We present a novel method for locating large amounts of local matches between images, with highly accurate localization. Point matching is one of the most fundamental tasks in computer vision, extensively used in applications such as object detection, object tracking and structure from motion. The major challenge in point matching is to preserve large numbers of accurate matches between corresponding scene locations under different geometric and radiometric conditions, while keeping the number of false positives low. Recent publications have shown that applying an affine transformation model on local regions is a particularly suitable approach for point matching. Yet, affine invariant methods are not used extensively for two reasons: first, because these methods are computationally demanding; and second because the derived affine estimations have limited accuracy. In this work, we propose a novel method of region expansion that enhances region matches detected by any state-of-the-art method. The method is based on accurate estimation of affine transformations, which are used to predict matching locations beyond initially detected matches. We use the improved estimations of affine transformations to locally verify tentative matches in an efficient way. We systematically reject false matches, while improving the localization of correct matches that are usually rejected by state-of-the-art methods. Source CodeThe source code and documentation are available from the web page of this article 1 . The code is mainly a Matlab code that requires some Matlab toolboxes detailed in the ReadMe.txt file attached to the source code. Specific instructions on how to run the code, including some other dependencies, are also found in the ReadMe.txt file.Editorial Warning: This paper appears as a useful supplementary material and online illustration of the SIIMS paper [5]. The referees have not confirmed that the published text is an accurate or complete account of the published code.
In many practical parameter estimation problems, such as coefficient estimation of polynomial regression and direction-of-arrival (DOA) estimation, model selection is performed prior to estimation. In these cases, it is assumed that the true measurement model belongs to a set of candidate models. The data-based model selection step affects the subsequent estimation, which may result in a biased estimation. In particular, the oracle Cramér-Rao bound (CRB), which assumes knowledge of the model, is inappropriate for post-model-selection performance analysis and system design outside the asymptotic region. In this paper, we analyze the estimation performance of post-modelselection estimators, by using the mean-squared-selected-error (MSSE) criterion. We assume coherent estimators that force unselected parameters to zero, and introduce the concept of selective unbiasedness in the sense of Lehmann unbiasedness. We derive a non-Bayesian Cramér-Rao-type bound on the MSSE and on the mean-squared-error (MSE) of any coherent and selective unbiased estimators. As an important special case, we illustrate the computation and applicability of the proposed selective CRB for sparse vector estimation, in which the selection of a model is equivalent to the recovery of the support. Finally, we demonstrate in numerical simulations that the proposed selective CRB is a valid lower bound on the performance of the post-model-selection maximum likelihood estimator for general linear model with different model selection criteria, and for sparse vector estimation with one step thresholding. It is shown that for these cases the selective CRB outperforms the existing bounds: oracle CRB, averaged CRB, and the SMS-CRB from [1].
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