Usual Structure-from-Motion (SfM) techniques require at least trifocal overlaps to calibrate cameras and reconstruct a scene. We consider here scenarios of reduced image sets with little overlap, possibly as low as two images at most seeing the same part of the scene. We propose a new method, based on line coplanarity hypotheses, for estimating the relative scale of two independent bifocal calibrations sharing a camera, without the need of any trifocal information or Manhattan-world assumption. We use it to compute SfM in a chain of up-to-scale relative motions. For accuracy, we however also make use of trifocal information for line and or point features, when present, relaxing usual trifocal constraints. For robustness to wrong assumptions and mismatches, we embed all constraints in a parameterless RANSAC-like approach. Experiments show that we can calibrate datasets that previously could not, and that this wider applicability does not come at the cost of inaccuracy.
More generally, when associating both points and lines in a Perspective-n-Features'' framework, a minimum of 3 features visible in 3 views is still required @cite_3 @cite_38 .
@cite_38 @cite_3
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A simple algorithm for computing the three-dimensional structure of a scene from a correlated pair of perspective projections is described here, when the spatial relationship between the two projections is unknown. This problem is relevant not only to photographic surveying1 but also to binocular vision2, where the non-visual information available to the observer about the orientation and focal length of each eye is much less accurate than the optical information supplied by the retinal images themselves. The problem also arises in monocular perception of motion3, where the two projections represent views which are separated in time as well as space. As Marr and Poggio4 have noted, the fusing of two images to produce a three-dimensional percept involves two distinct processes: the establishment of a 1:1 correspondence between image points in the two views—the ‘correspondence problem’—and the use of the associated disparities for determining the distances of visible elements in the scene. I shall assume that the correspondence problem has been solved; the problem of reconstructing the scene then reduces to that of finding the relative orientation of the two viewpoints. The viewpoint consistency constraint requires that the locations of all object features in an image must be consistent with projection from a single viewpoint. The application of this constraint is central to the problem of achieving robust recognition, since it allows the spatial information in an image to be compared with prior knowledge of an object's shape to the full degree of available image resolution. In addition, the constraint greatly reduces the size of the search space during model-based matching by allowing a few initial matches to provide tight constraints for the locations of other model features. Unfortunately, while simple to state, this constraint has seldom been effectively applied in model-based computer vision systems. This paper reviews the history of attempts to make use of the viewpoint consistency constraint and then describes a number of new techniques for applying it to the process of model-based recognition. A method is presented for probabilistically evaluating new potential matches to extend and refine an initial viewpoint estimate. This evaluation allows the model-based verification process to proceed without the expense of backtracking or search. It will be shown that the effective application of the viewpoint consistency constraint, in conjunction with bottom-up image description based upon principles of perceptual organization, can lead to robust three-dimensional object recognition from single gray-scale images. We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the Grassmann-Cayley algebra as the simplest way to make both geometric and algebraic statements in a very synthetic and effective way (i.e. allowing actual computation if needed). We have a fairly complete picture of the situation in the case of points; there are only three types of algebraic relations which are satisfied by the coordinates of the images of a 3-D point: bilinear relations arising when we consider pairs of images among the N and which are the well-known epipolar constraints, trilinear relations arising when we consider triples of images among the N, and quadrilinear relations arising when we consider four-tuples of images among the N. In the case of lines, we show how the traditional perspective projection equation can be suitably generalized and that in the case of three images there exist two independent trilinear relations between the coordinates of the images of a 3-D line. > In recent work, we have concentrated on the problem of lipreading from non-frontal views (poses). In particular, we have focused on the use of profile views, and proposed two approaches for lipreading on basis of visual features extracted from such views: (a) Direct statistical modeling of the features, namely use of view-dependent statistical models; and (b) Normalization of such features by their projection onto the space'' of frontal-view visual features, which allows employing one set of statistical models for all available views. The latter approach has been considered for two only poses (frontal and profile views), and for visual features of a specific dimensionality. In this paper, we further extend this work, by investigating its applicability to the case where data from three views are available (frontal, left- and right-profile). In addition, we examine the effect of visual feature dimensionality on the pose-normalization approach. Our experiments demonstrate that results generalize well to three views, but also that feature dimensionality is crucial to the effectiveness of the approach. In particular, feature dimensionality larger than 30 is detrimental to multi-pose visual speech recognition performance.