Homography

Summary

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive. It is a bijection that maps lines to lines, and thus a collineation. In general, some collineations are not homographies, but the fundamental theorem of projective geometry asserts that is not so in the case of real projective spaces of dimension at least two. Synonyms include projectivity, projective transformation, and projective collineation. Historically, homographies (and projective spaces) have been introduced to study perspective and projections in Euclidean geometry, and the term homography, which, etymologically, roughly means "similar drawing", dates from this time. At the end of the 19th century, formal definitions of projective spaces were introduced, which differed from extending Euclidean or affine spaces by adding points at infinity. The term "projective transformation" originated in these abstract construc

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https://en.wikipedia.org/wiki/Homography

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Combining Geometric and Appearance Priors for Robust Homography Estimation

Pascal Fua, Vincent Lepetit, Mustafa Özuysal

The homography between pairs of images are typically computed from the correspondence of keypoints, which are established by using image descriptors. When these descriptors are not reliable, either because of repetitive patterns or large amounts of clutter, additional priors need to be considered. The Blind PnP algorithm makes use of geometric priors to guide the search for matches while computing camera pose. Inspired by this, we propose a novel approach for homography estimation that combines geometric priors with appearance priors of ambiguous descriptors. More specifically, for each point we retain its best candidates according to appearance. We then prune the set of potential matches by iteratively shrinking the regions of the image that are consistent with the geometric prior. We can then successfully compute homographies between pairs of images containing highly repetitive patterns and even under oblique viewing conditions.

2010

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Tracking moving objects is a critical step for smart video surveillance systems. Despite the complexity increase, multiple camera systems exhibit the undoubted advantages of covering wide areas and handling the occurrence of occlusions by exploiting the different viewpoints. The technical problems in multiple camera systems are several: installation, calibration, objects matching, switching, data fusion, and occlusion handling. In this paper, we address the issue of tracking moving objects in an environment covered by multiple un-calibrated cameras with overlapping fields of view, typical of most surveillance setups. Our main objective is to create a framework that can be used to integrate object-tracking information from multiple video sources. Basically, the proposed technique consists of the following steps. We first perform a single- view tracking algorithm on each camera view, and then apply a consistent object labeling algorithm on all views. In the next step, we verify objects in each view separately for inconsistencies. Correspondent objects are extracted through a Homography transform from one view to the other and vice versa. Having found the correspondent objects of different views, we partition each object into homogeneous regions. In the last step, we apply the Homography transform to find the region map of first view in the second view and vice versa. For each region (in the main frame and mapped frame) a set of descriptors are extracted to find the best match between two views based on region descriptors similarity. This method is able to deal with multiple objects. Track management issues such as occlusion, appearance and disappearance of objects are resolved using information from all views. This method is capable of tracking rigid and deformable objects and this versatility lets it to be suitable for different application scenarios.

2009

Next Generation Frame Rate Conversion Algorithms

Engin Türetken

There is an increasing trend towards panel displays in consumer electronics, and they are already replacing conventional Cathode Ray Tube (CRT) displays due to their various advantages. However, the main problem of the panel displays, namely motion blur, still remains unsolved. This shortcoming should be overcome efficiently to satisfy increasing demands of viewers such as artifact-free interpolation in dynamic videos. Among many frame-rate up conversion (FRUC) methods that address this problem, motion-compensated frame interpolation (MCFI) algorithms yield superior results with relatively less artifacts. Conventional MCFI techniques utilize block-based translational motion models and, in general, linear interpolation schemes. These methods, however, suffer from blocking artifacts especially at object boundaries despite several attempts to avoid them. Region-based methods tackle this problem by segmenting homogeneous, or smoothly varying, motion regions that are supposed to correspond real objects (or their parts) in the scene. In this chapter, two region-based MCFI methods that adopt 2D homography and 3D rigid body motion models are presented in the order of increasing complexity. As opposed to the conventional MCFI approaches where motion model interpolation is performed in the induced 2D motion parameter space, the common idea behind both methods is to perform the interpolation in the parameter space of the original 3D motion and structure elements of the scene. Experimental results suggest that the proposed algorithms achieve visually pleasing results without halo effects on dynamic scenes with complex motion.

Springer-Verlag2010