Models, code, and papers for "Simon Korman":

We present a method that can evaluate a RANSAC hypothesis in constant time, i.e. independent of the size of the data. A key observation here is that correct hypotheses are tightly clustered together in the latent parameter domain. In a manner similar to the generalized Hough transform we seek to find this cluster, only that we need as few as two votes for a successful detection. Rapidly locating such pairs of similar hypotheses is made possible by adapting the recent "Random Grids" range-search technique. We only perform the usual (costly) hypothesis verification stage upon the discovery of a close pair of hypotheses. We show that this event rarely happens for incorrect hypotheses, enabling a significant speedup of the RANSAC pipeline. The suggested approach is applied and tested on three robust estimation problems: camera localization, 3D rigid alignment and 2D-homography estimation. We perform rigorous testing on both synthetic and real datasets, demonstrating an improvement in efficiency without a compromise in accuracy. Furthermore, we achieve state-of-the-art 3D alignment results on the challenging "Redwood" loop-closure challenge.

We present a novel approach to template matching that is efficient, can handle partial occlusions, and comes with provable performance guarantees. A key component of the method is a reduction that transforms the problem of searching a nearest neighbor among $N$ high-dimensional vectors, to searching neighbors among two sets of order $\sqrt{N}$ vectors, which can be found efficiently using range search techniques. This allows for a quadratic improvement in search complexity, and makes the method scalable in handling large search spaces. The second contribution is a hashing scheme based on consensus set maximization, which allows us to handle occlusions. The resulting scheme can be seen as a randomized hypothesize-and-test algorithm, which is equipped with guarantees regarding the number of iterations required for obtaining an optimal solution with high probability. The predicted matching rates are validated empirically and the algorithm shows a significant improvement over the state-of-the-art in both speed and robustness to occlusions.

Understanding the local behaviour of structured multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms, and specifically property testers, to understand local properties of the data. We focus on the natural local problem of testing pattern freeness: given a large $d$-dimensional array $A$ and a fixed $d$-dimensional pattern $P$ over a finite alphabet, we say that $A$ is $P$-free if it does not contain a copy of the forbidden pattern $P$ as a consecutive subarray. The distance of $A$ to $P$-freeness is the fraction of entries of $A$ that need to be modified to make it $P$-free. For any $\epsilon \in [0,1]$ and any large enough pattern $P$ over any alphabet, other than a very small set of exceptional patterns, we design a tolerant tester that distinguishes between the case that the distance is at least $\epsilon$ and the case that it is at most $a_d \epsilon$, with query complexity and running time $c_d \epsilon^{-1}$, where $a_d < 1$ and $c_d$ depend only on $d$. To analyze the testers we establish several combinatorial results, including the following $d$-dimensional modification lemma, which might be of independent interest: for any large enough pattern $P$ over any alphabet (excluding a small set of exceptional patterns for the binary case), and any array $A$ containing a copy of $P$, one can delete this copy by modifying one of its locations without creating new $P$-copies in $A$. Our results address an open question of Fischer and Newman, who asked whether there exist efficient testers for properties related to tight substructures in multi-dimensional structured data. They serve as a first step towards a general understanding of local properties of multi-dimensional arrays, as any such property can be characterized by a fixed family of forbidden patterns.