Wide baseline correspondence extraction beyond local features

Robust, affine covariant, feature extractors provide a means to extract correspondences between images captured by widely separated cameras. Advances in wide baseline correspondence extraction require looking beyond the robust feature extraction and matching approach. This study examines new techniques of extracting correspondences that take advantage of information contained in affine feature matches. Methods of improving the accuracy of a set of putative matches, eliminating incorrect matches and extracting large numbers of additional correspondences are explored. It is assumed that knowledge of the camera geometry is not available and not immediately recoverable. The new techniques are evaluated by means of an epipolar geometry estimation task. It is shown that these methods enable the computation of camera geometry in many cases where existing feature extractors cannot produce sufficient numbers of accurate correspondences.

Multiple camera management using wide baseline matching

Camera calibration information is required in order for multiple camera networks to deliver more than the sum of many single camera systems. Methods exist for manually calibrating cameras with high accuracy. Manually calibrating networks with many cameras is, however, time consuming, expensive and impractical for networks that undergo frequent change. For this reason, automatic calibration techniques have been vigorously researched in recent years. Fully automatic calibration methods depend on the ability to automatically find point correspondences between overlapping views. In typical camera networks, cameras are placed far apart to maximise coverage. This is referred to as a wide base-line scenario. Finding sufficient correspondences for camera calibration in wide base-line scenarios presents a significant challenge. This thesis focuses on developing more effective and efficient techniques for finding correspondences in uncalibrated, wide baseline, multiple-camera scenarios. The project consists of two major areas of work. The first is the development of more effective and efficient view covariant local feature extractors. The second area involves finding methods to extract scene information using the information contained in a limited set of matched affine features. Several novel affine adaptation techniques for salient features have been developed. A method is presented for efficiently computing the discrete scale space primal sketch of local image features. A scale selection method was implemented that makes use of the primal sketch. The primal sketch-based scale selection method has several advantages over the existing methods. It allows greater freedom in how the scale space is sampled, enables more accurate scale selection, is more effective at combining different functions for spatial position and scale selection, and leads to greater computational efficiency. Existing affine adaptation methods make use of the second moment matrix to estimate the local affine shape of local image features. In this thesis, it is shown that the Hessian matrix can be used in a similar way to estimate local feature shape. The Hessian matrix is effective for estimating the shape of blob-like structures, but is less effective for corner structures. It is simpler to compute than the second moment matrix, leading to a significant reduction in computational cost. A wide baseline dense correspondence extraction system, called WiDense, is presented in this thesis. It allows the extraction of large numbers of additional accurate correspondences, given only a few initial putative correspondences. It consists of the following algorithms: An affine region alignment algorithm that ensures accurate alignment between matched features; A method for extracting more matches in the vicinity of a matched pair of affine features, using the alignment information contained in the match; An algorithm for extracting large numbers of highly accurate point correspondences from an aligned pair of feature regions. Experiments show that the correspondences generated by the WiDense system improves the success rate of computing the epipolar geometry of very widely separated views. This new method is successful in many cases where the features produced by the best wide baseline matching algorithms are insufficient for computing the scene geometry.

Hessian-based affine adaptation of salient local image features

Affine covariant local image features are a powerful tool for many applications, including matching and calibrating wide baseline images. Local feature extractors that use a saliency map to locate features require adaptation processes in order to extract affine covariant features. The most effective extractors make use of the second moment matrix (SMM) to iteratively estimate the affine shape of local image regions. This paper shows that the Hessian matrix can be used to estimate local affine shape in a similar fashion to the SMM. The Hessian matrix requires significantly less computation effort than the SMM, allowing more efficient affine adaptation. Experimental results indicate that using the Hessian matrix in conjunction with a feature extractor that selects features in regions with high second order gradients delivers equivalent quality correspondences in less than 17% of the processing time, compared to the same extractor using the SMM.

Digit recognition using trispectral features

Features derived from the trispectra of DFT magnitude slices are used for multi-font digit recognition. These features are insensitive to translation, rotation, or scaling of the input. They are also robust to noise. Classification accuracy tests were conducted on a common data base of 256× 256 pixel bilevel images of digits in 9 fonts. Randomly rotated and translated noisy versions were used for training and testing. The results indicate that the trispectral features are better than moment invariants and affine moment invariants. They achieve a classification accuracy of 95% compared to about 81% for Hu's (1962) moment invariants and 39% for the Flusser and Suk (1994) affine moment invariants on the same data in the presence of 1% impulse noise using a 1-NN classifier. For comparison, a multilayer perceptron with no normalization for rotations and translations yields 34% accuracy on 16× 16 pixel low-pass filtered and decimated versions of the same data.

Negative determinant of Hessian features

Local image feature extractors that select local maxima of the determinant of Hessian function have been shown to perform well and are widely used. This paper introduces the negative local minima of the determinant of Hessian function for local feature extraction. The properties and scale-space behaviour of these features are examined and found to be desirable for feature extraction. It is shown how this new feature type can be implemented along with the existing local maxima approach at negligible extra processing cost. Applications to affine covariant feature extraction and sub-pixel precise corner extraction are demonstrated. Experimental results indicate that the new corner detector is more robust to image blur and noise than existing methods. It is also accurate for a broader range of corner geometries. An affine covariant feature extractor is implemented by combining the minima of the determinant of Hessian with existing scale and shape adaptation methods. This extractor can be implemented along side the existing Hessian maxima extractor simply by finding both minima and maxima during the initial extraction stage. The minima features increase the number of correspondences by two to four fold. The additional minima features are very distinct from the maxima features in descriptor space and do not make the matching process more ambiguous.

Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

Plane Detection Using Affine Homography

AIRES, Kelson R. T.; ARAÚJO, Hélder J.; MEDEIROS, Adelardo A. D. Plane Detection Using Affine Homography. In: CONGRESSO BRASILEIRO DE AUTOMÁTICA, 2008, Juiz de Fora, MG: Anais... do CBA 2008.

Affine Toda model coupled to matter and the string tension in 2D QCD

The sl(2) affine Toda model coupled to matter is shown to describe various features, such as the spectrum and string tension, of the low-energy effective Lagrangian of two-dimensional QCD (one flavor and N colors). The corresponding string tension is computed when the dynamical quarks are in the fundamental representation of SU(N) and in the adjoint representation of SU(2).

The sl(2) affine Toda model coupled to the matter: solitons and confinement

The so-called conformal affine Toda theory coupled to the matter fields (CATM), associated to the (s) over capl(2) affine Lie algebra, is studied. The conformal symmetry is fixed by setting a connection to zero, then one defines an off-critical model, the affine Toda model coupled to the matter (ATM). Using the dressing transformation method we construct the explicit forms of the two-soliton classical solutions, and show that a physical bound soliton-antisoliton pair (breather) does not exist. Moreover, we verify that these solutions share some features of the sine-Gordon (massive Thirring) solitons, and satisfy the classical equivalence of topological and Noether currents in the ATM model. We show, using bosonization techniques that the ATM theory decouples into a sine-Gordon model and a free scalar. Imposing the Noether and topological currents equivalence as a constraint, one can show that the ATM model leads to a bag model like mechanism for the confinement of the color charge inside the sine-Gordon solitons (baryons).

Metric-affine approach to teleparallel gravity

The teleparallel gravity theory, treated physically as a gauge theory of translations, naturally represents a particular case of the most general gauge-theoretic model based on the general affine group of spacetime. on the other hand, geometrically, the Weitzenbock spacetime of distant parallelism is a particular case of the general metric-affine spacetime manifold. These physical and geometrical facts offer a new approach to teleparallelism. We present a systematic treatment of teleparallel gravity within the framework of the metric-affine theory. The symmetries, conservation laws and the field equations are consistently derived, and the physical consequences are discussed in detail. We demonstrate that the so-called teleparallel GR-equivalent model has a number of attractive features which distinguishes it among the general teleparallel theories, although it has a consistency problem when dealing with spinning matter sources.

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Plane Detection Using Affine Homography

AIRES, Kelson R. T.; ARAÚJO, Hélder J.; MEDEIROS, Adelardo A. D. Plane Detection Using Affine Homography. In: CONGRESSO BRASILEIRO DE AUTOMÁTICA, 2008, Juiz de Fora, MG: Anais... do CBA 2008.

Plane Detection Using Affine Homography

AIRES, Kelson R. T.; ARAÚJO, Hélder J.; MEDEIROS, Adelardo A. D. Plane Detection Using Affine Homography. In: CONGRESSO BRASILEIRO DE AUTOMÁTICA, 2008, Juiz de Fora, MG: Anais... do CBA 2008.