boolean formula as a structure from motion problem of polynomial size, such that the structure from motion problem has a zero cost solution if and only if the Boolean formula is satisfiable. Hence, if there was a guaranteed way to minimize the error of the relevant family of structure from motion problems in polynomial time, the NP-complete problem 3SAT could be solved in polynomial time, which would imply that P=NP. The proof relies heavily on results from both structure from motion and complexity theory. 1

Visual Odometry

We present a system that estimates the motion of a stereo head or a single moving camera based on video input. The system operates in real-time with low delay and the motion estimates are used for navigational purposes. The front end of the system is a feature tracker. Point features are matched between pairs of frames and linked into image trajectories at video rate. Robust estimates of the camera motion are then produced from the feature tracks using a geometric hypothesize-and-test architecture. This generates what we call visual odometry, i.e. motion estimates from visual input alone. No prior knowledge of the scene nor the motion is necessary. The visual odometry can also be used in conjunction with information from other sources such as GPS, inertia sensors, wheel encoders, etc. The pose estimation method has been applied successfully to video from aerial, automotive and handheld platforms. We focus on results with an autonomous ground vehicle. We give examples of camera trajectories estimated purely from images over previously unseen distances and periods of time. 1

Estimating Global Uncertainty in Epipolar Geometry for Vehicle-Mounted Cameras

We present a method for estimating the global uncertainty of epipolar geometry with applications to autonomous vehicle navigation. Such uncertainty information is necessary for making informed decisions regarding the confidence of a motion estimate, since we must otherwise accept the estimate without any knowledge of the probability that the estimate is in error. For example, we may wish to fuse visual estimates with information from GPS and inertial sensors, but without uncertainty information, we have no principled way to do so. Ideally, we would perform a full search over the 7-dimensional space of fundamental matrices to yield an estimate and its related uncertainty. However, searching this space is computationally infeasible. As a compromise between fully representing posterior likelihood over this space and producing a single estimate, we represent the uncertainty over the space of translation directions in a calibrated framework. In contrast to finding a single estimate, representing the posterior likelihood is always a well-posed problem, albeit an often computationally challenging one. Given the posterior likelihood, we derive a confidence interval around the motion estimate. We verify the correctness of the confidence interval using synthetic data and show examples of uncertainty estimates using vehicle-mounted camera sequences