Geometric uncertainty models for correspondence problems in digital image processing

Many recent advances in technology rely heavily on the correct interpretation of an enormous amount of visual information. All available sources of visual data (e.g. cameras in surveillance networks, smartphones, game consoles) must be adequately processed to retrieve the most interesting user information. Therefore, computer vision and image processing techniques gain significant interest at the moment, and will do so in the near future. Most commonly applied image processing algorithms require a reliable solution for correspondence problems. The solution involves, first, the localization of corresponding points -visualizing the same 3D point in the observed scene- in the different images of distinct sources, and second, the computation of consistent geometric transformations relating correspondences on scene objects. This PhD presents a theoretical framework for solving correspondence problems with geometric features (such as points and straight lines) representing rigid objects in image sequences of complex scenes with static and dynamic cameras. The research focuses on localization uncertainty due to errors in feature detection and measurement, and its effect on each step in the solution of a correspondence problem. Whereas most other recent methods apply statistical-based models for spatial localization uncertainty, this work considers a novel geometric approach. Localization uncertainty is modeled as a convex polygonal region in the image space. This model can be efficiently propagated throughout the correspondence finding procedure. It allows for an easy extension toward transformation uncertainty models, and to infer confidence measures to verify the reliability of the outcome in the correspondence framework. Our procedure aims at finding reliable consistent transformations in sets of few and ill-localized features, possibly containing a large fraction of false candidate correspondences. The evaluation of the proposed procedure in practical correspondence problems shows that correct consistent correspondence sets are returned in over 95% of the experiments for small sets of 10-40 features contaminated with up to 400% of false positives and 40% of false negatives. The presented techniques prove to be beneficial in typical image processing applications, such as image registration and rigid object tracking

Feature controlled adaptive difference operators

AbstractDifferential operators are essential for many image processing applications which require the computation of typical characteristics of continuous surfaces, as e.g. tangents, curvature, flatness, shape descriptors. We propose to replace differential operators by the combined action of sets of feature detectors and locally adaptive difference operators, resulting in a more accurate computation of the required derivatives in each pixel neighborhood. Both the set of feature detectors and the set of difference operators have a rigid mathematical structure, which is described by a set of Groebner bases for each class of fitting functions. This representation allows a systematic description of the hierarchical structure with ordering relations for all different function classes. The explicit computation of fitting functions is avoided by our technique and replaced by a function classification process. A set of simple local feature detectors is used to find the class of fitting functions which locally yields the best approximation for the digitized image surface. By a systematic optimization process, we determine for each fitting function class a difference operator which is an optimal approximation for a particular differential operator. As an example, we describe how to compute the best discrete approximation for the Laplacian differential operator in each pixel neighborhood and illustrate how the Laplacian of Gaussian edge detection method can benefit from these results

Optimal difference operator selection

Differential operators are essential in many image processing applications. Previous work has shown how to compute derivatives more accurately by examining the image locally, and by applying a difference operator which is optimal for each pixel neighborhood. The proposed technique avoids the explicit computation of fitting functions, and replaces the function fitting process by a function classification process. This paper introduces a new criterion to select the best function class and the best template size so that the optimal difference operator is applied to a given digitized function. An evaluation of the performance of the selection criterion for the computation of the Laplacian for digitized functions shows better results when compared to our previous method and the widely used Laplacian operator

Transformation polytopes for line correspondences in digital images

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